About 10% of lung cancer patients are cured of the disease, i.e., the survive 5

Question

About 10% of lung cancer patients are cured of the disease, i.e., the survive 5 years after diagnosis with no evidence that the cancer has returned. Only 14% of lung cancer patients survive 5 years after diagnosis. Assume that the fraction of incurable lung cancer patients that survives a time t after diagnosis is given by exp(-kt). Find an expression for the fraction S(t) of lung cancer patients that survive a time t after being diagnosed with the disease. Be sure to determine the values of all of the contants in your answer. What fraction of lung cancer patients survives two years with the disease?

Explanation / Answer

Based on the given data,

4)

Incurable fraction that survives after 5 years = 0.14-0.10=0.04=4%

The equation for calculation is:

s(t)=0.04=e^(-k*5)

k=0.644/yr

s(t)=e^(-0.644t)

Fraction surviving after 2 years = e^(-0.644*2)=0.2757=27.58%

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