ABSTRACT
We present in this chapter an alternative method for estimating the conditional distributions, the Rank-Tracking Probabilities (RTP) and the RankTracking Probability Ratios (RTPR). This method is motivated by the recognition that the estimation method of Chapter 13 has two limitations in practice. First, when constructing the raw estimators at any two time points s1 < s2, we need a sufficiently large number of subjects with observations at time points around (s1, s2). Second, the smoothing step requires bivariate smoothing, which again requires a large sample. These limitations are caused by the fact that the time-varying transformation models (14.25) do not take into account the dependence structure between any two time points s1 < s2. To alleviate these drawbacks, the alternative approach here relies on estimating the conditional distributions using two simple steps: (a) predicting the subjects’ trajectory curves from the nonparametric mixed-effects models of Chapter 11; (b) constructing the conditional distribution estimators based on the predicted outcome trajectories. The trajectory prediction step in (a) is crucial for the accuracy of the estimators in (b). Unlike the modeling approaches of Chapters 13 and 14, the trajectory prediction gives a natural link between the conditional-mean based mixed-effects models and the conditional-distribution based estimation methods. The estimation method of this chapter has the advantage of evaluating the conditional means, conditional distributions and tracking abilities of an outcome variable under a unified regression framework.
15.1 Data Structure and Models
