Robust and efficient methods for analyzing complex longitudinal and survival data

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In clinical studies, we often encounter multivariate data featuring many complex issues including frailties in survival outcomes, correlations in longitudinal outcomes, left-censoring in biomarkers, measurement errors in covariates, and outliers in response variables. Joint modeling of longitudinal and survival data is often used when the focus is on the survival times of individuals and one wishes to study the effect of endogenous time-dependent covariates or biomarkers on the survival times. Often values of a clinical covariate or biomarker are unobserved but known to be below a threshold called the limit of detection (LOD). Naive approaches that ignore the problem of left-censoring due to the LOD, such as replacing the undetected value by the LOD or by half of the LOD, typically lead to biased estimators of the covariate effects. For a valid statistical inference, it is important to use proper statistical tools that adjust for the left-censored covariates when fitting the joint model. Also, clinical and survey data often contain outliers that can have profound influence on the ordinary maximum likelihood estimation or hypothesis testing. Robust methods are needed to bound the influence of outliers when estimating the model parameters. The aim of this proposal is to develop efficient robust methods that can simultaneously bound the influence of outliers and adjust for the LOD when jointly analyzing longitudinal and time-to-event data. Also, parameter orderings or constraints may naturally occur in practice, and in such cases, the efficiency of a statistical method can be improved by incorporating the parameter constraints into the estimation and hypothesis testing. This research will consider inference with joint models under linear inequality constraints. In some situations, covariates are observed with measurement error, where an ordinary estimator obtained by regressing on the observed covariates is asymptotically biased. This research will introduce a bias-adjusted estimator by correcting for both the LOD and measurement error in covariates in the framework of the joint model for analyzing multivariate outcomes. This research will also develop and explore flexible methods that can address uncertainties in the latent random effects distributions and can provide robust estimates under a misspecified latent process. The aforementioned developments will enable researchers in health sciences to engage in reliable estimation and assessment of their hypothesized models for analyzing data from surveys and clinical trials by addressing many practical issues including left-censoring in covariates, misspecification of latent processes, nonignorable missing responses, measurement errors in biomarkers and outliers in response variables, and hence will greatly benefit clinical practitioners for accurately predicting health outcomes on the basis of available risk factors.