A survival mediation model with Bayesian model averaging

Determining the extent to which a patient is benefiting from cancer therapy is challenging. Criteria for quantifying the extent of "tumor response" observed within a few cycles of treatment have been established for various types of solids as well as hematologic malignancies. These measures comprise the primary endpoints of phase II trials. Regulatory approvals of new cancer therapies, however, are usually contingent upon the demonstration of superior overall survival with randomized evidence acquired with a phase III trial comparing the novel therapy to an appropriate standard of care treatment. With nearly two-thirds of phase III oncology trials failing to achieve statistically significant results, researchers continue to refine and propose new surrogate endpoints. This article presents a Bayesian framework for studying relationships among treatment, patient subgroups, tumor response, and survival. Combining classical components of a mediation analysis with Bayesian model averaging, the methodology is robust to model misspecification among various possible relationships among the observable entities. A posterior inference is demonstrated via an application to a randomized controlled phase III trial in metastatic colorectal cancer. Moreover, the article details posterior predictive distributions of survival and statistical metrics for quantifying the extent of direct and indirect, or tumor response mediated treatment effects.

A Logit Model for Bivariate Binary Responses

This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with 3p degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

A penalized approach for the bivariate ordered logistic model with applications to social and medical data

Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios to be estimated also increases, and estimation gets problematic.

In this work we propose a non-parametric approach for the maximum likelihood (ML) estimation of a BOLM, wherein penalties to the differences between adjacent row and column effects are applied. Our proposal is then compared to the Goodman and Dale models. Some simulation results as well as analyses of two real data sets are presented and discussed.

Probabilistic self-organizing maps for qualitative data

We present a self-organizing map model to study qualitative data (also called categorical data). It is based on a probabilistic framework which does not assume any prespecified distribution of the input data. Stochastic approximation theory is used to develop a learning rule that builds an approximation of a discrete distribution on each unit. This way, the internal structure of the input dataset and the correlations between components are revealed without the need of a distance measure among the input values. Experimental results show the capabilities of the model in visualization and unsupervised learning tasks.