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A Joint Marginal-Conditional For Multivariate Longitudinal Data and A Cure-Rate Model For Left-Truncated and Right- Censored Data /


Multivariate longitudinal data frequently arise in biomedical applications, however their analysis, especially when adjusting for covariates, is often carried out one outcome at a time, or jointly using existing software in an adhoc fashion. A main challenge in the proper analysis of such data is the fact that the different outcomes are measured on different unknown scales. Methodology for handling the scale problem has been previously proposed for cross-sectional data, and here we extend it to the longitudinal setting. We consider modeling the longitudinal data using random effects, while leaving the joint distribution of the multiple outcomes unspecified. We propose an estimating equation together with an EM-type (ES) algorithm. The consistency and the asymptotic distribution of the parameter estimates are established. The method is evaluated using simulations, and applied to a longitudinal nutrition data set from a large dietary intervention trial on breast cancer survivors, the Women's Healthy Eating and Living (WHEL) Study. In some medical studies, a portion of the population that is being sampled may not be susceptible to the event. Cure-rate models are used to analyze the survival regression as well as the proportion "cured" individuals in the population. Analysis with these models has been limited to data featuring right-censoring only, however, for some data, such as pregnancy outcomes, the time to incident should not be measured from entry into the study. In these cases, the time of entry is a truncation time, and we propose a cure-rate model that accounts for this left-truncation. The primary challenge in developing a model for such data is that left- truncation incurs biased estimates of the cure-rate. To correct for this, we incorporate inverse probability weights (IPW) based on the estimated distribution of entry times into an augmented form of the complete data likelihood. From this estimating equations are derived, and we propose parameter estimation through an EM-type (ES) algorithm. The consistency and asymptotic distribution of the parameter estimates are established. The approach is illustrated through simulated data examples as well as pregnancy data from the Organization of Teratology Information Specialists (OTIS) where we consider the outcome spontaneous abortion (SAB)

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