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Finding Probability from a Table

The question is based on the following information:

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No. of Patients Alive
on each anniversary
Year of Treatment No. of Patients 1st 2nd 3rd
Treated

1991 75 60 56 48
1992 63 55 31
1993 42 37

Total 180 152 87 48
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180 patients were treated for disease X from 1991 to 1993, and their progress was followed to 1994. The treatment results are given in the table. No patients were lost to follow-up.

QUESTION: What is the probability of surviving for 3 years?
ANSWER: 54.7%

An important assumption in this type of analysis is that no change has occurred in the effectiveness of the treatment during the period of the study.

The review chapter I got this question from lacks a detailed rationale for how they arrived at the probability of 54.7%. Please explain how to find the answer. Thank you!

Solution Preview

This is complicated because you only have data spanning all three years for patients treated in 1991, but you also have to consider patients treated in 1992 and 1993. Here's how the book came up with the probability of 54.7%:

Looking at all the patients, there is an ...

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