In section 1.11 we discussed a study of the effect of ploidy on the sur- vival o

Question

In section 1.11 we discussed a study of the effect of ploidy on the sur- vival of patients with cancer of the tongue. Using the data on aneuploid tumors found in Table 1.6 4.1 (a) Estimate the survival function at one (12 months) and five years (60 months) after transplant. Find the standard errors for your estimates. (b) Estimate the cumulative hazard rate, H(t), at 60 months. Find the standard error of H( ) Estimate S(60) by exp{-H( )} and compare to your estimate in part a (c) Find a 95% linear confidence interval for S(60). (d) Find a 95% log-transformed confidence interval for s(60). (e) Find a 95% arcsine-square root confidence interval for S(60). (f) Using the log transformation find a 95% EP confidence band for the survival function over the range three years to six yearsi.e., 36-72 months) (v) Using the log iransformation íind a 9 )% all Wellner (x)(íidcnoc band for the survival function over the range three years to six years (i.e., 36-72 months). (h) Estimate the mean survival time restricted to 400 months. Also pro- vide a 95% confidence interval for the restricted mean survival time. (i) Estimate the median time to death and find a 95% confidence interval for the median survival time based on a linear confidence interval.

Explanation / Answer

The R program and the output gives answer to all the questions:

It can be seen that for (a), (c), (d), the answer is here:

For (b), the answer lies here:

Since for 60 months, the weeks is 260, the answer is 1.39191272.

For (h), 400 months means at least 1600 weeks, which is meaningless. Also, the data is given in weeks and the time asked in the questions is months which leads to chaos.

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