BSTA 6652 Survival Analysis Winter, 2016

Problem Set 6

Background

The data set, ps5.dat, is a subset of the data from The Worcester Heart Attack Study (see Problem Set 3) and is available on the class webpage. The table below describes the variables included in ps5.dat along with their codes and values.

Variable / Description / Codes/Values
id / Patient identification code / 1–481
time / Total length of follow-up / Days between date of last follow-up and hospital admission date
stat / Status of last follow-up / 0 = alive, 1 = dead
age / Age at hospital admission / Years
gender / Gender / 0 = male, 1 = female
cpk / Peak cardiac enzymes / International units (IU/100)
chf / Left heart failure complications / 0 = no, 1 = yes
ord / MI order / 0 = first, 1 = recurrent

Problems

(a)  Fit the Cox proportional hazards model containing age, gender, cpk, chf, and ord using the Breslow, Efron and exact methods for handling tied survival times. Show the output of parameter estimates. Compare the estimates of the coefficients and standard errors from the 3 methods. Which method would you recommend and why?

(b)  Using the method you pick and the (univariate) Wald test, which variables appear not to contribute to the model fit at the 5% significance level? Remove all such covariates and fit the reduced model. Also test for the adequacy of the reduced model (compared to the full model) using the likelihood ratio test.

(c)  Conduct Backwards Model Selection. Is the final model the same as the reduced model in part (b)? Test for the adequacy of the final model using the likelihood ratio test.

(d)  Fit your final model. What is the fitted model? Please do not print out the baseline survival estimates for all time points and draw the baseline cumulative hazard function instead. Interpret the effect of ALL five covariates. For insignificant covariates, you can just state the covariate is not significant.

(e)  Consider two patients both at age of 62, having cpk of 485, no recurrence so far but one has left heart failure complications and the other has no such complications. Draw their predicted survival curves and comment on the differences.