A comparison of smoothing techniques for CD4 data measured with error in a time-dependent Cox proportional hazards model

The use of CD4+ T-lymphocyte counts as a covariate presents some unique challenges in survivorship analyses due to the variability of this marker. If one does not account for the measurement error component of this variability in some manner, the estimate of the relative risk parameter in a time-dependent Cox model is biased towards zero, and coverage levels of confidence intervals may be seriously incorrect. We use a two-stage approach to reduce the variability in the observed CD4 counts in order to obtain a more accurate estimate of the relative risk parameter and more valid summary statistics. In the first stage, population based smoothing methods derived from a random-effects model plus a stochastic process or individual based smoothing methods are used to replace the observed longitudinal CD4 counts with less variable imputes at each failure time. In the second stage, we use the imputes in a time-dependent Cox model to estimate the risk parameter and its associated summary statistics. We compare the smoothing methods in simulation studies and find that the use of these smoothing methods results in a substantial reduction in bias for the true risk parameter estimate, better efficiency, and more accurate coverage rates in confidence intervals. We apply our two-stage smoothing methods to the marker CD4 in the ACTG-019 clinical trial part B.