Journal of Biometrics & Biostatistics

With the primary objective of developing fundamental probability models that can be used for drawing rigorous statistical inference from microarray data, we have presented in a previous publication, theoretical results for characterizing the entire microarray data set as an ensemble. Specifically, we established, from first principles, that under reasonable assumptions, the distribution of microarray intensities follows the gamma model, and consequently that the underlying theoretical distribution for the entire set of fractional intensities is a mixture of beta densities. This probabilistic framework was then used to develop a rigorous statistical inference methodology whose outcome, for each gene, is an ordered triplet: a raw computed fractional (or relative) change in expression level; an associated probability that this number indicates lower, higher, or no differential expression; and a measure of confidence associated with the stated result. In this paper we validate the probabilistic framework and associated statistical inference methodology through confirmatory experimental studies of gene expression in Saccharomyces cerevisiae using Affymetrix Genechips®. The array data were analyzed using the probabilistic framework, and 9 genes-with indeterminate expression status according to the standard 2-fold change criteria, but for which our probabilistic method indicated high expression status probabilities-were selected for higher precision characterization. In particular, for genes CGR1, GOS1, ICS2, PCL5 and PLB1, the high probabilities of being differentially expressed (up or down) were found to be in excellent agreement with the expression status determined by the independent, high precision confirmatory experiments. These confirmatory experiments, using the high precision, medium throughput polonies technique, confirmed that the probabilistic framework performs quite well in correctly identifying the expression status of genes in general, but especially differentially expressed genes that would otherwise not have been identifiable using the standard 2-fold change criteria.

In this paper, we introduce Bayesian quantile regression for longitudinal data in terms of informative priors and Gibbs sampling. We develop methods for eliciting prior distribution to incorporate historical data gathered from similar previous studies. The methods can be used either with no prior data or with complete prior data. The advantage of the methods is that the prior distribution is changing automatically when we change the quantile. We propose Gibbs sampling methods which are computationally efficient and easy to implement. The methods are illustrated with both simulation and real data.

Log-logistic and Weibull distributions have both accelerated survival time property. The log-logistic distribution has also proportional odds property. Log-logistic distribution has unimodal hazard curve which changes direction. Link [6,7] presented a confidence interval estimate of survival function using Cox\'s proportional hazard model with covariates. Her idea more recently extended by [1] to the exponential distribution and [2] to exponential proportional hazard model, respectively. The same idea has been extended to the Weibull proportional hazard regression model by [3]. In this study, it is formed on confidence interval for log-logistic distribution survival function for any values of the time provided that the survival times have a log-logistic distributed random variable. It is also extended the same results to the proportional odds regression. A Real time data and a simulation data examples are also considered in the study for illustration the discussed confidence interval.

Although Kaplan-Meier survival function is the most commonly used statistical technique of survival analysis, it possesses a disadvantage. It may occur that Kaplan-Meier gives same survival probabilities for two groups having the same number of events and censored observations, although time spans between consecutive events (i.e. waiting times) may considerable vary. Therefore, severity of a disease, in terms of survival times, has no role in the conventional concept of Kaplan-Meier. To overcome this problem, in this paper we propose an exact waiting time survival function by explicitly considering waiting times between events. A new variance estimator, reducing to binomial variance in case of data free from censoring and time differences between two consecutive events equalling to 1, is presented. In order to compare the performance of the new estimator with conventional Kaplan-Meier estimator for small to large sample sizes, as well as for small to heavy censoring, we conducted a simulation study. The outcome shows that on average Pitman Closeness Criteria gives results in favour of our new estimator and confidence intervals have higher coverage rates, as compared to that obtained by Kaplan-Meier estimator, especially for lower confidence limits. Furthermore widths of confidence intervals are smaller than those based on Kaplan-Meier and Greenwood standard error. The proposed procedures are applied to a lung cancer data set.