Statistical Methods in Medical Research

Abstract

Since John Snow first conducted a modern epidemiological study in 1854 during a cholera epidemic in London, statistics has been associated with medical research. After Austin Bradford Hill published a series of articles on the use of statistical methodology in medical research in 1937, statistical considerations and computational tools have been paramount in conductingmedical research [1]. For the past century, statistics has played an important role in the advancement of medical research and medical research has stimulated rapid development of statistical methods. For example, the development of modern survival analysis-an important branch of statistics has aimed to solve problems encountered in clinical trials and large-scale epidemiological studies. In this era of evidence-based medicine, the development of novel statistical methods will continue to be crucial in medical research. With the expansion of computer capacity and advancement of computational techniques, it is inevitable that modern statistical methods will likely incorporate, to a greater degree, complex computational procedures. This issue focuses on statistical methods in medical research. Several novel methods aiming on solving different medical research questions are introduced. Some unique approaches of statistical analysis are also present. Hanagal and Sharma contribute two papers. The first one deals with a bivariate survival model. They examine a parameter estimation issue when the samples are taken from a bivariate log-logistic distribution with shared gamma frailty. They propose to use a Bayesian approach along with theMarkov ChainMonte Carlo computational technique for implementation. The computer simulation is conducted for performance evaluation. Two well-known datasets, one about acute leukemia and the other about kidney infection are applied as examples. The second paper contributed by Hanagal and Sharma examines the shared inverse Gaussian frailty model with the bivariate exponential baseline hazard. They first derive the likelihood of the joint survival function. In their Bayesian approach, the parameters of the baseline hazard are assumed to follow a gamma distribution while the coefficients of the regression relationship are assumed to follow an independent normal distribution. The dependence of two components of the survival function is tested. Three information criteria are used for model comparisons. The proposed method is applied to analyze diabetic retinopathy data. The paper by Chang, Lyer, Bullitt and Wang provides a method to find determinants of the brain arterial system. They represent the brain arterial system as a binary tree and apply the mixed logistic regression model to find significant covariates. The authors also demonstrate model selection methods for both fixed and random effects. A case study is presented using the method. This paper provides a rigorous approach for analyzing the binary branching structure data. It is potentially applicable to other tree structure data. Chakraborty proposes two probabilistic models to estimate male-to-female HIV-1 transmission rate in one sexual contact. One model is applicable when the transmitter cell counts are known and the other model is applicable when the receptor cell counts are known. By first uniformizing each transmitter (or receptor) cell count and assuming as a beta distribution, this paper algebraically derives the transition probability by imposing some boundary conditions based on scientific phenomena related to HIV infection. The paper by Yeh, Jiang, Garrard, Lei and Gajewski proposes to use a zero-truncated Poisson model to analyze human cancer tissues transplanted to mice when the positive counts of affected ducts is subject to right censoring. A Bayesian approach choosing a Gamma distribution as the prior is adopted. After implementing through complex computational procedures, this paper obtains the estimates of the coefficients and demonstrates model fitting through