Matching estimators and optimal bandwidth choice

Optimal bandwidth choice for matching estimators and their finite sample properties are examined. An approximation to their MSE is derived, as a basis for a plug-in bandwidth selector. In small samples, this approximation is not very accurate, though. Alternatively, conventional cross-validation bandwidth selection is considered and performs rather well in simulation studies: Compared to standard pair-matching, kernel and ridge matching achieve reductions in MSE of about 25 to 40%. Local linear matching and weighting perform poorly. Furthermore, the scope for developing better bandwidth selectors seems to be limited for ridge matching, but non-negligible for kernel and local linear matching.     

Confirmatory analysis for phase III population pharmacokinetics

Population pharmacokinetics (POPPK) has many important uses at various stages of drug development and approval. At the phase III stage, one of the major uses of POPPK is to identify covariate influences on human pharmacokinetics, which is important for potential dose adjustment and drug labeling. One common analysis approach is nonlinear mixed‐effect modeling, which typically involves time‐consuming extensive search for best fits among a large number of possible models. We propose that the analysis goal can be better achieved with a more standard confirmatory statistical analysis approach, which uses a prespecified primary analysis and additional sensitivity analyses. We illustrate this approach using a phase III study data set and compare the result with that calculated using the common exploratory approach. We argue that the confirmatory approach not only substantially reduces analysis time but also yields more accurate and interpretable results. Some aspects of this confirmatory approach may also be extended to data analysis in earlier stages of clinical drug development, i.e. phase II and phase I. Copyright © 2009 John Wiley & Sons, Ltd.     

Partial orders with respect to continuous covariates and tests for the proportional hazards model

Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against ordered alternatives like monotone hazard ratio and monotone ratio of cumulative hazards. Here we propose a natural extension of these partial orders to the case of continuous and potentially time varying covariates, and develop tests for the proportional hazards assumption against such ordered alternatives. The work is motivated by applications in biomedicine and economics where covariate effects often decay over lifetime. The proposed tests do not make restrictive assumptions on the underlying regression model, and are applicable in the presence of time varying covariates, multiple covariates and frailty. Small sample performance and an application to real data highlight the use of the framework and methodology to identify and model the nature of departures from proportionality.     

Inference on Survival Data with Covariate Measurement Error – An Imputation-based Approach

Abstract.  We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerate distribution. Simulations indicate high efficiency and robustness. We consider the special case where error-prone replicates are available on the unobserved true covariates. As expected, increasing the number of replicates for the unobserved covariates increases efficiency and reduces bias. We illustrate the practical utility of the proposed method with an Eastern Cooperative Oncology Group clinical trial where a genetic marker, c- myc expression level, is subject to measurement error.     

Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models

This article develops a local partial likelihood technique to estimate the time-dependent coefficients in Cox's regression model. The basic idea is a simple extension of the local linear fitting technique used in the scatterplot smoothing. The coefficients are estimated locally based on the partial likelihood in a window around each time point. Multiple time-dependent covariates are incorporated in the local partial likelihood procedure. The procedure is useful as a diagnostic tool and can be used in uncovering time-dependencies or departure from the proportional hazards model. The programming involved in the local partial likelihood estimation is relatively simple and it can be modified with few efforts from the existing programs for the proportional hazards model. The asymptotic properties of the resulting estimator are established and compared with those from the local constant fitting. A consistent estimator of the asymptotic variance is also proposed. The approach is illustrated by a real data set from the study of gastric cancer patients and a simulation study is also presented.     

A Semiparametric Model for Recapture Experiments

Abstract. A two-step procedure based on the conditional likelihood is proposed to estimate the population size of a closed population using a semiparametric model for recapture studies. An asymptotic variance estimate and numerical results are presented. The method is applied to a bird banding dataset in Hong Kong.     

Bayesian analysis of covariance under inverse Gaussian model

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable from the Bayesian point of view. We develop a fully Bayesian model for ANCOVA based on the conjugate prior distributions for parameters contained in the model. The Bayes estimator of parameters, ANCOVA model and adjusted effects for both treatments and covariates along with predictive distribution of future observations are developed. We also provide the essentials for comparing adjusted treatments effects and adjusted factor effects. A simulation study and a real world application are also performed to illustrate and evaluate the proposed Bayesian model.     

Gompertz model with time-dependent covariate in the presence of interval-, right- and left-censored data

In this paper, the Gompertz model is extended to incorporate time-dependent covariates in the presence of interval-, right-, left-censored and uncensored data. Then, its performance at different sample sizes, study periods and attendance probabilities are studied. Following that, the model is compared to a fixed covariate model. Finally, two confidence interval estimation methods, Wald and likelihood ratio (LR), are explored and conclusions are drawn based on the results of the coverage probability study. The results indicate that bias, standard error and root mean square error values of the parameter estimates decrease with the increase in study period, attendance probability and sample size. Also, LR was found to work slightly better than the Wald for parameters of the model.     

Estimated Generalized Estimating Equation for Correlated Failure Time Data with Auxiliary Covariates

In this article, we study a marginal hazard model with common baseline hazard for correlated failure time data. We assume that the true covariate is measured precisely in a subset of the whole study cohort, whereas an auxiliary information for the true covariate is available for the whole cohort. We first estimate the relative risk function empirically. Then we obtain the estimator for the regression parameter by replacing the relative risk function with its estimator in a generalized estimating equation (GEE) proposed by Cai (1992 Cai , J. ( 1992 ). Generalized estimation equations for censored multivariate failure time data. Ph.D. thesis, University of Washington, Seattle, Washington . [Google Scholar]). A key feature of this method is that it is nonparametric with respect to the association between the missing covariate and the observed auxiliary covariate. The proposed estimator is shown to be consistent and asymptotically normal. Furthermore, we present a corrected Breslow-type estimator for the cumulative hazard function. Simulation studies are conducted to evaluate the proposed method.