If you liked
Sekai no Chuushin de, Ai wo Sakebu
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...then you might like
Dear Friends: Rina & Maki
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Both deal with how the main character copes in a situation related to Cancer. SiL concentrates more on how a person copes after their loved one has been diagnosed with the disease, whilst DF concentrates how the "patient" deals with their diagnosis (learning some life lessons along the way)