Auxiliary covariate in additive hazards regression for survival data

We consider the additive hazards regression analysis by utilising auxiliary covariate information to improve the efficiency of the statistical inference when the primary covariate is ascertained only for a randomly selected subsample. We construct a martingale-based estimating equation for the regression parameter and establish the asymptotic consistency and normality of the resultant estimator. Simulation study shows that our proposed method can improve the efficiency compared with the estimator which discards the auxiliary covariate information. A real example is also analysed as an illustration.     

Biomarker classification derived from finite growth mixture modeling with a time-varying covariate: an example with phosphorus and glomerular filtration rate

Finite growth mixture modeling may prove extremely useful for identifying initial pharmacotherapeutic targets for clinical intervention purposes in chronic kidney disease. The primary goal of this research is to demonstrate and describe the process of identifying a longitudinal classification scheme to guide timing and dose of treatment in future randomized clinical trials. After discussing the statistical architecture, we describe the model selection and fit criteria in detail before choosing and selecting our final 4-class solution (BIC = 1612.577, BLRT of p < .001). The first class (highly elevated group) had an average starting point of 3.969?mg/dl of phosphorus at Visit 1, and increased 0.143 every two years until Visit 4. The second, elevated class had an average starting point of 3.460?mg/dl of phosphorus at Visit 1, and increased 0.101 every two years until Visit 4. The normative class had an average starting point of 3.019?mg/dl of phosphorus at Visit 1, and increased 0.099 every two years until Visit 4. Lastly, the low class had an average starting point of 2.525?mg/dl of phosphorus at Visit 1, and increased 0.158 every two years until Visit 4. We hope that this example will spur future applications in biomedical sciences in order to refine therapeutic targets and/or construct long-term risk categories.     

Missing Data Mechanisms for Analysing Longitudinal Data with Incomplete Observations in Both Responses and Covariates

Missing observations in both responses and covariates arise frequently in longitudinal studies. When missing data are missing not at random, inferences under the likelihood framework often require joint modelling of response and covariate processes, as well as missing data processes associated with incompleteness of responses and covariates. Specification of these four joint distributions is a nontrivial issue from the perspectives of both modelling and computation. To get around this problem, we employ pairwise likelihood formulations, which avoid the specification of third or higher order association structures. In this paper, we consider three specific missing data mechanisms which lead to further simplified pairwise likelihood (SPL) formulations. Under these missing data mechanisms, inference methods based on SPL formulations are developed. The resultant estimators are consistent, and enjoy better robustness and computation convenience. The performance is evaluated empirically though simulation studies. Longitudinal data from the National Population Health Survey and Waterloo Smoking Prevention Project are analysed to illustrate the usage of our methods.     

Nonparametric testing for no covariate effects in conditional copulas

In dependence modelling using conditional copulas, one often imposes the working assumption that the covariate influences the conditional copula solely through the marginal distributions. This so-called (pairwise) simplifying assumption is almost standardly made in vine copula constructions. However, in recent literature evidence was provided that such an assumption might not be justified. Among the first issues is thus to test for its appropriateness. In this paper nonparametric tests for the null hypothesis of the simplifying assumption are proposed, and their asymptotic behaviours, under the null hypothesis and under some local alternatives, are established. The tests are fully nonparametric in nature: not requiring choices of copula families nor knowledge of the marginals. In a simulation study, the finite-sample size and power performances of the tests are investigated, and compared with these of the few available tests. A real data application illustrates the use of the tests.     

Proportional Rate Model with Incomplete Covariate and Complete Auxiliary Information

This paper deals with the analysis of proportional rate model for recurrent event data when covariates are subject to missing. The true covariate is measured only on a randomly chosen validation set, whereas auxiliary information is available for all cohort subjects. To further utilize the auxiliary information to improve study efficiency, we propose an estimated estimating equation for the regression parameters. The resulting estimators are shown to be consistent and asymptotically normal. Both graphical and numerical techniques for checking the adequacy of the model are presented. Simulations are conducted to evaluate the finite sample performance of the proposed estimators. Illustration with a real medical study is provided.     

Identification of Confounding versus Dispersing Covariates by Confounding Influence

As is well known, omission of non confounding covariates identified by the treatment assignment may lead to considerable bias for estimated treatment effect even in a simple randomized trial. In this article we identify confounding vs. dispersing covariates by the confounding influence characterizing variance change and bias risk of estimated treatment effect due to constraint on effects of these covariates. Consequently, consistent constraint on effects of identified confounding covariates reduces variance of estimated treatment effect whereas inconsistent constraint on effects of identified dispersing covariates—such as omission of identified dispersing covariates—leads to little bias for estimated treatment effect.     

Estimation of multi-state models with missing covariate values based on observed data likelihood

Abstract

Continuous-time multi-state models are commonly used to study diseases with multiple stages. Potential risk factors associated with the disease are added to the transition intensities of the model as covariates, but missing covariate measurements arise frequently in practice. We propose a likelihood-based method that deals efficiently with a missing covariate in these models. Our simulation study showed that the method performs well for both “missing completely at random” and “missing at random” mechanisms. We also applied our method to a real dataset, the Einstein Aging Study.     

Information borrowing methods for covariate‐adjusted ROC curve

In medical diagnostic testing problems, the covariate adjusted receiver operating characteristic (ROC) curves have been discussed recently for achieving the best separation between disease and control. Due to various restrictions such as cost, the availability of patients, and ethical issues quite frequently only limited information is available. As a result, we are unlikely to have a large enough overall sample size to support reliable direct estimations of ROCs for all the underlying covariates of interest. For example, some genetic factors are less commonly observable compared with others. To get an accurate covariate adjusted ROC estimation, novel statistical methods are needed to effectively utilize the limited information. Therefore, it is desirable to use indirect estimates that borrow strength by employing values of the variables of interest from neighbouring covariates. In this paper we discuss two semiparametric exponential tilting models, where the density functions from different covariate levels share a common baseline density, and the parameters in the exponential tilting component reflect the difference among the covariates. With the proposed models, the estimated covariate adjusted ROC is much smoother and more efficient than the nonparametric counterpart without borrowing information from neighbouring covariates. A simulation study and a real data application are reported. The Canadian Journal of Statistics 40: 569–587; 2012 © 2012 Statistical Society of Canada     

An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data

Several survival regression models have been developed to assess the effects of covariates on failure times. In various settings, including surveys, clinical trials and epidemiological studies, missing data may often occur due to incomplete covariate data. Most existing methods for lifetime data are based on the assumption of missing at random (MAR) covariates. However, in many substantive applications, it is important to assess the sensitivity of key model inferences to the MAR assumption. The index of sensitivity to non-ignorability (ISNI) is a local sensitivity tool to measure the potential sensitivity of key model parameters to small departures from the ignorability assumption, needless of estimating a complicated non-ignorable model. We extend this sensitivity index to evaluate the impact of a covariate that is potentially missing, not at random in survival analysis, using parametric survival models. The approach will be applied to investigate the impact of missing tumor grade on post-surgical mortality outcomes in individuals with pancreas-head cancer in the Surveillance, Epidemiology, and End Results data set. For patients suffering from cancer, tumor grade is an important risk factor. Many individuals in these data with pancreas-head cancer have missing tumor grade information. Our ISNI analysis shows that the magnitude of effect for most covariates (with significant effect on the survival time distribution), specifically surgery and tumor grade as some important risk factors in cancer studies, highly depends on the missing mechanism assumption of the tumor grade. Also a simulation study is conducted to evaluate the performance of the proposed index in detecting sensitivity of key model parameters.     

Two‐stage model selection procedures in partially linear regression

The authors propose a two‐stage estimation procedure for the partially linear model Y = f_o(T) + X'β_o + ψ. They show how to estimate consistently the location of the nonzero components of β_o. Their approach turns out to be compatible with minimax adaptive estimation of f_o over Besov balls in the case of penalized least squares. Their proofs are based on a new type of oracle inequality.