Antiretroviral drugs for HIV patients

Terry Beirn Community Programs for Clinical Research on AIDS (1990 - 1992) conducted a randomized clinical trial on 467 HIV-infected patients with the goal to compare the effect of two antiretroviral drugs: zalcitabine (ddC) and didanosine (ddI). The absolute number of CD4 lymphocyte cells in the peripheral blood is used extensively as a prognostic factor and a surrogate marker for progression of disease and for death in clinical studies of human immunodeficiency virus (HIV) infection. Absolute CD4 counts were recorded at study entry and at as many as four visits (0, 2, 6, 12, 18 months). Patients were followed for clinical disease progression and survival.

The primary goal will be to construct a Cox proportional hazards model to compare the effect of the drugs on survival while appropriately adressing the effect of CD4 count and other covariates. The data can be found in library(JM) under variable aids:

library(JM)
?aids
head(aids, 10)
tail(aids, 12)
summary(aids)

1. Getting familiar with the data

Read the help page ?aids to understand the individual columns of the data.

  • What is the distribution of number of observations per patient?
  • What is the difference between time variables Time, obstime, start and stop? What values do these variables take?
  • Which variables are constant and which are piecewise-constant?
  • Check how balanced the study design is. Is the drug type related to other recorded characteristics?
  • Visualize the changing trend of CD4 count. How does CD4 count change between two consecutive measurements on patient level?

2. Time to death by groups - non-parametric approach

  • Create and plot non-parametric estimates of survival and cumulative hazard functions for time to death. Be careful about the data format.
  • Do the survival functions differ with respect to categorical variables? Support your claim with statistical tests and plots
  • Aggregate somehow (mean, last value, …) the CD4 count variable and categorize patients into several groups according to it. Does it have an effect on survival? Again tests and plots are expected.
  • Is the assumption of proportional hazards between categories reasonable enough?

3. Cox proportional hazards models

  • Choose a reasonable parametrization for CD4 count and compare the following two Cox models for time to death:
    • CD4 assumed constant (by your aggregation on patient level for previous task),
    • piecewise constant CD4 (as in the original aids data). How do the estimates for the coefficient(s) differ? What about the coefficient for drug variable, when added?
  • Take one of the approaches above and enrich the model with other covariates. Construct a final model which contains only relevant covariates. Evaluate and interpret the effect on hazard, focus especially on drug - the primary objective of the study.
  • Plot estimated survival functions for two patients with stable (and reasonable) CD4 count who are given different drug. Compare with estimates from previous task.