Using trajectories from a bivariate growth curve as predictors in a Cox regression model

Abstract

An important research objective in most psychiatric clinical trials of maintenance treatment is to find predictors of recurrence of illness. In those trials, patients are first admitted into an open treatment period also called acute treatment. If they respond to the treatment and are considered to have stable remission from the illness, they enter the second phase of the trial where they are randomized into different arms of the 'maintenance treatments'. Often, more than one response variable is measured longitudinally in the acute treatment phase to monitor treatment responses. Trajectories of these response measures are believed to have predictive ability for recurrences in the maintenance phase of the trial. By using a bivariate growth curve from two such longitudinal measures, we developed a method to use the estimated trajectories of each subject in a Cox regression model to predict recurrence in the maintenance phase. To adjust for the parameter estimation errors, we applied a full likelihood approach based on the conditional expectations of the predictors. Simulation studies indicate that the estimation error corrected estimators for the Cox model parameters are less biased when compared to the naive regression estimators without accounting for these errors. The uniqueness of this method lies in estimating trajectories from bivariate unequally spaced longitudinal response measures. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. Visual Fortran 90 programs were developed to implement the algorithm.