Joan (left) and Jackie Collins  09/27/2015 AT 12:15 PM EDT  doesn't think she'll "ever recover" from the sadness of losing her "baby sister," author  last week after a secret six-and-a-half year battle.  In an emotional new essay for the  , Joan wrote that she's focused on celebrating the way the best-selling British novelist lived her life in the wake of her death.  "In her inimitable way she had more concern for others than for herself to the end, and anyone who knew Jackie well will tell you how courageous and selfless she was," Joan, 82, wrote. "This was one of the reasons for her great success in both her personal and professional life, and why she was loved and admired by so many."  Joan Collins and Jackie Collins  Kevin Mazur / VF15 / WireImage  Jackie was diagnosed with stage 4 breast cancer in 2009, and chose to mainly keep her illness to herself – she only  her health problems to Joan just two weeks before her passing.  The novelist told PEOPLE in her  , just days before her death, that she chose to keep the diagnosis a secret because she felt "sympathy can weaken you."  "Jackie really enjoyed her life so much and lived it to the hilt, and when we were together, even if we hadnât seen each other for a few months, we were thick as thieves," Joan wrote in her  Joan called her sibling "strong, independent, loyal, caring," among other things, and said "she wasn't just a star – to me she was an entire galaxy."  "As Jackie said in her last interview, she did things her way," she wrote.  to PEOPLE following her sister's death and said that she was "completely devastated" to lose her "best friend."  "I admire how she handled this," she told PEOPLE. "She was a wonderful, brave and a beautiful person and I love her."
Joan Collins shared sweet memories and anecdotes about life with her late sister Jackie Collins in a new essay