A semiparametric approach for the nonparametric transformation survival model with multiple covariates

The nonparametric transformation model makes no parametric assumptions on the forms of the transformation function and the error distribution. This model is appealing in its flexibility for modeling censored survival data. Current approaches for estimation of the regression parameters involve maximizing discontinuous objective functions, which are numerically infeasible to implement with multiple covariates. Based on the partial rank (PR) estimator (Khan and Tamer, 2004), we propose a smoothed PR estimator which maximizes a smooth approximation of the PR objective function. The estimator is shown to be asymptotically equivalent to the PR estimator but is much easier to compute when there are multiple covariates. We further propose using the weighted bootstrap, which is more stable than the usual sandwich technique with smoothing parameters, for estimating the standard error. The estimator is evaluated via simulation studies and illustrated with the Veterans Administration lung cancer data set.     

A semiparametric cure model for interval‐censored data

There is a growing interest in the analysis of survival data with a cured proportion particularly in tumor recurrences studies. Biologically, it is reasonable to assume that the recurrence time is mainly affected by the overall health condition of the patient that depends on some covariates such as age, sex, or treatment type received. We propose a semiparametric frailty‐Cox cure model to quantify the overall health condition of the patient by a covariate‐dependent frailty that has a discrete mass at zero to characterize the cured patients, and a positive continuous part to characterize the heterogeneous health conditions among the uncured patients. A multiple imputation estimation method is proposed for the right‐censored case, which is further extended to accommodate interval‐censored data. Simulation studies show that the performance of the proposed method is highly satisfactory. For illustration, the model is fitted to a set of right‐censored melanoma incidence data and a set of interval‐censored breast cosmesis data. Our analysis suggests that patients receiving treatment of radiotherapy with adjuvant chemotherapy have a significantly higher probability of breast retraction, but also a lower hazard rate of breast retraction among those patients who will eventually experience the event with similar health conditions. The interpretation is very different to those based on models without a cure component that the treatment of radiotherapy with adjuvant chemotherapy significantly increases the risk of breast retraction.     

Generalized log-rank tests for partly interval-censored failure time data

In this paper, we consider incomplete survival data: partly interval-censored failure time data where observed data include both exact and interval-censored observations on the survival time of interest. We present a class of generalized log-rank tests for this type of survival data and establish their asymptotic properties. The method is evaluated using simulation studies and illustrated by a set of real data from a diabetes study.     

Strategies for analysing missing item response data with an application to lung cancer

Missing data problems persist in many scientific investigations. Although various strategies for analyzing missing data have been proposed, they are mainly limited to data on continuous measurements. In this paper, we focus on implementing some of the available strategies to analyze item response data. In particular, we investigate the effects of popular missing data methods on various missing data mechanisms. We examine large sample behaviors of estimators in a simulation study that evaluates and compares their performance. We use data from a quality of life study with lung cancer patients to illustrate the utility of these methods.     

A modification of Peto's nonparametric estimation of survival curves for interval-censored data

Peto (1973, Applied Statistics, 22, 86-91) gave a nonparametric generalized maximum-likelihood estimate of the survival function for interval-censored data. His method has a tendency to concentrate probability masses at the endpoints of the intervals, even for the ordinary grouped data, instead of spreading them through the intervals, as one might expect them to be in the underlying distribution. We describe a modification that overcomes this. The new estimate reduces to the standard binomial estimate when applied to grouped data. It also reduces to the Kaplan-Meier estimate when applied to survival data that consist of only exact or right-censored observations. Both estimates are maximum-likelihood estimates but are based on different interpretations of the endpoints of the intervals.     

Multiple imputation methods for multivariate one-sided tests with missing data

Multivariate one-sided hypotheses testing problems arise frequently in practice. Various tests have been developed. In practice, there are often missing values in multivariate data. In this case, standard testing procedures based on complete data may not be applicable or may perform poorly if the missing data are discarded. In this article, we propose several multiple imputation methods for multivariate one-sided testing problem with missing data. Some theoretical results are presented. The proposed methods are evaluated using simulations. A real data example is presented to illustrate the methods.     

Nonparametric quantile inference with competing risks data

A conceptually simple quantile inference procedure is proposedfor cause-specific failure probabilities with competing risksdata. The quantiles are defined using the cumulative incidencefunction, which is intuitively meaningful in the competing–risksset–up. We establish the uniform consistency and weakconvergence of a nonparametric estimator of this quantile function.These results form the theoretical basis for extensions of standardone–sample and two–sample quantile inference forindependently censored data. This includes the constructionof confidence intervals and bands for the quantile function,and two–sample tests. Simulation studies and a real dataexample illustrate the practical utility of the methodology.     

The gamma-frailty Poisson model for the nonparametric estimation of panel count data

In this article, we study nonparametric estimation of the mean function of a counting process with panel observations. We introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo-likelihood estimate with the frailty variable. Three simulated examples are given to show that this estimation procedure, while preserving the robustness and simplicity of the computation, improves the efficiency of the nonparametric maximum pseudo-likelihood estimate studied in Wellner and Zhang (2000, Annals of Statistics 28, 779-814). A real example from a bladder tumor study is used to illustrate the method.     

Multiple imputation for model checking: completed-data plots with missing and latent data

In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset--corresponding to the observed data and imputed unobserved data--using standard procedures for complete-data inference. Here, we extend this approach to model checking by demonstrating the advantages of the use of completed-data model diagnostics on imputed completed datasets. The approach is set in the theoretical framework of Bayesian posterior predictive checks (but, as with missing-data imputation, our methods of missing-data model checking can also be interpreted as "predictive inference" in a non-Bayesian context). We consider the graphical diagnostics within this framework. Advantages of the completed-data approach include: (1) One can often check model fit in terms of quantities that are of key substantive interest in a natural way, which is not always possible using observed data alone. (2) In problems with missing data, checks may be devised that do not require to model the missingness or inclusion mechanism; the latter is useful for the analysis of ignorable but unknown data collection mechanisms, such as are often assumed in the analysis of sample surveys and observational studies. (3) In many problems with latent data, it is possible to check qualitative features of the model (for example, independence of two variables) that can be naturally formalized with the help of the latent data. We illustrate with several applied examples.     

Isotonized CDF estimation from judgment poststratification data with empty strata

In applications that require cost efficiency, sample sizes are typically small so that the problem of empty strata may often occur in judgment poststratification (JPS), an important variant of balanced ranked set sampling. In this article, we consider estimation of population cumulative distribution functions (CDF) from JPS samples with empty strata. In the literature, the standard and restricted CDF estimators (Stokes and Sager, 1988, Journal of the American Statistical Association 83, 374381; Frey and Ozturk, 2011, Annals of the Institute of Statistical Mathematics, to appear) do not perform well when simply ignoring empty strata. In this article, we show that the original isotonized estimator (Ozturk, 2007, Journal of Nonparametric Statistics 19, 131-144) can handle empty strata automatically through two methods, MinMax and MaxMin. However, blindly using them can result in undesirable results in either tail of the CDF. We thoroughly examine MinMax and MaxMin and find interesting results about their behaviors and performance in the presence of empty strata. Motivated by these results, we propose modified isotonized estimators to improve estimation efficiency. Through simulation and empirical studies, we show that our estimators work well in different regions of the CDF, and also improve the overall performance of estimating the whole function.     

A hidden Markov model for continuous longitudinal data with missing responses and dropout

We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three different types of missing pattern: (I) partially missing outcomes at a given time occasion, (II) completely missing outcomes at a given time occasion (intermittent pattern), and (III) dropout before the end of the period of observation (monotone pattern). The missing-at-random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation-maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.