Additive mixed effect model for clustered failure time data

We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and includes a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.     

A goodness-of-fit test for the marginal Cox model for correlated interval-censored failure time data

The marginal Cox model approach is perhaps the most commonly used method in the analysis of correlated failure time data (Cai, 1999; Cai and Prentice, 1995; Lin, 1994; Wei, Lin and Weissfeld, 1989). It assumes that the marginal distributions for the correlated failure times can be described by the Cox model and leaves the dependence structure completely unspecified. This paper discusses the assessment of the marginal Cox model for correlated interval-censored data and a goodness-of-fit test is presented for the problem. The method is applied to a set of correlated interval-censored data arising from an AIDS clinical trial.     

A test of homogeneity of distributions when observations are subject to measurement errors

When the observed data are contaminated with errors, the standard two-sample testing approaches that ignore measurement errors may produce misleading results, including a higher type-I error rate than the nominal level. To tackle this inconsistency, a nonparametric test is proposed for testing equality of two distributions when the observed contaminated data follow the classical additive measurement error model. The proposed test takes into account the presence of errors in the observed data, and the test statistic is defined in terms of the (deconvoluted) characteristic functions of the latent variables. Proposed method is applicable to a wide range of scenarios as no parametric restrictions are imposed either on the distribution of the underlying latent variables or on the distribution of the measurement errors. Asymptotic null distribution of the test statistic is derived, which is given by an integral of a squared Gaussian process with a complicated covariance structure. For data-based calibration of the test, a new nonparametric Bootstrap method is developed under the two-sample measurement error framework and its validity is established. Finite sample performance of the proposed test is investigated through simulation studies, and the results show superior performance of the proposed method than the standard tests that exhibit inconsistent behavior. Finally, the proposed method was applied to real data sets from the National Health and Nutrition Examination Survey. An R package MEtest is available through CRAN.     

Why we should take care of the competing risk bias in survival analysis: A phase II trial on the toxicity profile of radiotherapy for prostate cancer

AimThe aim of the present study is to evaluate and quantify the bias of competing risks in an Italian oncologic cohort comparing results from different statistical analysis methods.BackgroundCompeting risks are very common in randomized clinical trials and observational studies, in particular oncology and radiotherapy ones, and their inappropriate management causes results distortions widely present in clinical scientific articles.Materials and methodsThis is a single-institution phase II trial including 41 patients affected by prostate cancer and undergoing radiotherapy (IMRT-SIB) at the University Hospital of Udine.Different outcomes were considered: late toxicities, relapse, death.Death in the absence of relapse or late toxicity was considered as a competing event.ResultsThe Kaplan Meier method, compared to cumulative incidence function method, overestimated the probability of the event of interest (toxicity and biochemical relapse) and of the competing event (death without toxicity/relapse) by 9.36%. The log-rank test, compared to Gray's test, overestimated the probability of the event of interest by 5.26%.The Hazard Ratio's and cause specific hazard's Cox regression are not directly comparable to subdistribution hazard's Fine and Gray's modified Cox regression; nonetheless, the FG model, the best choice for prognostic studies with competing risks, found significant associations not emerging with Cox regression.ConclusionsThis study confirms that using inappropriate statistical methods produces a 10% overestimation in results, as described in the literature, and highlights the importance of taking into account the competing risks bias.     

A Comparison Between Several Goodness of Fit Tests for Cox's Model

A comparison is made between two approaches to testing goodness of fit of Cox's regression model for survival data. The first approach is based on the inclusion of time dependent covariates, whereas the second one is based on the autocovariance of successive contributions to the derivative of the loglikelihood. It appears that the second test is most appropriate for testing in situations where the structure of the departure from proportional hazards is not known a priori. An approximate expression for the relative efficiency of the two test procedures is presented.     

A stochastic repair—misrepair model for the effects of radiation on cells

The purpose of this paper is to present a stochastic model for effects of radiation on cells. The model includes provisions for lethal effects and for transformation to malignant status. Empirical findings indicate the presence of some repair mechanism in the cells, and a way to incorporate this idea into the model is discussed. Comparisons of the derived survival and transformation probabilities with actual data are favorable. The interpretation of the estimated values leads to questions to be investigated by the experimenters.Supported in part by the Graduate Research Board, University of Maryland     

A semiparametric model for the analysis of recurrent-event panel data

In many longitudinal studies, interest focuses on the occurrence rate of some phenomenon for the subjects in the study. When the phenomenon is nonterminating and possibly recurring, the result is a recurrent-event data set. Examples include epileptic seizures and recurrent cancers. When the recurring event is detectable only by an expensive or invasive examination, only the number of events occurring between follow-up times may be available. This article presents a semiparametric model for such data, based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function. A random subject-specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data. Estimators are determined from quasi-likelihood estimating functions. Because only first- and second-moment assumptions are required for quasi-likelihood, the method is more robust than those based on the specification of a full parametric likelihood. Consistency of the estimators depends only on the assumption of the proportional intensity model. The semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators. As with semiparametric methods in survival analysis, the method provides useful diagnostics for specific parametric models, including a quasi-score statistic for testing specific baseline intensity functions. The techniques are used to analyze cancer recurrences and a pheromone-based mating disruption experiment in moths. A simulation study confirms that, for many practical situations, the estimators possess appropriate small-sample characteristics.