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### SSC ENGLISH BOARD EXAM REVISION

Q.1. (A) Read the following passage and answer the questions given below :
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antabai Wali laughs heartily as she declares she is an ‘angutha chhap’ who cannot even sign her name. Yet as this woman from one of the most backward regions of Maharashtra expounds on her latest business venture, cattle rearing, she demonstrates her ease in the world of micro-financing and marketing.
Kantabai is the president of the Nalanda Bachatghat Gat, a selfhelp group (SHG), that was loaned Rs. 4 lakh by the State Bank of Hyderabad in Parbhani. The money was shared among the 11 members of the group for various income-generating activities such as buffalo-rearing, goat-raising, welding, vermiculture and candle and aggarbatti making. Jayshree Pandurang Kamble, another recipient of the loan, sifts compost made from vermiculture through her fingers and announces that she will not only make a profit but carve out her own brand name. “I will not sell my compost to any company because no one will associate my name with the compost. Even if there is an initial loss I will sell it under my own name,” she declares.
These women of Kundi Village in Pathri taluka, who formed self-help groups two years ago, were able to translate their collective savings into a bank loan, thanks to ‘Sankalp Manav Sanstha’, a nongovernmental development organization.
Questions :
1. What is Kantabai Wali’s business venture?
2. Why does Jayshree Kamble not want to sell the compost to any company? What is her plan ?
3. Why does Kantabai Wali laugh?
4. (a) Kantabai laughs heartily. (Add a Question Tag)
(b) She is an angutha chhap, who cannot sign her name. (Analyse the Clause and state the relation)
5. (i) Write 2 compound words from the passage. (ii) Write the antonyms of : (a) profit (b) rural
6. Write down some qualities that are required for a small enterprise. Explain how these qualities would help the enterprise to grow.

Q.1. (B) Read the following passage and answer the questions given below :
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hat Monday at school, Keryn sat with her chin propped up on one hand. "You're looking very thoughtful today, Keryn," said her teacher, Mrs.Ngeru. As soon as she got home, Keryn hurried to her bedroom mirror. The spot was bigger. She could see it even when she stood right back from her mirror, against her bedroom wall.
She took a book, curled up on the corner of the living room sofa, and tried to forget about her chin. She was still reading when her father came home from work half an hour later. "That's a nice little spot you've found there, love," he said. Keryn jumped up and slammed into her room. "What's the matter? What did I say?" She heard her father asking behind her.
At dinner that night, Keryn said she didn't want any lemon meringue, thank you. She'd just have a raw carrot instead. "You want to be careful of those raw carrots," Jason told Keryn while he ate her share of the lemon meringue. "They might be good for your skin, but they make your top teeth grow, and your ears get all long floppy,"
On Tuesday morning, Keryn got out of bed, washed her whole face hard with warm soapy water, and then looked in the mirror. The spot on her chin was even bigger than it had been the night before. "I'll never get rid of this spot before Thursday afternoon's prizegiving!" She wailed at breakfast time. "Isn't there anything I can do?" "You could try plastic surgery," suggested Jason, "or a flamethrower."
Questions :
1. What did Keryn do to try and forget about her chin?
2. How did Jason tease her about eating carrots?
3. Bring out Jason's sarcasm.
4. (a) "You want to be careful of those raw carrots," Jason told Keryn. (Use Reported Speech)
(b) She'd just have a raw carrot instead. (Make Negative)
5. (i) Give the noun form of : (a) thoughtful (b) grow
(ii) Supply homophones for the words given below : (a) sea (b) be
6. What type of relation do you find between the members of Keryn’s family?

Q.1. (C) Read the following passage and answer the questions given below :
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tto Frank's vision of hope gave my husband and me the courage to become parents. We had two sons, Ethan and Jeese. My trip to Switzerland was the first time I had been away from them. The train was slowing. The conductor announced the stop and the doors flew open. I looked into the crowd and saw a man with a straight back and rugged face. Snow-white hair surrounded a balding head. A tall, elderly man, still strong and handsome. It was really him. Otto Frank.
"Cara! At last!" he said warmly. I was actually hugging him. A real bearhug. Thank God. No formal handshakes or polite hellos. Suddenly a little shy, he put his arm in mine. Fritzi linked my other arm, and we walked off.
When I stepped into the Frank's house, I felt that I was home. Otto took me into their little study. A pile of fresh mail lay stacked on his desk. He showed me wall-to-wall notebooks bursting with letters. Then Otto brought out another notebook. "These are your letters, Cara. I saved them all." I couldn't believe it. I was facing myself through twenty years of letters. I saw my twelve year old's scrawl evolve into an adult's script and then change to typewritten pages. Masses of exclamation points and underlinings, outpourings of feeling. Then Otto said, "You are not the only one to write all these years."
Smiling, he told me about some of the others. There was Sumi from Japan, who had lost her father. She read Anne's diary and was moved to write to Otto. She told him that she would like to become his "Letter-daughter" and signed all her letters "Your daughter, Sumi." Otto advised her through the years. Then there was John Neiman who, as a college student, reread Anne Frank : The Diary of a Young Girl and wrote to Mr Frank. Otto told him, "If you want to honour Anne's memory and the people that died, do what Anne wanted so very much-do good for other people."
Questions :
1. Besides Cara, whom did Otto write to?
2. How did Otto greet Cara?
3. Why had Otto saved all of Cara’s letters?
4. (a) Otto advised her through the years. (Change the underlined word into a noun form the sentence)
(b) It was really him. (Make it Interrogative)
5. (i) Write two compound words from the passage. (ii) Make sentences : (a) brought out (b) stacked on
6. How would you have felt in Cara’s place?
Q.1. (D) Read the following passage and answer the questions given below :
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ad called out, "I thought you were going to bed." "I'm on my way," she said. She put some water into the dog's
dish and put the cat outside, then made sure the doors were locked and the verandah light was on. She looked in on each of the kids and turned out their bedside lamps and TV's hung up a shirt, threw some dirty socks into the hamper, and had a brief conversation with the one up still doing homework.
In her own room, she set the alarm; laid out clothing for the next day, straightened up the shoe rack. She added three things to her six most important things to do list. She said her prayers, and visualized the accomplishment of her goals. About that time, Dad turned off the TV and announced to no one in particular. "I'm going to bed." And he did… without another thought. What a beautiful piece and so true isn't it? I don't know who wrote it but it's someone who really observed his mother, and as I read it, tears came to my eyes as I remembered days and nights when my mother did exactly the same. Today I see the same in my wife, another mother. It'll be mother's day in a few days but today as I think of my
mother on her birthday far away in Baltimore, I thank God for all the mothers in our world. Women who said good night and took a long detour to bed…..!
Questions :
1. What does the narrator remember?
2. What did mother do in her room?
3. What precautions did mother take to secure the house for night ?
4. (a) I’m on my way. (Add a Question Tag)
(b) Dad turned off the TV and announced to no one in particular. (Rewrite using ‘ing’ form of underlined word)
5. Match the column: -
 A B i.                    Yawnii.                  Washiii.                Flossediv.                File a.       To make smooth and evenb.      To open mouth wide to take air into lungsc.       Act of cleaning something with soap and waterd.      Clean teeth with fine thread
Q.1. (E) Read the following passage and answer the questions given below :
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t bedtime, we put a camp cot in the children's room for him.When I got up in the morning, the bed linens were neatly folded and the little man was out on the porch. He refused breakfast, but just before he left for his bus, haltingly, as if asking a great favour, he said, "Could I please come back and stay the next time I have a treatment? Your children made me feel at home. Grown-ups are bothered by my face, but children don't seem to mind." I told him he was welcome to come again. And on his next trip he arrived a little after seven in the morning. As a gift, he brought a big fish and a quart of the largest oysters I had ever seen! He said he had shucked them that morning before he left so that they'd be nice and fresh. I knew his bus left at 4 a.m. and I wondered what time he had to get up in order to do this for us. In the years he came to stay overnight with us, there was never a time that he did not bring us fish or oysters or vegetables from his
garden. From him we learned what it was to accept the bad without complaint and the good with gratitude to God.
Recently, I was visiting a friend, who showed me her flowers. We came to the most beautiful one of all, a golden chrysanthemum, bursting with blooms. But it was growing in an old, dented, rusty bucket. "I ran short of pots," she explained, "and knowing how beautiful this one would be, I thought it wouldn't mind starting out in this old pail."
"Here's an especially beautiful one," God might have said when he came to the soul of the sweet old fisherman. He won't mind starting in this small body.
Questions :
1. What precaution had the old man taken to see that the oysters remained fresh ?
2. What did the narrator realise when she got up?
3. What might God have said when he came to the soul of the old fisherman?
4. (a) I was visiting a friend, who showed me her flowers. (Identify the clauses and state their kind)
(b) They were the largest oysters I had ever seen. (Change to the comparative degree)
5. (i) Explain : (a) gratitude (b) blooms
(ii) Complete the following table :
 Noun Verb Adjective ------------ ---------- Beautiful ------------ Accept --------
6. What, according to you, are the outstanding qualities of the fisherman?
Q.1. (F) Read the following passage and answer the questions given below :
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nder this objective, the women in the leadership training were taught how to apply for bank loans. Kantabai Wali, one of those who underwent the special training programme, had already demonstrated her courage and leadership qualities years ago when she registered a case under the Atrocity Act against a shopkeeper who had harassed her. Her complaint was taken seriously by the local authorities who even provided her with protection of a plainclothes policeman.
Her application for a loan was sanctioned after an initial seed capital of Rs25,000 was given and the SHG demonstrated its ability to repay in time and generate more money. Ten of the women in the group were able to claim a special subsidy of Rs 10, 000 each because they were below the poverty line. Sankalp has helped a total of 22 SHGs in Aurangabad, Jalna and Parbhani to procure loans amounting to close to Rs.19 lakhs in one year. The increased income of anything between Rs.2,000 and Rs3,000 a month for each member has given the women a new sense of confidence. Besides, they have learned how to collectively anticipate challenges and work them out at a community level. Says Kantabai Wali, who bought buffaloes with her part of the loan, "We realized that if we all bought cattle we would have grazing
problems as there is very little land in our village. So Bhagwat Kadam decided she would buy a welding machine as her husband knows welding. They plan to setup a small shop in Shelu. Jayshree Kamble decided on vermiculture because she has extensive knowledge on the subject. We help each other particularly if someone is facing a financial crunch because we know the importance of repaying the loan in time. Like an army of ants, we can march ahead, even if one falls sometimes."
Questions :
1. How did the local police help Kantabai?
2. Why did the villagers take up different activities?
3. What is the purpose of this text?
4. (a) Her complaint was taken seriously by the local authorities. (Change the Voice)
(b) We can march ahead. (Pick out the Auxiliary and State its kind)
5. (i) Write the verb form of : (a) application (b) collective. (ii) Write a simile from the text.
6. What can we do to help the village women who are trying to seek self employment?
Q.1. (G) Read the following passage and answer the questions given below :
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wo weeks later, I visited Mom, eager to show her a videotape of the home run. But when I walked into her room, I was shocked to see the physical condition of my dear mother. I knew that this would probably be the last visit I would ever have with her. We were both watching the tape for the first time, so I didn't anticipate the commentator's story that would unfold. After I hit the home run, the announcer, Harry Kalas, explained that it had been six long weeks since my last hit. Mom and I held hands and listened to Kalas continue,"John Morris had really struggled the second half of this season, and this couldn't have happened to a nicer guy." I could feel the tears building up inside the two of us, as he showed a slow motion replay of my dramatic home run. As the pitcher wound up, Kalas uttered the sweetest words my mom had ever heard. "John's
mom has been quite ill for some time," and as the ball connected with the bat, he finished, "and this one was probably for his mom."
Mom and I broke down. She hugged me as tightly as she could and whispered into my ear, "I love you son, and I'm very proud of you. I'm going to miss you very much." The season was ending the last weekend of September when I
received a call that Mom was not expected to make it through the weekend. That Sunday afternoon, the last out of the season was recorded, and on Monday morning she passed away with me at her bedside. It was as if she knew the season was complete, and that it was all right to let go.
Questions :
1. Why didn’t the writer anticipate the commentator’s story that would unfold?
2. What emotions did the writer and his mother go through while watching the tape together?
3. Point out the lines that indicate the most emotional moments between the writer and his Mom.
4. (a) I could feel the tears building up inside us. (Make Complex)
(b) This one was probably for his mom. (Rewrite as a negative sentence)
5. (i) Write meanings : (a) sensational (b) expect
(ii) Create a word register of four words specially related to the game mentioned in the passage above.
6. What do you think was the greatest moment of joy and pride for the narrator’s mother? Why?

Q.1. (H) Read the following passage and answer the questions given below :
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y father was in UK between 1928 and 1931 working at his Ph.D in the University of London. He had taught history at Government College, Lahore. One day the professor, who was his guide, complimented him on his work. My father was so pleased that he decided to splurge a bit. He went to an expensive tailoring emporium on Saville Row and ordered a suit for himself. He was pleased with the result and wore that suit, with pride, for many years.
Fifty years later, in 1978, I attended an international teachers' programme in France; and from there, my wife and I proceeded to London. Despite the enormous increase in the price of almost everything, I decided to visit Saville Row and order a suit for myself, as my father had done decades earlier. I will not name the establishment, which I located after some effort. I walked in with a feeling of trepidation but was determined to go through with my resolve to order a suit. The shop's interior was a model of subdued elegance. The dapper gentleman, Mr. Robinson, who greeted me, was dressed in a dark suit and was affability itself. He seated me in comfortable chair and asked me what he could do for me. With some hesitation I mentioned my father's name and the fact that he had a suit stitched in 1930. The man smiled, said he would be back shortly and disappeared inside. He emerged 15 minutes later, still smiling, and told me he had successful in locating my father's order in his books. I was impressed and told of my desire to have a suit made for myself.
Questions :
1. Who complimented the writer’s father ? Why ?
2. What did the writer’s father do when the professor complimented him ?
3. Why must the writer have walked in with a feeling of ‘trepidation’ ?
4. (a) I will not name the establishment which I located after some effort. (Identify the Clause)
(b) He emerged 15 minutes later. (Make it Interrogative)
5. (i) Find words from the passage which mean : (a) anxiety (b) very large
(ii) Write antonyms of : (a) pride (b) expensive
6. Do you think splurging to be a good habit?

Q.1. (I) Read the following passage and answer the questions givenbelow :
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ur next thoughts must-be of the unknown volunteers and  soldiers of freedom who, without praise or reward, have served India even unto death. We think also of our brothers and sisters who have been cut off from us by political boundaries and who unhappily cannot share at present in the freedom that has come. They are of us and will remain of us whatever may happen, and we shall be sharers in their good and ill fortune alike. The future beckons to us. Whiter do we go and what shall be our endeavour? To bring freedom and opportunity to the common man, to the peasants and workers of India, to fight and end poverty and ignorance and disease; to build up a prosperous, democratic progressive nation, and to create social, economic, and political institutions which will ensure justice and fullness of life to every man and woman.
We have hard work ahead. There is no resting for any one of us till we redeem out pledge in full, till we make all the people of India what destiny intended them to be. We are citizens of a great country, on the verge of bold advance, and we have to live up to that high standard. All of us, to whatever religion we may belong, are equally the children of India with equal rights, privileges and obligations. We cannot encourage communalism or narrow-mindedness, for no
nation can be great whose people are narrow in thoughts or in action. To the nations and peoples of the world we send greetings and pledge ourselves to co-operate with them in furthering peace, freedom and democracy. And to India, our much-loved motherland, the ancient, the eternal and the ever-new, we pay our reverent homage and we bind ourselves afresh to her service. Jai Hind.
Questions :
1. How does Nehru describe our motherland?
2. What role does Nehru visualize for India in the world?
3. What is Nehru’s message to the people of free India ?
4. (a) They have served India. (Identify the tense)
(b) No nation can be great whose people are narrow in thoughts. (Make it Interrogative)
5. (i) Give the adjective form of (a) nation (b) economic                    (ii) Pick out two adverbs from the passage.
6. What objectives of the Constitution of India are reflected in Nehru’s message.

Q.1. (J) Read the following passage and answer the questions given below :
 I
was trying to figure out a way to tell this fellow, without being too blunt, that he just wasn't what I had in mind at all. I asked him about his background. He said he had a degree in agriculture from Oklahoma State University and that he had been a ranch hand in Bartlesville, Oklahoma, for the past few years during the summers.
He announced that was all over now, he was ready to be a success in "biness," and he would just "shore appreciate a chance."
We continued to talk. He was so focused on success and how he would "shore appreciate a chance" that I decided to give him a chance. I told him I would spend two days with him. In those two days I would teach him everything I thought he needed to know to sell one type of very small telephone system. At the end of those two days he would be on his own. He asked me how much money I thought he could make. I told him, "Looking like you look and knowing what you know,
the best you can do is about $1,000 per month." I went on to explain that the average commission on the small telephone systems he would be selling was approximately$ 250 per system. I told him if he would see 100 prospects per month, that he would sell four of those prospects a telephone system. Selling four telephone systems would give him $1,000. I hired him on straight commission with no base salary. He said that sounded great to him because the most he had ever made was$ 400 per month. The next morning, I sat him down to cram as much of the telephone "business" I could into a 22-yearsold
cowboy with no business experience, no telephone experience and no sales experience. He looked like anything but a professional salesperson in the telecommunications business. In fact, he had none of the qualities I was looking for in an employee, expect one: He had an incredible focus on being a success.
Questions :
1. On what terms was Cowboy appointed on the job?
2. How much money could Cowboy make according to the writer?
3. Why did the writer want to spend two days with the cowboy?
4. (a) He was ready to be a success in biness. (Change the underlined word to an Adjective and Rewrite)
(b) I hired him on straight commission with no base salary. (Make it Affirmative)
5. (i) Make adjective : (a) appreciated (b) system
(ii) Write expressions meaning : (a) to think about (b) to be very frank
6. What impressed you the most about the cowboy from the passage?

Write a speech on "India of my dreams".
INDIA OF MY DREAMS
Respected Principal, teachers and my dear friends, A warm welcome to all of you to the awareness program of ‘India of my dreams’ I am honoured to express my feelings in front of everybody about a topic that is so close to my heart. I have often thought about this-India of my dreams’, everytime. I am sure each one of you must be having your own perception on how would India look like if things were really in shape. I first of all think of a hundred percent educated India with no
poverty and unemployment. Is that possible? Yes, I believe it is our attitude towards things that make things happen. Nothing is impossible. When I take a look at the railway tracks and the hutments nearby, from the train, with all the filth and rubbish
littered all around, it hurts me. Can’t we have garbage free India? A place where everybody feels fresh and relaxed, a place with no pollution, no corruption, no selfishness, no violence and of course, we know the list is endless. Wish all of us start understanding each other and have sensitivity towards each and every individual. Sensitivity towards nature is also of paramount significance. When you come to think of it , things are not difficult at all, we can make our country a better place to live in. India can reach the top pedestal and can do a great job in the field of science and technology.I always wish a day comes when, the foreign countries will be importing machineries, technicians, scientists, doctors and teachers and reporters give our example to the entire world to reach the path of progress and development. I hope you and me together can involve ourselves in as many social projects as possible for the good of our country. And a day will come where I will be able to proudly say, yes this is my India- a country of my dreams.

Write a report of about 100 words on the Diwali Festival highlighting the various artistic activities such as drawing Rangoli, makinglanterns etc.

The Excitement called Diwali
Mumbai, October 25 :
This year, Diwali came during the weekend, making it a joyous time for even those who normally couldn’t get off from their busy schedules. Shopping for new clothes and crackers was on the agenda even for the poorest of poor (according to their budget) and the annual bonus put a smile on even the meanest and stingiest of scrooges. Electric lights competed with earthen lamps lit in a row, to welcome Laxmi, the Goddess of wealth. Houses were cleaned and decorated with ‘torans’ and ‘rangoli’ paper lanterns were made to create a fairyland effect and everything/everyone seemed to be happy and gay. Having had a good monsoon and a bumper crop, the farmers had a truly ‘HAPPY DIWALI’. Businessmen opened new books of accounts hoping for a prosperous year. Savories and sweetmeats filled the air with an aroma of celebration. It was indeed a joyous Deepawali.

Write a dialogue between a manager of electronic store and yourself.
Manager : Good evening Sir, what would you like to see?
You : A 100 % Indian T.V. - the model that was advertised a couple of months ago.
Manager : Sorry Sir, I wish we had it here today but there is no stock.
You : But, just last month one of my friend had purchased it from this outlet.
Manager : That’s right, but we have sold all the models of that brand.
You : How sad ! I don’t believe this. Hasn’t the company despatched fresh stock?
Manager : Well you see, we will be receiving new stock next week.
You : Oh ! I will have to wait then.
Manager : I am extremely sorry. I would have helped you but I am helpess.
You : Well, it’s Ok. I’ll come again.
Write an Interview with your favourite star. Frame ten questions.
Interviewer : Hailing from a political family, how difficult was it for you to come to films?
Interviewer : Was there ever a time when you felt like quitting?
Interviewer : It is a wonder how effortlessly you convey the plight of the less fortunate characters. How do you do that?
Interviewer : On what basis do you choose your films?
Interviewer : We learnt that you have a degree in psychology. How does it help you understand the characters you play?
Interviewer : Your social work has never suffered at the hands of your film career. How is managing so much possible for you?
Interviewer : Most of your films are called moral science lessons by your critics. Is that a conscious effort?
Interviewer : Do you have any specific people in mind that you would like to work with?
Interviewer : As a youth icon, what is your message to them?
As an interviewer for the Press interview the forest keeper/officer of SGNP. Frame ten questions.
(The X STD students got an opportunity to interview the officer of SGNP)
1. What is the total area that has been allocated to SGNP?
2. What is your criteria for the selection of the care-takers?
3. How many animals are there in all in this National Park?
4. Which species of animals are there in the park?
5. Do you limit the number of people coming to the National Park on public holidays?
6. What problems are encountered by you and your care-takers just in case the number rises on public holidays?
7. What measures do you follow to discipline the crowd and make it less stressful for the animals?
8. What is the ratio of the care-takers to animals?
9. Do you get any extra funds for the maintenance of the National Park?
10. Do you think with the growing human population, you will be able to take care of the animals of this National Park?

Write a speech on ''Farewell to the senior students''.
Farewell To The Senior Students
Respected Principal, teachers and our dear students of class X whom we will miss immensely and my own fellow students,
The students of class X are all poised on the threshold of the next phase of their lives. In school we learn to walk, but in college they will have to learn to run to win in the race of the future. I remember the last sports day when you all won awards for different events like inter school sports and quizzes and made our school proud of you. You also took time off to coach us, your juniors, so that we could do better. Open house was a resounding success last year and every planning, organising and execution was so well co-ordinated by all of you. Academically, the percentiles and averages put up by your batch
is unmatched. Your score raises the benchmark for all of us and we all will have to work doubly hard to achieve your standard. As a class passing out, you will be passing on the baton of responsibility to us and your stellar examples will serve us well to emulate you.  We wish you a fond adieu and farewell. With best wishes for your forthcoming Board exam.

Honesty Is The Best Policy
Honesty is the best policy is a maxim we have heard since our childhood. But is it really? Ask how honesty is helpful in a
world where money and power rule many people well, to those people I say that an honest person has an advantage over others. People who lie are always afraid of being found out. They can’t look people in the eye. Honest people aren’t afraid. They are confident and self-assured. This attitude makes them better suited for success. Dishonest people always look to exploit situations. But they don’t realize that they are wasting precious time and energy that could be utilized better in an honest manner. For example, a student who is looking to cheat in the exams spends valuable time preparing chits, time that he could have spent studying the lessons. Being honest would have meant he would score well in his exams on his own accord. This would have boosted his confidence and he would have remembered the lesson, which he may need later in his life. Thus, honesty is the best policy and a key to being successful.

Every Dark Cloud has a silver lining
Success comes to those who see opportunity in adversity. For it is only after being put through the heat of adversity that pure gold is brought out. From the womb of pain emerges a baby of hope. The difficult period is the time that an intelligent man will use to learn and equip himself to deal better with the next dark cloud and emerge on top. Yes, it is painful and difficult, but nobody said success could be achieved easily. Take the opportunity presented by the dark clouds to learn more about them, learn about others who have encountered such times and come out with the pearls of wisdom from the depths of their despair. Take time to re-examine your life and check your flaws and strengths. This will help you improve the quality of your life. For example, children who have braces on their teeth. Of course, it is torturous at first. The kids have to endure the ridicule of their classmates and friends. But kids who can bear the discomfort of public ridicule and physical pain end up with perfectly aligned teeth, stronger character and more tolerant personality. So never despair if dark clouds cast a shadow over your world. Wait, learn how to live in that state and you will never let gloom take control of your heart. After all, the dark clouds will lift sooner or later and sunlight will breakthrough and brighten your life.
Travel is the rubber band that stretches your outlook of life. Travelling even if it is till that shop at the corner of your society
can teach you a lot. What? Next time you go to that shop observe the people. You will see that each individual has special mannerisms, one person scratches his head when nervous, another has the annoying habit of digging his nose. You may also see that they are handicapped and have only one leg but still managing a store. This single trip has taught you not to judge people at face value. Travelling introduces us to other people and helps educate us. It makes us more tolerant, especially if one is travelling by the Mumbai local trains. It opens our eyes to different cultures. For instance, if snakes and dogs are pets for you, well there are places in the world where people look on these as food items. Exposure to different values, ideas and cultures will thus inevitably make us more mature and broadminded.

Honesty Pays
To understand the maxim ‘Honesty Pays’ one has to just read another proverb, ‘crime never pays’. Dishonest people may succeed for a while, but would ultimately always get his just desserts. An honest person, on the other hand, may suffer the trials and tribulations of life but will in the final equation emerge a winner. An honest person puts in the effort to be  successful and in the long run the effort always pays dividends. That is because an honest person is better equipped to overcome obstacles due to his training. Honest people are uncomplicated in their approach to life and their straightforwardness wins them a lot of friends. Finally it is people with true friends who are the winners in life.

Handsome is as handsome does
They say looks are deceptive yet people form opinions based on the outward appearence of an Individual. Instead we should
bear in mind that it is the character and the deeds of a person that should be given more importance. Inner beauty is more important than outward appearence. If we go through the pages of history we will realize that the greatest people, the most respected souls are known for their good deeds and inner beauty. For instance Mother Teresa who is even venerated as a saint today, didn’t have a beautiful face yet the compassion in her heart and the expression of earnest devotion to care for the down-trodden on her face makes her the most beautiful woman who lived on this planet; many other great name can be enumerated here like Mahatma Gandhi for his adherence to truth and non - violence and unswerving courage changed the
destiny of the Indians and he hardly falls in the parameters of so called handsome men. Great people like Nelson Mandela, Martin Luther King Jr. etc. too didn’t look impressive but left behind an impact on the world by the strength of their characters. Thus we can say that these great souls truly prove the saying ‘Handsome is as handsome does’.

A.1. (A) Read the following passage and answer the questions given below :

1. Kantabai Wali's business venture is cattle rearing.
2. Jayshree Kamble wants to create her own brand name so she does not want to sell the compost to any company because no one will relate her name with the compost.
3. Inspite of being an illiterate, Kantabai Wali has undertaken a business venture and also has knowledge of finance and marketing. Thus she laughs at the irony of the situation.
4. (a) Kantabai laughs heartily, doesn’t she? (b) She is an angutha chhap - Main Clause. who cannot sign her name - Adjective Clause qualifying the noun ‘an angutha chhap’.
5. (i) (a) cattle-rearing (b) income-generating. (ii) (a) loss (b) urban
6. For a small enterprise one should have a sound knowledge of business, should be ready to take risks, he should be hard-working, sincere and focused in his work. This will help the enterprise to grow to a great extent.

A.1. (B) Read the following passage and answer the questions given below :

1. To try to forget about her chin, Keryn curled up on the corner of the living room sofa and read a book.
2. Jason teased Keryn that though eating carrots might be good for her skin, it would make her top teeth grow and make her ears long and floppy like a rabbit.
3. By suggesting that Keryn could try plastic surgery or a flame thrower, Jason was only being sarcastic.
4. (a) Jason told Keryn to be careful of those raw carrots. (b) She would have nothing except a raw carrot instead.
5. (i) (a) thought / thoughtfulness  (b) growth (ii) (a) see (b) bee
6. The relationship shared by the members of Keryn’s family seems to be like that of any other normal close knit family. They discuss matters while having meals together. They care for and support each other whenever required.
A.1. (C) Read the following passage and answer the questions given below :

1. Besides Cara, Otto wrote to Sumi from Japan and John Neiman, a college student.
2. Otto greeted Cara with a lot of warmth and eagerness and gave her a real bearhug. There were no formal handshakes or polite hellos as Cara had feared.
3. Otto had saved all of Cara’s letters as each person who wrote to him was significant to him.
4. (a) Otto gave her advice through the years. (b) Wasn’t it really him?
5. (i) (a) letter - daughter, (b) snow – white      (ii) (a) brought out - The lawyer brought out all the documents, as evidence before the jury. (b) stacked on - Old newspapers were stacked on the sofa and all across the room.
6. I would have felt on the top of the world, absolutely elated on receiving such a warm welcome from Otto. It would have been like a father-daughter re-union. In Indian style, I would have touched Otto Frank’s feet as a mark of respect for an elder.

A.1. (D) Read the following passage and answer the questions given below :

1. The narrator remembers days and nights when his mother worked continuously like the mother in the write up.
2. Mother set the alarm, laid out clothing for the next day straightened up the shoe rack and said her prayers in her own room.
3. Mother made sure the doors were locked and the verandah light was on.
4. (a) I’m on my way, aren’t I ?           (b) Turning off the TV, dad announced to no one in particular.
5. (i - b), (ii - c), (iii - d), (iv - a)
6. I think, I should help mother. This will give her some time for herself and also some respite from the numerous chores she has to perform. It will also make me independent.

A.1. (E) Read the following passage and answer the questions given below :

1. He had shucked them that morning before he left so that they’d be fresh.
2. The narrator realised that the bed linens were neatly foldedand the old man was out on the porch.
3. God might have said that the old man wouldn’t mind starting in his small body as he had a beautiful soul.
4. (a) I was visiting a friend - Main Clause who showed me her flowers-Subordinate Adjective Clause qualifying the noun ‘friend’ in the Main Clause.        (b) They were larger than any other oysters I had ever seen.
5. (i) (a) thankfulness (b) flowers
 Noun Verb Adjective beauty Beautify Beautiful acceptance Accept acceptable
6. The fisherman seems to be a man with loads of courage and positive attitude. He was a very humble person who considered life to be God’s most precious gift. Inspite of facing so many hardships he was grateful to God as he only looked at the positive aspect of life.

A.1. (F) Read the following passage and answer the questions given below :
1. Kantabai’s complaint was taken seriously by the local authorities who provided her with the protection of a plainclothes policeman.
2. They all realized that if they all bought cattle they would have grazing problems as there was very little land in their village, so each one of them decided to take up different activities.
3. The purpose of this text is to help one understand that one can be independent by starting a small enterprise and one has to empowerthe villagers to help them improve their conditions.
4. (a) The local authorities took her complaint seriously. (b) can - ability.
5. (i) (a) apply (b) collect (ii) Like an army of ants.
6. We can buy products made by them like the compost, handicraft items,etc. We can encourage everybody to buy products made by the villagers which will widen their business prospects. We can create awareness about the SHGs and problems of villages.

A.1. (G) Read the following passage and answer the questions given below :
1. The writer didn’t anticipate the commentator’s story as he was watching the tape for the first time with his mother.
2. The writer could feel the tears building up inside the two of them as they watched the tape of the dramatic home run. Both of them broke down as the commentator announced that the home run was for his mother.
3. The lines that indicate the most emotional moments between the writer and his Mom are, “I love you son, and I’m very proud of you. I’m going to miss you very much.”
4. (a) I could feel that the tears were building up inside us.     (b) This one was probably for none other than his mom.
5. (i) (a) dramatic (b) anticipate                       (ii) home run, pitcher, foul, strike.
6. The narrator’s game had been affected as his mother’s condition had worsened. For six long weeks he had not been able to connect with the ball. This was also disturbing the mother. She could sense the pain that her son was going through. So the day, the narrator hit the home run, was the greatest moment of joy and pride for his mother.

A.1. (H) Read the following passage and answer the questions given below :
1. The writer’s father’s professor, who was his guide complimented him for his work.
2. When the professor complimented the writer’s father, he decided to splurge a bit and ordered a suit for himself from an expensive tailoring emporium on Saville Row.
3. The writer entered with a feeling of trepidation wondering whether he would be able to afford the suit due to the increase in prices.
4. (a) I will not name the establishment - Main Clause which I located after some effort - Subordinate Adjective Clause
qualifying the noun establishment in the Main Clause.  (b) Didn’t he emerge 15 minutes later?
5. (i) (a) trepidation (b) enormous (ii) (a) humility (b) cheap
6. To splurge at times, to boost one’s ego or to celebrate a special occasion is fine but falling prey to such a habit is harmful. One must always spend within one’s means and save, too.
A.1. (I) Read the following passage and answer the questions given below :

1. Nehru describes our Motherland as much-loved, the ancient, the eternal and the ever-new.
2. Nehru visualizes Indias the role to co-operate with the world in furthering peace, freedom and democracy.
3. Nehru’s message is that Indians should live in equality, be aware of their rights, privileges and obligations and not indulge in communalism or narrow - mindedness.
4. (a) Present Perfect Tense. (b) Can any nation be great whose people are narrow in thoughts?
5. (i) (a) national (b) economical         (ii) (a) equally (b) unhappily
6. The objectives of the Constitution of India that are reflected in Nehru’s message are : to bring freedom and opportunity, to build up a prosperous, democratic, progressive nation, and to create social, economic, and political institutions which will ensure justice and fullness of life to every man and woman and to have a secularistic attitude.

A.1. (J) Read the following passage and answer the questions given below :

1. Cowboy was appointed on straight commission with no base salary.
2. According to the writer, Cowboy could probably sell four telephone systems at the rate $250 per system thus making$ 1000 per month.
3. The writer wanted to spend two days with the cowboy to teach him  everything he needed to know to sell one type of a very small telephone system as the cowboy had no experience in sales.
4. (a) He was ready to be successful in business. (b) I hired him on straight commission without base salary.
5. (i) (a) appreciative (b) systematic     (ii) (a) to figure out (b) to be blunt
6. I am impressed about the cowboy’s incredible focus on being a success despite having none of the required qualification of a salesman. He was mentally prepared to be a success in business and had left his past behind him. His determination to move ahead with life is very inspiring.


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# Tag Info

## Hot answers tagged abelian-groups

7

I claim that the colimit of the sequence of inclusions $\frac{1}{1!}\mathbb{Z}\,/\,\mathbb{Z} \hookrightarrow \frac{1}{2!}\mathbb{Z}\,/\,\mathbb{Z} \hookrightarrow \frac{1}{3!}\mathbb{Z}\,/\,\mathbb{Z} \hookrightarrow \dotsc$ exists in $\mathsf{FinAb}$. Namely, it is zero, in contrast to the colimit in $\mathsf{Ab}$, which is $\mathbb{Q}/\mathbb{Z}$. This is ...

4

Use the fundamental theorem of finitely generated abelian groups, which states that every such group is a product of cyclic groups. If you cannot use this, note that every element has either order $p$ or order $p^2$. If an element has order $p^2$, then we have a cyclic group of order $p^2$. Otherwise every element has order $p$. Choose two elements neither ...

3

Lemma :$T/Z(T)$ is cyclic implies $T$ is abelian. Proof:Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian. Can you conclude now?

3

Your first paragraph is in some sense backwards: you should hurry to incorporate the Eckmann-Hilton argument into your intuition, and then you can use it to predict lots of other things, including but not limited to the fact that topological groups have abelian fundamental groups! For example, you can also use it to predict that the higher homotopy groups ...

3

It's not true for $M=C_2\times C_4$. Let $x$ and $y$ be generators of the two factors. Then every endomorphism $\varphi$ is of the form \begin{align} \varphi(x)&=ax+2by\\ \varphi(y)&=cx+dy \end{align} for integers $a,b,c$ determined$\pmod{2}$ and $d$ determined$\pmod{4}$. But if $\varphi$ is an automorphism then $\varphi(y)$ has order $4$, and ...

2

Hint. First, you missed $\def\Z{\mathbb Z}\Z_9^2$. For elements of order 27, recall that in a direct product $G \times H$, we have for $g \in G$, $h \in H$ that $$\def\ord{\mathop{\rm ord}}\ord (g,h) = \def\lcm{\mathord{\rm lcm}}\lcm(\ord g, \ord h)$$

2

It appears that this is correct: the only countable LCA groups are discrete. Using the first structure theorem for LCA groups, we can reduce this to the case where the group $G$ is compact. According to this, there is a theorem: "Every countable compact Hausdorff space is homeomorphic to some well-ordered set with the order topology." However, the only ...

2

There is a free abelian group of rank $n$ and an epimorphism $\pi: F \to G$. Given a subgroup $H \leq G$, its preimage under $\pi$ is a subgroup of $F$, hence is free abelian of rank $\leq n$ and so is generated by at most $n$ elements; furthermore, a basis for $\pi^{-1}(H)$ may be chosen so that the basis elements of $\ker\pi$ are multiples of the basis ...

2

The finite Abelian group $G$ is a direct product of at most $t$ cyclic groups if and only if each of its Sylow $p$-subgroups is a direct product of at most $t$ cyclic groups. Hence it is enough to consider the case that $G$ is a $p$-group, so suppose it is. Now if $G$ is the direct product of exactly $t$ cyclic subgroups, then $G_{p} = \{g \in G: g^{p} = ... 2 The issue with your proof is that canceling$a$from the left and$b$from the right of $$ababab=aaabbb$$ only gives you$baba=aabb$. Notice that this is different from what you got which is$abab=aabb$. Perhaps the issue for you was cancelling from the middle as Steven Stadnicki has suggested. It looks like this question has been created to answer that ... 2 Suppose$(ab)^3 = a^3b^3$, that is:$ababab = aaabbb$Multiplying on the left by$a^{-1}$and on the right by$b^{-1}$, we have:$baba = a^{-1}abababb^{-1} = a^{-1}aaabbbb^{-1} = aabb$That is,$(ba)^2 = a^2b^2$. Since we know$(ab)^5 = a^5b^5$as well:$(ab)^5 = ababababab = a(babababa)b = a(ba)^4b$, so$a(ba)^4b = a^5b^5$, and multiplying on the ... 2 If$H$is any group then you can think of a group$G$as a subgroup of$H \times G$by the mapping$x\mapsto (0,x)$. 2 For any$x \in H_1, y\in H_2$, we have $$xyx^{-1}y^{-1} \in H_1\cap H_2$$ since both are normal. However,$|H_1\cap H_2|$divides both$p_1$and$p_2$, and so must be 1. Hence,$xy=yx$. Thus the map $$H_1\times H_2\times H_3 \to G \text{ given by } (x_1,x_2,x_3) \mapsto x_1x_2x_3$$ is a homomorphism. This gives the isomorphism you need. 2 The cyclic group generated by an element is always Abelian (since anything commutes with itself, so powers of an element commute with powers of the same element). This is the cyclic group generated by$\sigma$so it is abelian. 1 Hint : Assume$a,b$are non-commuting elements of$S_4$. What can you say about the elements$\{0\} \times a$and$\{0 \} \times b$? Remember how is defined the group law on the product. As @MPW said, the same argument works for a product$\prod_{a \in A}G_a$of groups, when only one group is non-abelian. 1 When we have$xyz=x'yz'$and cancel out the middle factor, we can only do that if we know that the commutes with$x$and$x'$, or with$z$and$z'$. From being so accustomed to working with commutativity, we lose sight of this fact. In reality, we can only cancel from the left or right, and the only way we can do more is if we can move a factor to the left ... 1 There is an equivalent of Euler's theorem for polynomials: Theorem: (Euler's Theorem for Polynomials). Let$m \in K[x]$, where$K$is a finite field, and let $$\varphi(m) = \#\{f \in K[x] : 0 <= deg(f)< deg(m) \text{ and } gcd(f, m) = 1\}$$ Where here$\#(A)$denotes the cardinal of the set$A$up to a multiplication by a constant ($f$and ... 1 The proof that the multiplicative group of a finite field is cyclic uses the property of a cyclic group$C$that for every natural number$n > 0$, there are at most$n$elements in$C$of order$n$. This is an elementary (first-order) statement, for each$n\$, which also holds for the infinite cyclic group (vacuously). For the finite cyclic groups, it is ...

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# MILC: A microsimulation model of the natural history of lung cancer

1. Brown University School of Public Health, United States
Research article
Cite this article as: S. A Chrysanthopoulou; 2017; MILC: A microsimulation model of the natural history of lung cancer; International Journal of Microsimulation; 10(3); 5-26. doi: 10.34196/ijm.00164

## Abstract

The Microsimulation Lung Cancer (MILC) model was developed to simulate individual trajectories and predict outcomes of lung cancer for populations. The model describes the natural history of lung cancer from a disease-free state to death. Predictions of individual trajectories depend on a set of covariates including age, sex, and smoking behaviors. The module presented here is designed as part of a comprehensive decision-making toolkit for evaluating lung cancer prevention, screening and treatment policies. The MILC package implements the model in the open-source statistical software R. This paper introduces the main components, simulation algorithm, and specifics of the MILC model, validates it by reproducing observed lung cancer incidence trends in the US population, and uses it to make plausible predictions for 50-year-old men and women with a range of smoking histories.

## 1. Introduction

Micro-Simulation Models (MSMs) are predictive models designed to describe complex processes and simulate unit level data (Orcutt, 1957). Predicted trends about the quantities of interest, resulting from aggregation of a large number of microsimulations, are intended to guide policy decisions. In medical decision making MSMs usually describe the natural history of a disease, often in conjunction with the effect of some intervention, such as screening, treatment, etc. (Kopec, Edwards, Manuel, & Rutter, 2012). To this end they employ mathematical equations with stochastic assumptions to describe both observed and latent characteristics of the underlying process (Rutter, Zaslavsky, & Feuer, 2011).

MSMs are useful because they provide a handy way to simulate intricate phenomena involving dynamic systems for which observed data are either hard or even unethical to collect (for instance, exposing the subjects to unnecessary risks) or not available (for example, latent characteristics). They also constitute a practical tool for combining information from various sources, including observational studies, clinical trials, expert opinions, etc., and simulating large pseudo-samples. Due to the great flexibility they provide to researchers, MSMs have proven so far one of the best ways to model the progression of chronic diseases (Oderkirk, Sassi, & Cecchini, 2012). The focus on the individual rather than the average patient can also prove them a very useful tool for assisting improvement of individualized patient care. Therefore microsimulation has risen to prominence as a promising tool for making projections about the impact of interventions (such as screening) when applied to population cohorts, and thus informing health policies and improving medical decision making (Kopec et al., 2012). For example MSMs are often used in Comparative Effectiveness Research (CER) studies, aimed at evaluating public health policies and their effect on health status of target populations Zucchelli, Jones, & N., 2012.

The development of an MSM is a challenging undertaking. Due to their complexity (combination of several stochastic and deterministic models, a usually large number of parameters, description of latent characteristics, etc.), model calibration requires advanced statistical techniques, and a huge number, usually of an order of magnitude of 12 or more, of microsimulations. The same holds for an extensive validation of the model, let alone a sensitivity analysis, hence it is self evident that the development of an MSM is a computationally highly intensive problem that necessitates special resources for implementing high performance computing techniques. Furthermore, the complexity of an MSM along with the fact that it often tries to describe latent phenomena lead to identifiability problems. The degree of accuracy and the validity of an MSM highly depend on the available information and data for building and calibrating the model. In addition, MSMs are subject to several sources of uncertainty, the combination and expression of which on the final outcomes is a problem not satisfactorily addressed yet (Li & O’Donoghue, 2013; Rutter et al., 2011).

Several MSMs have been developed in order to predict lung cancer related outcomes. Some of the most comprehensive ones are part of the research conducted by the Cancer Intervention and Surveillance Modeling Network (CISNET) of the National Cancer Institute (NCI).1 Examples of other MSMs for lung cancer can also be found in the literature (Bongers et al., 2016, 2013; Flanagan et al., 2015; Goldwasser, 2009). All these models, as part of interdisciplinary work, have been proven extremely useful, especially for evaluating intervention strategies and informing public health decisions, with numerous applications. Depending on the specific purpose to fulfill, each of these MSMs focuses on particular aspects of the natural history of lung cancer, exhibiting large variation from the structure (methods used to describe each component, etc.) and required input data, to the predicted outcomes.

Despite the evident usefulness, and unquestionable value and contribution in the field of lung cancer research, MSMs for lung cancer suffer from some limitations. Until today, at least to our knowledge, there is no publicly available source code for running these models. In addition, the high level of complexity, and the lack, in many cases, of sufficient details about their structure, render these models “black boxes’’, hard to understand and evaluate, and impossible to reproduce (Kopec et al., 2010; Rutter et al., 2011). The implementation, and reporting practices for MSMs require a lot of discussion, and some standardization, in order to facilitate evaluation and enhance comprehensiveness.

The Microsimulation Lung Cancer (MILC) model (Chrysanthopoulou, 2013), is a new, dynamic, continuous time microsimulation model that simulates individual trajectories focusing on lung-cancer related outcomes. In its current version, the model comprises a module describing the natural history of lung cancer in the absence of any screening or treatment components, and incorporates several best current practices for modeling lung cancer states. The model simulates the course of lung cancer from the disease-free state to the local, regional, and distant disease states and eventually to death either from lung cancer or some other cause. Prediction of individual trajectories involves incorporation of unit-level baseline information about three important factors, namely age, sex, and smoking, including current smoking status, start and quit smoking ages, and average number of cigarettes smoked per day when relevant.

One of the main objectives of creating MILC was to use the model as a tool for studying the statistical properties of, and suggesting appropriate statistical methods for the development of MSMs with analogous characteristics. Furthermore we wanted to create a streamlined, yet valid MSM for lung cancer, and make it publicly available to potential end users in the field of lung cancer research. The MILC package (Chrysanthopoulou, 2014) includes the required source code and data for implementing this model in the open-source statistical software R, and is available on the Comprehensive R Archive Network (CRAN) repository.

This article introduces the MILC model and describes its main components, simulation algorithm, and specifications. We also present two examples of how the MILC model can be used in practice. In the first example we validate the model against observed lung cancer incidence rates in the US population, while in the second we use the MILC model to predict individual risks for smokers based on sex and smoking intensity. Finally we discuss the main differences between our model and other MSMs used in lung cancer research, and outline future work to develop the MILC model into a comprehensive tool for assisting decision making for lung cancer.

## 2. Methods

### 2.1 Model components

The MILC model defines five distinct states in the natural history of lung cancer. Starting from the disease-free state (S0) it is possible for an individual to have transition to the local (S1), regional (S2), and distant (S3) disease state, and eventually to the absorbing state of death (S4) either from lung cancer or from some other cause. States S1-S3 are sometimes called tunnel states because of their special arrangement, namely they can only be visited in this particular fixed order (Sonnenberg & Beck, 1993). The Markov state diagram in Figure 1 depicts the five distinct MILC model states, and the underlying transition rules.

Figure 1

The onset of the first malignant cell signifies the beginning of the local disease state (S1). The tumor in that state is limited to the place where it started, with no sign of spread elsewhere in the body. The first malignant cell can proliferate up to the point of nearby lymph nodes, tissues, or organs involvement thus transitioning to the regional disease state (S2). The tumor may further progress to the distant state (S3), namely metastasize to distant parts of the body, and eventually cause death (S4), unless death from some other cause precedes. Within the three tunnel states tumor can range from Stage 0 to Stage IV, depending on the size and spread (National Cancer Institute, 2017a).

The MILC model makes some important assumptions. First of all it assumes that the transition to subsequent states depends only on the present state (Markov property). Furthermore the disease progression is irreversible, namely once the first malignant cell occurs lung cancer will either remain to the local or transition to subsequent states, depending on the total time of the follow-up period and a number of risk factors. Finally a death can be attributed to lung cancer if and only if it occurs after transition to the distant state.

#### 2.1.1 Onset of the first malignant cell

We model the onset of the first malignant cell using the exact solutions for the expression of the hazard rates and the survival probabilities of the biological two-stage clonal expansion (TSCE) model suggested by Moolgavkar and Luebeck (1990). According to this model the hazard function for the development of the first malignant cell (Heidenreich, Luebeck, & Moolgavkar, 1997) can be expressed as:

(1) $h\left(t\right)=\frac{v\mu X\left({e}^{{\left(\gamma +2B\right)}^{t}}-1\right)}{\gamma +B\left({e}^{{}^{{\left(\gamma +2B\right)}^{t}}}+1\right)}$

with γ = α − β − µ, and $B=12(−γ+γ2+4αμ)$. In Equation 1 X is the total number of normal cells, ν is the normal cell initiation rate, and α, β, µ are the division, apoptosis (death or differentiation), and malignant conversion rates of initiated cells respectively.

Studies (Hazelton, Clements, & Moolgavkar, 2005; Hazelton, Luebeck, Heidenreich, & Moolgavkar, 2001) have shown that power laws are good approximations to the effect of smoking on the onset of the first malignant cell. If q(t) denotes the smoking intensity at age t, expressed as average number of cigarettes smoked per day, then:

(2) ${\alpha }_{s}={\alpha }_{ns}\cdot \left[1+{\alpha }_{1}\cdot q{\left(t\right)}^{\alpha 2}\right]$

and

(3) ${\gamma }_{s}={\gamma }_{ns}\cdot \left[1+{\alpha }_{1}\cdot q{\left(t\right)}^{\alpha 2}\right]$

where αns and γns are the respective coefficients for non-smokers. To account for sex and smoking history differences, we assume different hazards (as functions of age t) for each combination of sex (male/female), and smoking status (never/former/current smoker) categories.

For each individual the time period from birth (t = 0) to the onset of the first malignant cell can be split into intervals within which the hazard rate is constant and depends on the person’s smoking status. The hazard for never smokers is constant throughout their entire life and of course independent of smoking. Smokers have two different hazards, one before (the same with non-smokers), and one after (depending on the smoking intensity) they start smoking. In its current version MILC also assumes that former smokers had only two changes in their smoking behavior, namely one when they started and one when they quit smoking. However the model is flexible and can accommodate multiple changes of smoking behavior in a person’s lifetime.2

#### 2.1.2 Tumor growth

The Gompertz distribution is more flexible than the exponential, and therefore provides a better approximation of tumor growth for most cancer types (Detterbeck & Gibson, 2008). The Gompertz distribution models proliferation of tumor cells as a modified exponential process in which successive doubling times occur at increasingly longer time intervals (Laird, 1964). This enables us to capture the reality of shorter pre-clinical periods with longer survival after diagnosis.

We define V(t) to be the tumor volume when a person reaches age t (in years). The MILC model assumes a Gompertzian tumor growth (Laird, 1964), according which:

(4)

where V0 represents the initial tumor volume (namely the volume of the first malignant cell), while m is the scale, and s is the shape parameter of the Gompertz probability density function.

We further assume a spherical tumor growth (Gallaher, Babu, Plevritis, & Anderson, 2014), thus making the tumor size a function of its diameter d(t) at age t, namely:

(5) $V\left(t\right)=\frac{\text{π}}{6}{\left[d\left(t\right)\right]}^{3}$

In the literature (Detterbeck & Gibson, 2008; Geddes, 1979; McMahon, 2005) we find that the minimum tumor diameter (one cancerous cell) is d0 = 0.01µm, and the maximum possible diameter (tumor that causes death) is dmax = 13cm. To simplify model parameterization we assume the same Gompertz distribution for all tumors irrespective of their histological type and stage.

#### 2.1.3 Disease progression

Disease progression of an existing lung cancer can occur via nodal involvement and distant metastases (McMahon, 2005). Current MSMs for lung cancer (Goldwasser, 2009; McMahon, 2005) in their disease progression parts adopt methods developed to describe the progress of breast cancer (Garg, Rao, & Redmond, 1970; Koscielny, Tubiana, & Valleron, 1985; Plevritis, Salzman, Sigal, & Glynn, 2007; Thames, Buchholz, & Smith, 1999). Given a Gompertzian tumor growth, the log-normal distribution can adequately describe the distribution of tumor volumes at specific time points, starting from the local state, that is the onset of the first malignant cell (Koscielny et al., 1984, 1985; Spratt & Spratt, 1964; Steel, 1977).

We define three different log-normal distributions to simulate the tumor volume at the transition to regional (Vreg), and distant (Vdist) disease states, as well as the tumor at diagnosis (Vdiag). Given the simulated tumor volume, and growth rate, and assuming a spherical growth, the model calculates the age at which the tumor has reached a specific size, and hence the age at the transition to each of the respective three MILC states.

#### 2.1.4 Survival

Because smoking is an important risk factor for dying not only from lung cancer (National Cancer Institute, 2017b), we follow a competing risks approach to simulate mortality, distinguishing between death from lung cancer or other causes. We estimate the probability of death from lung cancer in the presence of other causes of death, using the Cumulative Incidence Function (CIF) non-parametric technique (Klein & Moeschberger, 2003). We derive estimates using information from both the National Health Interview Survey (NHIS, 2006) and Surveillance, Epidemiology and End Results (SEER, 2006) data.

We employ the inverse transform approach to simulate both age and cause of death (lung cancer or other) based on CIF estimates. The MILC simulations depend on the strong assumption that the observed death patterns and smoking behaviors do not change dramatically over time, hence they are also relevant to the prediction period we are interested in. Furthermore, given the data used, the model currently represents survival patterns observed in the US population. Depending on the available information, the MILC model can be also calibrated and used to simulate other (sub-)populations.

### 2.2 Model specifics

#### 2.2.1 Structure and parameterization

Table 1 summarizes the parameterization of the MILC model. Figure 2 depicts how the model functions, namely the required input and the anticipated output for each simulated individual trajectory. In particular, to predict one trajectory, we “feed” the model with three sets of input: (i) Baseline characteristics X (age, sex, smoking habits) of the individual. Smoking includes status (never, former, or current smoker), as well as start and quit smoking ages, and smoking intensity (average number of cigarettes smoked per day), where relevant. (ii) Values for the model parameters θ. These values can be either ad-hoc estimates or the result of some calibration procedure. (iii) Cumulative incidence function estimates S for lung cancer and other cause survival.

Possible MILC outputs (predictions) can be classified into three broad categories, namely those regarding the disease progressionprog), diagnosis (Õdiagn), and deathdeath). Disease progression output (Õprog = {Tmal, Treg, Tdist}), comprises prediction of the ages at the beginning of the local, regional, and distant tumor states respectively. In the MILC model diagnosis signifies the time when lung cancer is confirmed and assessed for its size and stage. Diagnosis output (Õdiagn = {Tdiagn, ddiagn, stage}) includes predicted age, tumor size, and tumor stage at diagnosis. Finally, death output (Õdeath = {Tdeath, cause}) has information about the age and cause of death, if the model predicts that the individual dies before the end of the follow-up period. Otherwise it provides the age at the end of the prediction period, if the person is still alive by then.

Table 1
Figure 2

#### 2.2.2 Calibration

Specifying the parameter values of an MSM requires extensive calibration with results heavily depending on the quality of the available data. The microdata used and the calibration targets set are key components of the calibration procedure. Microdata is essentially individual-level information for a sample of subjects representative of the target population in the study and is used as input to the model for simulating individual trajectories. Calibration targets are quantities of interest (usually summary statistics from the target population) that the MSM should accurately predict.

The high level of complexity usually renders impossible the determination of closed-form expressions of the outcomes as functions of the model parameters. This along with the fact that an MSM usually involves description of latent characteristics, as is the case with the MILC model, dictates the use of calibration procedures for the specification of sets of plausible values for the model parameters. Detailed calibration of an MSM is a computationally intensive and time consuming process. For the examples presented in this paper we have used the MILC model after calibrating four parameters, and setting ad-hoc estimates or fixed values from the literature for the others as indicated in Table 2.

The microdata used for this calibration, included individual-level information randomly extracted from the 1980 US population. The four parameters that we chose to calibrate represent several aspects in the natural history of lung cancer; one is related to the tumor growth (m), and the others to the disease progression component of the model (μregj, μdist, and μdiagn). We used fixed values for all the other MILC parameters, based on literature review about the natural history of lung cancer (Table 2). For parameters related to the onset of the first malignant cell we retrieved values from Hazelton et al. (2005), while values for the tumor growth component were found in Koscielny et al. (1985).

We implemented the Bayesian calibration method, suggested by Rutter, Miglioretti, and Savarino (2009), to calibrate the MILC model on lung-cancer incidence trends observed in the 2006 US population of males. The method involves a large number of Gibbs sampler iterations with embedded approximate Metropolis-Hastings steps for drawing values from the joint posterior distribution, assuming that lung cancer incidence rates approximately follow a Poisson distribution. The result from this calibration method is a set of random draws from the approximate joint posterior h(θ | Y ) of the parameter vector θ. Table 2 presents medians and interquartile ranges for the four calibrated MILC parameters (m, µregdist, and µdiagn).

Details on the Bayesian calibration procedure are provided in another paper in preparation (Chrysan-thopoulou, 2017). This paper discusses results from a comprehensive comparative analysis of two of the most broadly used calibration methods for MSMs, the aforementioned Bayesian method, and another Empirical technique which employs the Latin Hypercube Sampling design for an efficient search of the multidimensional parameter space.

#### 2.2.3 Validation

We validated the model predictions against lung cancer incidence trends observed in the US population. For this purpose we simulated individual-level characteristics (age, sex and smoking) for a pseudo-sample of size N=10,000 people, representative of the 1980 US population, combining information from the 1980 US census, and the 1980 Statistical Abstract of the US. We used the calibrated MILC model to simulate individual trajectories for people in the pseudo-sample, and predicted lung cancer incidence rates 26 years ahead. We compared the predicted rates (aggregated results) with age-group specific ones reported in the SEER 2002–2006 database (Figure 3). The MILC model can also be calibrated to other data, so as to simulate various (sub-)populations, and/or even reproduce other lung cancer related outcomes, such as mortality, age and tumor stage at diagnosis.

#### 2.2.4 Functionality

The most typical use, and essentially the primary reason which has driven the development and implementation of MSMs in medical decision making, is the application of this model to a cohort of people for which individual-level information at baseline is available. Given this information, the model tries to accurately predict individual disease trajectories, and estimate outcomes of interest by aggregating relevant quantities from the predicted trajectories (Meza et al., 2014; Rutter & Savarino, 2010; Wolf-son, 2011). Those estimates can result in after a single or multiple runs of the model on the same cohort. Multiple repetitions are preferable because they can provide a better sense of the inherent uncertainty, and reveal interesting correlation structures of the underlying system components.

Table 2

In this paper we also suggest another potential use of a well calibrated MSM. Given certain baseline characteristics, the model can be run multiple times on the same individual so as to produce a set of possible patient-specific trajectories. Summarizing information from these simulated trajectories can result in useful estimates about disease-related outcomes, and inform clinical decisions for the particular person. In another paper in preparation (Chrysanthopoulou, 2018) we emphasize the need for MSMs that can accurately predict individual-level outcomes, and help with improving individualized-patient care. In that paper we also discuss statistical methods for assessing the predictive accuracy of continuous time, dynamic MSMs, using MILC as a tool for the implementation and comprehensive comparison of those techniques.

We exemplify the functionality of our model by presenting results from two applications. The first example is related to model validation, namely MILC is used to predict lung cancer incidence rates for the US population, as described in Section 2.2.3. Comparison of these predictions with observed lung cancer incidence rates from the SEER database constitutes an external validation of the MILC model in the sense that the microdata for this procedure were different from the sample used for calibrating the model.

Furthermore we used MILC to estimate individual risk of developing lung cancer under different scenarios. To accomplish this we ran the model multiple times (n = 1000) on the same individual (fixed baseline characteristics), and simulated lifetime trajectories. We considered scenarios for smokers (males and females), who were 50 years old at baseline, and started smoking around the age of 20 years. We varied smoking intensity to an average of 10,30, or 50 cigarettes per day, in order to assess the effect of this important risk factor on the predicted lung cancer incidence. We summarized predicted event (lung cancer diagnosis) or censoring (if the person is not diagnosed with lung cancer before death) times with Kaplan-Meier curves.

#### 2.2.5 Implementation in R

One of the main objectives of this research was to create an MSM for lung cancer fully developed in open source software, thus enhancing the transparency of the model. To this end Chrysanthopoulou (2014) built MILC, a new R-package that implements the MILC model in R, and is available on the CRAN repository. This package can be used to simulate individual trajectories, and predict lung-cancer related outcomes following the structure and assumptions of the MILC model.

Table A.1 outlines the algorithm for simulating one individual trajectory (one microsimulation). The computational cost for running in parallel 1,000,000 independent microsimulations (individual trajectories) was approximately 7.5 CPU-hours; with simulations distributed across 16 nodes (8-core Intel Xeon E5540 at 2.53 GHz with 24GB of memory) the total required time is 3.5 minutes.

## 3. Results

Figure 3 shows the results from the validation of the MILC model. The box plots summarize the distributions of the predicted lung cancer incidence rates by age-group for male and female current smokers. All observed rates fall within the resulting range of model-predicted values, thus suggesting an overall good performance of the Bayesian calibrated MILC model with respect to predicting lung cancer incidence trends in the particular US sub-population.

Figure 3

We also used the calibrated MILC model to simulate lifetime trajectories for individuals given certain baseline characteristics (Section 2.2.4). We summarized predictions about the development of lung cancer with Kaplan-Meier curves. Figure 4, Figure 5, and Figure 6 compare predicted survival curves by sex and smoking intensity. According to model’s predictions, males have a greater risk of lung cancer than females. In addition, as expected, the risk of developing lung cancer increases with the average number of cigarettes smoked per day. Both these findings are consistent with current lung cancer research (Doll, 1998; American Cancer Society, 2017; IARC, 1986), thus indicating that the MILC model can provide plausible predictions.

Figure 4

## 4. Discussion

This paper introduces the MILC microsimulation model that describes the natural history of lung cancer, and predicts lung cancer related outcomes. The model simulates individual trajectories given age, sex and smoking, including smoking status (never, former, or current smoker), intensity (average number of cigarettes smoked per day), as well as start and quit smoking ages when relevant. Each simulated trajectory includes information regarding the age of transition to any of four distinct states in the course of lung cancer (that is, local, regional, distant, death), the age, tumor size and stage at diagnosis, and the cause of death (lung cancer, or other) where relevant. The MILC package (Chrysanthopoulou, 2014) implements the MILC model in R, and is available on the CRAN repository.

We outlined the model structure and parameterization, and described the simulation algorithm for predicting individual trajectories. We calibrated and validated the model against lung-cancer incidence rates observed in the US population. We further used the calibrated MILC model to predict lung cancer incidence risk for different subpopulations of smokers classified by sex and smoking intensity. The results showed an overall good fit of the MILC model to observed data, as well as plausible predictions with respect to the effects of sex and smoking on lung cancer incidence.

Figure 5
Figure 6

The CISNET lung cancer group has developed some of the most comprehensive, and broadly used microsimulation models, among the several predictive models for lung cancer in the literature. This group has currently six predictive models for lung cancer, among which four are microsimulation models. The SimSmoke model (Levy, Bauer, & Lee, 2006; Levy & Friend, 2002) and the Yale University model (Holford, Zhang, & Mckay, 1994; Holford, Zhang, Zheng, & McKay, 1996) are not microsimulation models, as they adopt the cohort-simulation representation of the underlying Markov process, rather than a Monte Carlo simulation.

Among the other four CISNET MSMs for lung cancer, the RICE-MDA model by Foy, Deng, Spitz, Gorlova, and Kimmel (2012) predicts lung-cancer mortality without any detail on disease progression, such as tumor growth, age, tumor type and stage at diagnosis, etc. The FHCRC model by Hazelton, Jeon, Meza, and Moolgavkar (2012) only comprises a natural history component, as the module we suggest in this article. However, unlike the MILC, the FHCRC model focuses on the effect of smoking on lung-cancer mortality without providing an explicit definition of the distinct disease states, or information on tumor diagnosis. The MISCAN-lung model by Habbema, van Oortmarssen, Lubbe, and van der Maas (1985), on the other hand, does not monitor tumor size in the simulation procedure. Finally, the key difference between the MILC and the Lung Cancer Policy Model (LCPM) by McMa-hon et al. (2012) lies in the way they simulate the initiation of the local stage. The LCPM employs a logistic regression approach to estimate the risk for the onset of the first malignant cell, rather than the TSCE approach followed in the MILC model.

To our knowledge, no other microsimulation model for lung cancer is readily available to potential end users. The motivation for creating the MILC model, and a major strength, is that it has been fully developed in R. The MILC package makes the source code publicly available thus enhancing the transparency of the model. This is the first MSM for lung cancer built in open source statistical software.

The implementation of MILC in an open source statistical software also facilitates the research on the statistical properties of continuous time MSMs by providing a handy tool for developing, testing and comparing statistical methods applied to this type of models. Two papers in preparation, study statistical methods for calibration, and evaluation of the predictive accuracy of dynamic, continuous time MSMs. These working papers use the MILC model as a tool for assessing the performance of the investigated techniques.

In addition, potential end users, especially people in health services, policy, and practice, could use MILC in its current version, or easily modified (calibration) to represent different (sub-)populations depending on the available data and research questions. It can also serve as a good starting point for building a more comprehensive MSM for lung cancer incorporating further assumptions, adding extra components (involving interventions), and predicting more detailed information about the development and progression of lung tumors in a person’s lifetime.

Despite its usefulness, the MILC model has some limitations. In its current version it only models the natural history of lung cancer in the absence of any screening or treatment components. In addition, this is a streamlined MSM that, when simulating individual lung-cancer trajectories, it only takes into account age, sex, smoking. It is well known that there are several other potential risk factors for lung cancer such as exposure to environmental hazards, second-hand smoking, family history, etc. These are important risk factors that, in certain cases, should be considered for a more accurate and realistic representation of the natural history of lung cancer.

We plan to expand the MILC model so as to describe the natural history of lung cancer in more detail, including screening and treatment components, and incorporating further information from lung cancer research (more complex smoking patterns, additional risk factors, etc.). We envisage to develop MILC into a comprehensive microsimulation model that can constitute an integral part of decision models aimed to inform health policy and clinical practice related to lung cancer.

## Footnotes

### 2.

The program can be expanded to describe more complicated patterns by incorporating more hazard functions.

## Appendix

### A.1 Simulation algorithm

Table A.1 presents the steps followed for the simulation of an individual trajectory using the natural history module of the MILC model.

Table A.1

### A.2 Individual trajectories

Figure A.1 presents four possible individual trajectories predicted by the MILC model. According to these trajectories, only Individual 1 and Individual 2 die from lung cancer, while only the first one is diagnosed before death. Individual 3 and Individual 4 die from some other cause, while at regional and local tumor stage respectively. Estimates of lung cancer related outcomes can be obtained by aggregating multiple simulated trajectories, either for the same individual or for a sample of people.

Figure A.1

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## Article and author information

### Author details

1. #### Stavroula A Chrysanthopoulou

Brown University School of Public Health, United States
##### For correspondence
stavroula_chrysanthopoulou@brown.edu

### Acknowledgements

The author is deeply grateful to Dr. Carolyn M. Rutter and Dr. Constantine A. Gatsonis for the inspiration to specialize in micro-simulation modeling, and the very helpful comments on this manuscript; Dr. Samir S. Soneji for calculation of the CIF survival estimates based on real data; Dr Arlene Ash and Dr Kate Lapane for their useful comments that improved clarity. The reviewers’ comments which have considerably improved the final version of this manuscript. The work presented in this paper constitutes part of the author’s PhD research, conducted with support received from the American College of Radiology Imaging Network (ACRIN) (grant number: U01-CA-79778 from the National Cancer Institute).

### Publication history

1. Version of Record published: December 31, 2017 (version 1)


text:
# Cuts in models of PA and independence results

## Diversity in elementary cuts

Let $M\models PA$ be countable and recursively saturated.

Smorynski proved that here are $2^{\aleph_0}$ theories of pairs $(M,K)$, such that $K$ is not semiregular in $M$.

Kossak proved that there are $2^{\aleph_0}$ theories of pairs $(M,K)$, such that $K$ is strong in $M$.

Problem: How many theories of pairs $(M,K)$ are there, such that $K$ is semiregular, but not regular in $M$.

By recent results of Kaye and Tin Lok Wong, every countable recursively saturated $M$ has $K$ and $L$ as in the question, such that $(M,K)\not\cong (M,L)$.

The problem was stated in [1] related results can be found in [2, 3, 4, 5].

## Stu Smith's question

Question 6.6 of [6]: Let $M\models PA$ be nonstandard and let $I$ be a cut of $M$ definable in $(M,\omega)$. Is $\omega$ the (arithmetic) cofinality of $I$ in $M$?

## "Star" schemata

Answering a question from [7] Kanovei [8] gave a forcing construction to show that for every $n$, every countable recursively saturated $M\models PA$ has an elementary end extension $N$ such that for every $X\subseteq M$ which is coded in $N$, $(M,X)\models I\Sigma_n$ and for some such $X$, $(M,X)\not\models I\Sigma_{n+2}$. Later in [9] $n+2$ was reduced to $n+1$ by another method.

Problem: The assumption that $M$ is recursively saturated is not necessary for $n=1,2$ [7]. Is it necessary for higher $n$?

## References

1. Roman Kossak and James H. Schmerl. On cofinal extensions and elementary interstices. Notre Dame J. Formal Logic 53(3):267--287, 2012. www   bibtex
2. C. Smoryński. A note on initial segment constructions in recursively saturated models of arithmetic. Notre Dame J. Formal Logic 23(4):393--408, 1982. www   MR   bibtex
3. C. Smoryński. Elementary extensions of recursively saturated models of arithmetic. Notre Dame J. Formal Logic 22(3):193--203, 1981. www   MR   bibtex
4. Roman Kossak. A note on satisfaction classes. Notre Dame J. Formal Logic 26(1):1--8, 1985. www   DOI   MR   bibtex
5. Richard Kaye and Tin Lok Wong. Truth in generic cuts. Ann. Pure Appl. Logic 161(8):987--1005, 2010. www   DOI   MR   bibtex
6. Stuart T. Smith. Extendible sets in Peano arithmetic. Trans. Amer. Math. Soc. 316(1):337--367, 1989. www   DOI   MR   bibtex
7. Roman Kossak and Jeffrey B. Paris. Subsets of models of arithmetic. Arch. Math. Logic 32(1):65--73, 1992. www   DOI   MR   bibtex
8. Vladimir Kanovei. On "star" schemata of Kossak and Paris. Logic Colloquium '96 (San Sebastián)12:101--114, Berlin, 1998. MR   bibtex
9. Roman Kossak. A note on a theorem of Kanovei. Arch. Math. Logic 43(4):565--569, 2004. www   DOI   MR   bibtex
Main library


text:
# Show $u=\sup(S)$ if $u+\frac{1}{n}$ is an upper bound and $u-\frac{1}{n}$ is a lower bound, for all $n$

Suppose $$S\subset R$$ is nonempty. Prove $$u=\sup(S)$$ if $$\forall n\in\mathbb{N}$$, $$u-\frac{1}{n}$$ is not an upper bound of $$S$$ and $$u+\frac{1}{n}$$ is an upper bound of $$S$$.

I was hoping someone could check my form of proof for validity:

Since $$u+\frac{1}{n}$$ is an upper bound of $$S$$, $$\sup(S)$$ exists in $$\mathbb{R}$$ and is such that $$\sup(S)\leq u+\frac{1}{n}$$

Similarly, since $$u-\frac{1}{n}$$ is not an upper bound $$\forall n$$, $$\exists s_n\in S$$ such that for every $$n$$ $$u-\frac{1}{n}

But also recall by definition of the supremum, $$s_n=s\leq\sup(S)$$ for all $$s\in S$$. Hence combining the inequalities $$\implies$$ $$u-\frac{1}{n} which further implies $$|\sup(S)-u|<\frac{1}{n}$$

By the Archimedean property, $$\forall \epsilon>0,$$ there exists a sufficiently large $$N$$ such that $$\frac{1}{N}<\epsilon$$. Hence $$\forall \epsilon>0$$ $$|\sup(S)-u|<\frac{1}{N}<\epsilon$$ thus $$|\sup(S)-u|=0\iff u=\sup(S)$$

QED.

Is this okay?

• FYI: Your title doesn't quite match your question. "$u - \tfrac{1}{n}$ is a lower bound" is not the same thing as "$u - \tfrac{1}{n}$ is not an upper bound". – JimmyK4542 Oct 9 at 18:04
• The proof seems too long, but it is correct. – Matt Samuel Oct 9 at 18:09