Non-crossing weighted kernel quantile regression with right censored data.

Regarding survival data analysis in regression modeling, multiple conditional quantiles are useful summary statistics to assess covariate effects on survival times. In this study, we consider an estimation problem of multiple nonlinear quantile functions with right censored survival data. To account for censoring in estimating a nonlinear quantile function, weighted kernel quantile regression (WKQR) has been developed by using the kernel trick and inverse-censoring-probability weights. However, the individually estimated quantile functions based on the WKQR often cross each other and consequently violate the basic properties of quantiles. To avoid this problem of quantile crossing, we propose the non-crossing weighted kernel quantile regression (NWKQR), which estimates multiple nonlinear conditional quantile functions simultaneously by enforcing the non-crossing constraints on kernel coefficients. The numerical results are presented to demonstrate the competitive performance of the proposed NWKQR over the WKQR.

Median regression model with interval censored data.

Quantile regression methods have been used to estimate upper and lower quantile reference curves as the function of several covariates. Especially, in survival analysis, median regression models to the right-censored data are suggested with several assumptions. In this article, we consider a median regression model for interval-censored data and construct an estimating equation based on weights derived from interval-censored data. In a simulation study, the performances of the proposed method are evaluated for both symmetric and right-skewed distributed failure times. A well-known breast cancer data are analyzed to illustrate the proposed method.

Analysis of recurrent event data with incomplete observation gaps.

In analysis of recurrent event data, recurrent events are not completely experienced when the terminating event occurs before the end of a study. To make valid inference of recurrent events, several methods have been suggested for accommodating the terminating event (Statist. Med. 1997; 16:911-924; Biometrics 2000; 56:554-562). In this paper, our interest is to consider a particular situation, where intermittent dropouts result in observation gaps during which no recurrent events are observed. In this situation, risk status varies over time and the usual definition of risk variable is not applicable. In particular, we consider the case when information on the observation gap is incomplete, that is, the starting time of intermittent dropout is known but the terminating time is not available. This incomplete information is modeled in terms of an interval-censored mechanism. Our proposed method is applied to the study of the Young Traffic Offenders Program on conviction rates, wherein a certain proportion of subjects experienced suspensions with intermittent dropouts during the study.

Cure rate model with interval censored data.

In cancer trials, a significant fraction of patients can be cured, that is, the disease is completely eliminated, so that it never recurs. In general, treatments are developed to both increase the patients' chances of being cured and prolong the survival time among non-cured patients. A cure rate model represents a combination of cure fraction and survival model, and can be applied to many clinical studies over several types of cancer. In this article, the cure rate model is considered in the interval censored data composed of two time points, which include the event time of interest. Interval censored data commonly occur in the studies of diseases that often progress without symptoms, requiring clinical evaluation for detection (Encyclopedia of Biostatistics. Wiley: New York, 1998; 2090-2095). In our study, an approximate likelihood approach suggested by Goetghebeur and Ryan (Biometrics 2000; 56:1139-1144) is used to derive the likelihood in interval censored data. In addition, a frailty model is introduced to characterize the association between the cure fraction and survival model. In particular, the positive association between the cure fraction and the survival time is incorporated by imposing a common normal frailty effect. The EM algorithm is used to estimate parameters and a multiple imputation based on the profile likelihood is adopted for variance estimation. The approach is applied to the smoking cessation study in which the event of interest is a smoking relapse and several covariates including an intensive care treatment are evaluated to be effective for both the occurrence of relapse and the non-smoking duration.

Bootstrap tests for overdispersion in a zero-inflated Poisson regression model.

Ridout, Hinde, and Demétrio (2001, Biometrics 57, 219-223) derived a score test for testing a zero-inflated Poisson (ZIP) regression model against zero-inflated negative binomial (ZINB) alternatives. They mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases. To remedy this problem, a parametric bootstrap method is proposed. It is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis.