ERASMUS

Survival Analysis

Exercises for Thursday (Day 4)

Checking Proportional Hazards:

1. In this exercise we will revisit the CCG803 data from Exercises #1 and #2, and evaluate whether the proportional hazards assumption appears satisfied for the predictors.

Recall that in Exercise #2 we used Cox regression to investigate the relationship between treatment (with dactinomycin) and disease relapse. In our regression model we controlled for Institution and white blood cell count, WBC. Using these data, evaluate whether treatment (e.g. Rx) and WBC appear to satisfy the proportional hazards assumption after controlling for both the other covariate, and institution. Specifically:

(a) Using Schoenfeld residuals, and scaled Schoenfeld residuals conduct appropriate tests to evaluate whether the PH assumption appears adequate for your Cox regression model.

(b) Plot scaled Schoenfeld residuals for Rx and WBC and comment on the patterns that are suggested.

Time-dependent Covariates:

2. In the lecture notes on pages 355—378 we fit a Cox regression with prison and newdose as the predictors of interest, while stratifying on clinic. However, Caplehorn & Bell also wanted to make some simple clinic comparisons using Cox regression so restricted follow-up to the first 450 days since the PH assumption appeared satisfied for this duration. In the analysis below, we will recreate (approximately) their analysis, and then show the potential for a complete follow-up time analysis that retains simple regression comparisons of the two clinics, but where the comparison between clinics depends on the follow-up time.

The data and documentation can be found in the Lecture Material section of the web page.

2(a) First, since the two clinics were known to have different retention plans,

we can apriori decide to conduct analysis restricted to the first year of follow-up only (we don't need testing to choose this). Conduct a Cox regression analysis that restricts follow-up to the first 365 days. In order to do this a new time variable will need to be created, time365 that is the minimum of the observed follow-up time and 365. Second, a new censoring indicator will need to be created that censors all follow-up beyond 365 days (so what values of the full follow-up censoring variable will need to be recoded?) Given this new time and censoring variable fit a Cox model and interpret each coefficient.

2(b) Now fit a Cox model restricting attention to follow-up time>365. In order to do this one can simple fit a Cox model with an ``if'' statement regarding time (note this would not work for part (a) -- why?). Interpret the resulting coefficient estimates. Given this time period fit a Cox model and interpret each coefficient

2(optional) Next use STATA's tvc() option for all three predictors simultaneously allowing them to have a hazard ratio that depends on time -- specifically choose

texp( \_t>365 ). Interpret the resulting Cox model estimates. Compare your estimates here to those obtained in part (a). Based on your analysis decide which coefficients appear to vary with time?

2(optional) Finally, fit a Cox model with only clinic as the tvc() (and using the 365 day step function for texp. Does the PH assumption appear adequate for variables in this model? Specifically, using stphtest is there evidence for departure for any of prison, newdose, and clinic? Notice that although clinic is allowed to have a non-proportional hazards relationship over all time, within each time interval (before and after 365 days) it is assumed to have a constant hazard ratio. What do you conclude about the adequacy of this model?

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