Semi-Parametric Estimation of the Mean Trajectory of a Marker Using Data from a Prevalent Cohort

In natural history studies of disease, the population mean trajectory of markers of disease progression is of interest. This is particularly true for immunological measures in persons infected with the Human Immunodeficiency Virus (HIV). The natural time scale for such studies is time since infection. Most data available for analysis, however, arise from prevalent cohorts, where the time of infection is only known up to an interval. As a result, standard curve fitting algorithms are not immediately applicable. In previous work we proposed two methods to circumvent this difficulty. One of these, a nonparametric smooth of repeated measures of the marker on the expected time since the origin of the disease process, was shown to perform well in situations where the marker is highly variable, but its mean trajectory is not sharply curved. Calculation of the expected time requires a prior estimate of the distribution of infection times in the population from which the sample is drawn. Here we compare this method to its natural extension, a semi-parametric adaptation of the EM algorithm, which uses all the information available from the prior. We present simulations indicating that the EM algorithm outperforms the simpler method in situations where the mean trajectory is sharply curved. The penalty is in computational complexities. Both methods are applied to data from a prevalent cohort of HIV-infected homosexual men, giving estimates of the population mean trajectory of CD4 lymphocyte decline