Unit upper truncated Weibull distribution with extension to 0 and 1 inflated model - Theory and applications.

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the 0-1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval.

Residual-based model diagnosis methods for mixture cure models.

Model diagnosis, an important issue in statistical modeling, has not yet been addressed adequately for cure models. We focus on mixture cure models in this work and propose some residual-based methods to examine the fit of the mixture cure model, particularly the fit of the latency part of the mixture cure model. The new methods extend the classical residual-based methods to the mixture cure model. Numerical work shows that the proposed methods are capable of detecting lack-of-fit of a mixture cure model, particularly in the latency part, such as outliers, improper covariate functional form, or nonproportionality in hazards if the proportional hazards assumption is employed in the latency part. The methods are illustrated with two real data sets that were previously analyzed with mixture cure models.

A Comparison between Accelerated Failure-time and Cox Proportional Hazard Models in Analyzing the Survival of Gastric Cancer Patients.

BACKGROUND: Gastric cancer is the one of the most prevalent reason of cancer-related death in the world. Survival of patients after surgery involves identifying risk factors. There are various models to detect the effect of risk factors on patients' survival. The present study aims at evaluating these models. METHODS: Data from 330 gastric cancer patients diagnosed at the Iran cancer institute during 1995-99 and followed up the end of 2011 were analyzed. The survival status of these patients in 2011 was determined by reopening the files as well as phone calls and the effect of various factors such as demographic, clinical, treatment, and post-surgical on patients' survival was studied. To compare various models of survival, Akaike Information Criterion and Cox-Snell Residuals were used. STATA 11 was used for data analyses. RESULTS: Based on Cox-Snell Residuals and Akaike Information Criterion, the exponential (AIC=969.14) and Gompertz (AIC=970.70) models were more efficient than other accelerated failure-time models. Results of Cox proportional hazard model as well as the analysis of accelerated failure-time models showed that variables such as age (at diagnosis), marital status, relapse, number of supplementary treatments, disease stage, and type of surgery were among factors affecting survival (P<0.05). CONCLUSION: Although most cancer researchers tend to use proportional hazard model, accelerated failure-time models in analogous conditions - as they do not require proportional hazards assumption and consider a parametric statistical distribution for survival time - will be credible alternatives to proportional hazard model.

Comparison of statistics in association tests of genetic markers for survival outcomes.

Computationally efficient statistical tests are needed in association testing of large scale genetic markers for survival outcomes. In this study, we explore several test statistics based on the Cox proportional hazards model for survival data. First, we consider the classical partial likelihood-based Wald and score tests. A revised way to compute the score statistics is explored to improve the computational efficiency. Next, we propose a Cox-Snell residual-based score test, which allows us to handle the controlling variables more conveniently. We also illustrated the incorporation of these three tests into a permutation procedure to adjust for the multiple testing. In addition, we examine a simulation-based approach proposed by Lin (2005) to adjust for multiple testing. We presented the comparison of these four statistics in terms of type I error, power, family-wise error rate, and computational efficiency under various scenarios via extensive simulation.

Multi-state models for colon cancer recurrence and death with a cured fraction.

In cancer clinical trials, patients often experience a recurrence of disease prior to the outcome of interest, overall survival. Additionally, for many cancers, there is a cured fraction of the population who will never experience a recurrence. There is often interest in how different covariates affect the probability of being cured of disease and the time to recurrence, time to death, and time to death after recurrence. We propose a multi-state Markov model with an incorporated cured fraction to jointly model recurrence and death in colon cancer. A Bayesian estimation strategy is used to obtain parameter estimates. The model can be used to assess how individual covariates affect the probability of being cured and each of the transition rates. Checks for the adequacy of the model fit and for the functional forms of covariates are explored. The methods are applied to data from 12 randomized trials in colon cancer, where we show common effects of specific covariates across the trials.