Recent methodologic developments in the analysis of longitudinal data have typically addressed one of two aspects: (i) the modelling of repeated measurements of a covariate as a function of time or other covariates, or (ii) the modelling of the effect of a covariate on disease risk. In this paper, we address both of these issues in a single analysis by modelling a continuous covariate over time and simultaneously relating the covariate to disease risk. We use the Markov chain Monte Carlo technique of Gibbs sampling to estimate the joint posterior distribution of the unknown parameters of the model. Simulation studies showed that jointly modelling survival and covariate data reduced bias in parameter estimates due to covariate measurement error and informative censoring. We illustrate the methodology by application to a data set that consists of repeated measurements of the immunologic marker CD4 and times of diagnosis of AIDS for a cohort of anti-HIV-1 positive recipients of anti-HIV-1 positive blood transfusions. We assume a linear random effects model with subject-specific intercepts and slopes and normal errors for the true log and square root CD4 counts, and a proportional hazards model for AIDS-free survival time expressed as a function of current true CD4 value. On the square root scale, the joint approach yielded a mean slope for CD4 that was 7 per cent steeper and a log relative risk of AIDS that was 35 per cent larger than those obtained by analysis of the component sub-models separately.

We develop an approach, based on multiple imputation, to using auxiliary variables to recover information from censored observations in survival analysis. We apply the approach to data from an AIDS clinical trial comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable. To facilitate imputation, a joint model is developed for the data, which includes a hierarchical change-point model for CD4 counts and a time-dependent proportional hazards model for the time to AIDS. Markov chain Monte Carlo methods are used to multiply impute event times for censored cases. The augmented data are then analyzed and the results combined using standard multiple-imputation techniques. A comparison of our multiple-imputation approach to simply analyzing the observed data indicates that multiple imputation leads to a small change in the estimated effect of ZDV and smaller estimated standard errors. A sensitivity analysis suggests that the qualitative findings are reproducible under a variety of imputation models. A simulation study indicates that improved efficiency over standard analyses and partial corrections for dependent censoring can result. An issue that arises with our approach, however, is whether the analysis of primary interest and the imputation model are compatible.

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We compare approaches for analysis of gene-environment (G x E) interaction, using segregation and joint segregation and linkage analyses of a quantitative trait. Analyses of triglyceride levels in a single large pedigree demonstrate the two methods and show evidence for a significant interaction (P=.015 when segregation analysis is used; P=.006 when joint analysis is used) between a codominant major gene and body-mass index. Genotype-specific correlation coefficients, between triglyceride levels and body-mass index, estimated from the joint model are rAA=.72, rAa=.49, and raa=. 20. Several simulation studies indicate that joint segregation and linkage analysis leads to less-biased and more-efficient estimates of a G x E-interaction effect, compared with segregation analysis alone. Depending on the heterozygosity of the marker locus and its proximity to the trait locus, we found joint analysis to be as much as 70% more efficient than segregation analysis, for estimation of a G x E-interaction effect. Over a variety of parameter combinations, joint analysis also led to moderate (5%-10%) increases in power to detect the interaction. On the basis of these results, we suggest the use of combined segregation and linkage analysis for improved estimation of G x E-interaction effects when the underlying trait gene is unmeasured.