Generalized semiparametrically structured ordinal models

Robust estimates of regional treatment effects in multiregional randomized clinical trials with ordinal responses

Global clinical trials involving multiple regions are common in current drug development processes. Determining the regional treatment effects of a new therapy over an existing therapy is important to both the sponsors and the regulatory agencies in the regions. Existing methods are mainly for continuous primary endpoints and use subjectively specified models, which may deviate from the true model. Here, we consider trials that have ordinal responses as the primary endpoint. This article extends the recently developed robust semiparametric ordinal regression model to estimate regional treatment effects, in which the regression coefficients and regional effects are modeled parametrically for ease of interpretation, and the regression link function is specified nonparametrically for robustness. The model parameters are estimated by semiparametric maximum likelihood estimation, and the null hypothesis of no regional effect is tested by the Wald test. Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the commonly used parametric model. The results of the former show an improved overall performance over the latter. In particular, the model yields much higher precision in estimation and prediction than the fixed-link model. This result is especially appealing since our interest is to estimate the treatment effect more efficiently and the estimand is of particular interest in multiregional clinical trials. We then apply the method by analyzing real multiregional clinical trials with ordinal responses as their primary endpoint.

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.

Semiparametric Multinomial Ordinal Model to Analyze Spatial Patterns of Child Birth Weight in Nigeria

Background: Birth weight is an important health parameter for obstetricians and gynaecologists. It is a good health indicator of a child-bearing mother and a strong predictor of infant morbidity and mortality. Methods: This paper utilizes data on 28,647 children born between 2003–2008 obtained from the 2008 Nigeria Demographic and Health Survey (NDHS). For a simple epidemiological convenience, the occurrence of a newborn weight can intuitively be considered to be categorical in nature and the thresholds can be put on a continuous scale. In survey reporting, the mothers frequently estimate their infant’s birth weight and make a classification in ordinal category (low, normal, large) instead of actual birth weight. The study fits a multinomial regression model to analyze the relationships between the polytomous response and different kind of covariates in a unified manner. We estimate the fixed effects of bio-social covariates parametrically and the non-linear effect modeled using P-spline. The spatial component was modeled using conditional autoregressive error. A penalized maximum likelihood estimation was performed to estimate the model parameters. Results: We found risk factors that are positively associated with low birth weight, which include multiple birth, short birth interval, death of sibling, childhood diarrhea, fever, mother’s smoking, firewood/dung cooking and poor household. Results further showed that iron syrup supplementation, antenatal attendance, mother literacy and household wealth had significant association with low probability of low birth weight. The finding also showed spatial patterns, which are not captured by the underlying determinants, and we produced probability predictive maps of the spatial residual effects. Conclusions: In addition to the statistical relevance of our method, the generated spatial maps identify highly endemic areas of low birth weight that can assist government agency to channel scarce health resources. A comprehensive approach which institutes a combination of interventions to improve the overall health care of the women is needed.

MEASURING THE PERFORMANCE OF ORDINAL CLASSIFICATION

Ordinal classification is a form of multiclass classification for which there is an inherent order between the classes, but not a meaningful numeric difference between them. The performance of such classifiers is usually assessed by measures appropriate for nominal classes or for regression. Unfortunately, these do not account for the true dimension of the error.

The goal of this work is to show that existing measures for evaluating ordinal classification models suffer from a number of important shortcomings. For this reason, we propose an alternative measure defined directly in the confusion matrix. An error coefficient appropriate for ordinal data should capture how much the result diverges from the ideal prediction and how "inconsistent" the classifier is in regard to the relative order of the classes. The proposed coefficient results from the observation that the performance yielded by the Misclassification Error Rate coefficient is the benefit of the path along the diagonal of the confusion matrix. We carry out an experimental study which confirms the usefulness of the novel metric.

Semiparametric regression during 2003-2007

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology - thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.