Model Assisted Statistics and Applications

In the analysis of survival data with parametric models, it is well known that the Weibull model is not suitable for modeling survival data where the hazard rate is non-monotonic. For such cases, where hazard rates are bathtub-shaped or unimodal (or hump-shaped), log-logistic, lognormal, Birnbaun-Saunders, and inverse Gaussian models are used for the computational simplicity and popularity among users. When models are inadequate and inappropriate, compound Rayleigh, arctangent, generalized Weibull, and Weibull-Pareto composite models are also used. Out of these models log-logistic (LL) model is frequently used. The log-logistic distribution (LLD) has the advantage of having simple algebraic expressions for its survivor and hazard functions and a closed form for its distribution function. In this paper, we consider gamma distribution as frailty distribution and LLD as baseline distribution for bivariate survival times. The problem of analyzing and estimating parameters of bivariate LLD with shared gamma frailty is of interest and the focus of this paper. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model. We present a simulation study and two real data examples to compute Bayesian estimates of the parameters and their standard errors and then compare the true values of the parameters with the estimated values for different sample sizes. A search of the literature suggests there is currently no work has been done for bivariate log-logistic regression model with shared gamma frailty using Bayesian approach.

The dependence between individuals in a group is modeled by the group specific quantity, which can be interpreted as an unobserved covariates or “frailties” common to the individuals in the group and assumed to follow some distribution. We consider the shared frailty model in the frame work of parametric Cox proportional hazard model. The Cox regression model with the shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing life time data. In this paper, we consider shared inverse Gaussian frailty model with bivariate exponential of Marshall-Olkin [20] distribution as baseline hazard for bivariate survival times. We fit the model to the real life bivariate survival data set of diabetic retinopathy data. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty for diabetic retinopathy data is the interest of this paper. Also, we carried out a test for independence using information criteria.

Study of factors affecting the functioning of the human brain has been of considerable interest for more than a century. In this paper, we focus on the structure of brain arterial systems in humans and study how this might be related to factors such as age, gender or handedness (left or right handed). To facilitate this study we first represent brain arterial systems using tree-structured objects and construct stochastic systems whose realizations are such tree-structured objects. We show that the parameters of the stochastic system, primarily the branching probabilities, may be effectively studied using a logistic regression framework. This appears to be a fruitful approach for understanding tree-structured data. Applying this novel approach to actual data collected on 98 subjects, we are able to conclude that age and gender do seem to influence brain artery branching patterns. Most brain arteries have decreasing branching probabilities with increasing age, and brain arteries of females are slightly more likely to branch than those of males. In addition, we find an interesting phenomenon that, as age increases, branching probabilities of thick arteries decrease while those of thin arteries increase. Possible medical/biological interpretations of this finding are provided.

To develop effective public-health intervention strategies for preventing person-to-person disease transmission, it is extremely essential to know the underlying biological processes and the probability of transmission. However, it is unethical to design studies to estimate the probability of person-to-person disease transmission because such studies would involve infecting an uninfected person with a disease. Statistical modeling is a very important technique used to estimate disease transmission probabilities among individuals. By using data from different independent studies, researchers may be able to obtain enough information about an infected person's infectiousness and the susceptibility of an uninfected person to estimate disease transmission probabilities. In this paper, we developed a statistical modeling technique to estimate probabilities of person-to-person disease transmission from an infected to an uninfected person. We used this new modeling technique to estimate the probability of male-to-female, penile – vaginal human immunodeficiency virus (HIV) transmission in one sexual contact. We developed two different sets of male-to-female HIV transmission probability estimates for different infectiousness and susceptibility values using two models. This newly developed modeling technique can be used to estimate person-to-person transmission probabilities for different diseases and routes of transmission.

Basic science researchers transplant human cancer tissues from patients with ductal carcinoma in situ (DCIS) to animals and observe the progression of the disease. Successful transplants show invasion of human tissues across mammary ducts in animal fat pads and cause DCIS-like lesions in one or more ducts. In this work, we consider data from a recent publication of breast cancer research where positive counts of affected ducts may be subject to censoring. We fit the data with zero-truncated Poisson (ZTP) models with an informative prior of gamma. Due to the zero-truncation and right censoring, posterior distributions may not be conventional gamma and are estimated through Markov chain Monte Carlo and grid approximation. For each of the two cell lines, we fit a model with group-specific parameters for DCIS subtypes classified by the cell surface biomarkers, and another model with a homogeneous parameter across groups. Models are compared by the Deviance Information Criterion (DIC). For the chosen prior parameter values, Bayes estimates are comparative to the maximum likelihood estimates, and the DIC favors the simpler model in both cell lines.

One important application of the statistical analysis of microarray gene expression data is to predict the clinical outcomes of diseased patients. The accurate selection of significant genes is crucial to establishing an effective predictive model. Statistical p-value and Cox score are used to rank the lung cancer patients' genes, and principal component analysis, supervised principal components and the partial least squares methods are used to study the effect of the number of top ranked genes. Simulations are performed to evaluate the performance of the proposed methods. A real-life dataset is analyzed using the proposed methods, which are compared to each other. The predictive performance of each method is evaluated using three evaluation criteria. The results show that our predictive methods that involve gene selection have better predictive performance then other currently used methods [5].

Generally dietary factors may influence liver biochemical parameters. It is well known that wine drinking is a principal risk factor for liver-disorder. Alcoholic cirrhosis is a liver disease which is due to excessive alcohol intake.

We have investigated blood pressure and heart rate variability characteristics of 160 persons in the age range from 30 to 70 years in this research using different methods of statistical data analysis. By their systolic blood pressure values, participants of this investigation were grouped in optimal, normal, high normal and first grade hypertension blood pressure categories according to guidelines for Management of Hypertension. Data sets of measured as well as calculated characteristics such as systolic and diastolic pressures, pulse pressure, the mean arterial pressure and heart rate of participants have been analyzed.

By this analysis we aimed to investigate relation between the level of blood pressure and statistical and distributional features of mentioned characteristics in different classification categories. The most important task was to compare variability features of arterial pressure and heart rate characteristics for persons falling into normal and high normal hypertension categories. This was caused by the fact that grouping of patients in these close groups do not ensure that variability features of their blood pressure and heart rate characteristics will necessarily differ.

The results of our analysis have convinced that there is clear reference between variability features of analyzed characteristics (systolic, diastolic, pulse pressure, the mean arterial pressure and heart rate) and the level of blood pressure in different categories. Moreover, despite of closeness of threshold values of the blood pressure, established by guidelines for normal and high normal categories of a hypertension, the analyzed features of patients from these categories were found significantly different by their statistical and distributional features.