Efficient estimation of the distribution of time to composite endpoint when some endpoints are only partially observed.

Two common features of clinical trials, and other longitudinal studies, are (1) a primary interest in composite endpoints, and (2) the problem of subjects withdrawing prematurely from the study. In some settings, withdrawal may only affect observation of some components of the composite endpoint, for example when another component is death, information on which may be available from a national registry. In this paper, we use the theory of augmented inverse probability weighted estimating equations to show how such partial information on the composite endpoint for subjects who withdraw from the study can be incorporated in a principled way into the estimation of the distribution of time to composite endpoint, typically leading to increased efficiency without relying on additional assumptions above those that would be made by standard approaches. We describe our proposed approach theoretically, and demonstrate its properties in a simulation study

Comment: Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data

Comment on ``Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data'' [arXiv:0804.2958]Comment: Published in at http://dx.doi.org/10.1214/07-STS227B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Joint longitudinal and survival-cure models in tumour xenograft experiments

In tumour xenograft experiments, treatment regimens are administered, and the tumour volume of each individual is measured repeatedly over time. Survival data are recorded because of the death of some individuals during the observation period. Also, cure data are observed because of a portion of individuals who are completely cured in the experiments. When modelling these data, certain constraints have to be imposed on the parameters in the models to account for the intrinsic growth of the tumour in the absence of treatment. Also, the likely inherent association of longitudinal and survival‐cure data has to be taken into account in order to obtain unbiased estimators of parameters. In this paper, we propose such models for the joint modelling of longitudinal and survival‐cure data arising in xenograft experiments. Estimators of parameters in the joint models are obtained using a Markov chain Monte Carlo approach. Real data analysis of a xenograft experiment is carried out, and simulation studies are also conducted, showing that the proposed joint modelling approach outperforms the separate modelling methods in the sense of mean squared errors

Semiparametric theory

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified and unrestricted, and can often yield robust estimators that nonetheless behave similarly to those based on parametric likelihood assumptions, e.g., fast rates of convergence to normal limiting distributions. We discuss the basics of semiparametric theory, focusing on influence functions.Comment: arXiv admin note: text overlap with arXiv:1510.0474

Longitudinal quantile regression in presence of informative drop-out through longitudinal-survival joint modeling

We propose a joint model for a time-to-event outcome and a quantile of a continuous response repeatedly measured over time. The quantile and survival processes are associated via shared latent and manifest variables. Our joint model provides a flexible approach to handle informative drop-out in quantile regression. A general Monte Carlo Expectation Maximization strategy based on importance sampling is proposed, which is directly applicable under any distributional assumption for the longitudinal outcome and random effects, and parametric and non-parametric assumptions for the baseline hazard. Model properties are illustrated through a simulation study and an application to an original data set about dilated cardiomyopathies

Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data

We consider semiparametric transition measurement error models for longitudinal data, where one of the covariates is measured with error in transition models, and no distributional assumption is made for the underlying unobserved covariate. An estimating equation approach based on the pseudo conditional score method is proposed. We show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also discuss the issue of efficiency loss. Simulation studies are conducted to examine the finite-sample performance of our estimators. The longitudinal AIDS Costs and Services Utilization Survey data are analyzed for illustration

Application of the Time-Dependent ROC Curves for Prognostic Accuracy with Multiple Biomarkers

The rapid advancement in molecule technology has lead to the discovery of many markers that have potential applications in disease diagnosis and prognosis. In a prospective cohort study, information on a panel of biomarkers as well as the disease status for a patient are routinely collected over time. Such information is useful to predict patients\u27 prognosis and select patients for targeted therapy. In this paper, we develop procedures for constructing a composite test with optimal discrimination power when there are multiple markers available to assist in prediction and characterize the accuracy of the resulting test by extending the time-dependent receiver operating characteristic(ROC) curve methodology (Heagerty, Lumley and Pepe, 2000). We employ a modified logistic regression model to derive optimal linear composite scores such that their corresponding ROC curves are maximized at every false positive rate. We provide theoretical justification for using such a model for prognostic accuracy. The proposed method allows for time-varying marker effects and accommodates censored failure time outcome. When the effect of markers are approximately constant over time, we propose more efficient estimating procedures under such model. We conduct numerical studies to evaluate the performance of the proposed procedures. Our results indicate the proposed methods are both flexible and efficient. We contrast these methods with an application to real data concerning the prognostic accuracies of expression levels of 6 genes

Doubly Robust Inference when Combining Probability and Non-probability Samples with High-dimensional Data

Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a probability sample which provides high-dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded-concave penalties to select important variables for the sampling score of selection into the non-probability sample and the outcome model. We show that the penalized estimating equation approach enjoys the selection consistency property for general probability samples. The major technical hurdle is due to the possible dependence of the sample under the finite population framework. To overcome this challenge, we construct martingales which enable us to apply Bernstein concentration inequality for martingales. In the second step, we focus on a doubly robust estimator of the finite population mean and re-estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first-step selection error and renders the doubly robust estimator root-n consistent if either the sampling probability or the outcome model is correctly specified