Study of the Left Censored Data from the Gumbel Type II Distribution under a Bayesian Approach

Based on left type II censored samples from a Gumbel type II distribution, the Bayes estimators and corresponding risks of the unknown parameter were obtained under different asymmetric loss functions, assuming different informative and non-informative priors. Elicitation of hyper-parameters through prior predictive approach has also been discussed. The expressions for the credible intervals and posterior predictive distributions have been derived. Comparisons of these estimators are made through simulation study using numerical and graphical methods

An investigation into the two-stage meta-analytic copula modelling approach for evaluating time-to-event surrogate endpoints which comprise of one or more events of interest

Clinical trials of experimental treatments must be designed with primary endpoints that directly measure clinical benefit for patients. In many disease areas, the recognised gold standard primary endpoint can take many years to mature, leading to challenges in the conduct and quality of clinical studies. There is increasing interest in using shorter-term surrogate endpoints as substitutes for costly long-term clinical trial endpoints; such surrogates need to be selected according to biological plausibility, as well as the ability to reliably predict the unobserved treatment effect on the long-term endpoint. A number of statistical methods to evaluate this prediction have been proposed; this paper uses a simulation study to explore one such method in the context of time-to-event surrogates for a time-to-event true endpoint. This two-stage meta-analytic copula method has been extensively studied for time-to-event surrogate endpoints with one event of interest, but thus far has not been explored for the assessment of surrogates which have multiple events of interest, such as those incorporating information directly from the true clinical endpoint. We assess the sensitivity of the method to various factors including strength of association between endpoints, the quantity of data available and the effect of censoring. In particular, we consider scenarios where there exist very little data on which to assess surrogacy. Results show that the two-stage meta-analytic copula method performs well under certain circumstances and could be considered useful in practice, but demonstrates limitations that may prevent universal use

Testing for sufficient follow-up in censored survival data by using extremes

In survival analysis, it often happens that some individuals, referred to as cured individuals, never experience the event of interest. When analyzing time-to-event data with a cure fraction, it is crucial to check the assumption of `sufficient follow-up', which means that the right extreme of the censoring time distribution is larger than that of the survival time distribution for the non-cured individuals. However, the available methods to test this assumption are limited in the literature. In this article, we study the problem of testing whether follow-up is sufficient for light-tailed distributions and develop a simple novel test. The proposed test statistic compares an estimator of the non-cure proportion under sufficient follow-up to one without the assumption of sufficient follow-up. A bootstrap procedure is employed to approximate the critical values of the test. We also carry out extensive simulations to evaluate the finite sample performance of the test and illustrate the practical use with applications to leukemia and breast cancer datasets.Comment: 16 pages, 2 figures and 4 tables are adde

Parameter estimations and copula methods for burr type III and type XII distributions

Continuous Burr distributions have gained popularity recently due to their potential use in practical situations. In particular, Burr Type III and Type XII distributions are suitable to describe lifetime data since these distributions, not only have flexible shape but also controllable scale and location parameters which are needed in characterizing lifetime distributions. In this study, 2-parameter and 3-parameter Burr Type III and XII distributions are employed to fit a set of simulated lifetime data. These lifetime data are assumed to be either complete, that is uncensored, or censored at varying levels of censoring, and are simulated from the specified Burr distributions using their inverse cumulative distribution functions. The distribution parameters are then estimated by using the classical maximum likelihood estimation (MLE) and expectation-maximization (EM) algorithm approaches. The performance of parameter estimates are then compared in terms of their accuracy and efficiency by comparing its bias and mean square errors. The study finds that as the censoring level varies, the EM estimates perform better than the MLE estimates for 2-parameter and 3-parameter Burr Type III and XII distributions with complete and censored lifetime data at certain censoring levels. In addition, the study also investigates a number of copula methods to join specific Burr Type III and XII distributions. The result reveals that Ali-Mikhail-Haq, Clayton and Gumbel methods fit well with Burr distributions for uncensored lifetime data since the values of copula lie within (0,1) interval