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Separation or monotone likelihood can be observed in fitting process of both Poisson or generalized Poisson (GP) regression, particularly in case of small and/or sparse count data, using maximum likelihood estimation (MLE) when one or more regression coefficients diverge to infinity. The study investigates the consequence of separation in the MLE based standard Poisson or GP model and addressed the problems by introducing a penalized likelihood approach. The penalized likelihood function is derived by adding a penalty term to the standard maximum likelihood function, which was originally proposed by Firth (1993) for reducing first order bias in MLE. The corresponding penalized likelihood score equation has shown to achieve convergence and provide finite estimate of the regression coefficient, which was not possible for the maximum likelihood method score equation. The simulation study, with different forms of separation, showed that penalized Poisson model or penalized GP outperform the standard Poisson and even the Zero-inflated Poisson (ZIP) in the presence of complete or quasi-complete separation by achieving convergence and providing finite estimate of the regression coefficients. Even in the presence of near-to-quasi-complete separation, which is very common in practice, the penalized method showed better results than the standard Poisson, GP and ZIP in all simulation scenarios. The method was illustrated using antenatal care data extracted from database of the Bangladesh demographic health survey 2018. [ABSTRACT FROM AUTHOR]

The potential performance of bio-marker in classifying diseased from healthy population may be affected by baseline covariates (X) that are associated with both the bio-marker (Y) and the disease status (D). Some existing approaches can be able to adjust for the effect of a single covariate at a time. However, several potential covariates can be available in practice for which simultaneous adjustment in the ROC curve is essential. This study proposed a propensity score (PS) based adjustment for the effects of several covariates in the ROC curve. The PS is first derived from a linear transformation of several covariates and the PS-adjusted (and PS-specific) ROC curve was then estimated using the existing non-parametric induced ROC regression framework. The method is illustrated for both continuous and binary bio-markers. The simulation study suggests that the PS-based adjustment performed well by providing a consistent estimate of the true ROC curve and showing robustness to the mis-specification of the propensity score model as well as to a non-linear function of covariates. Further, an application of the method is provided to evaluate the effectiveness of the body-mass-index in classifying patients with hypertension or diabetes after adjusting for the potential covariates such as age, sex, education, socio-economic status. [ABSTRACT FROM AUTHOR]

The Concordance statistic (C-statistic) is commonly used to assess the predictive performance (discriminatory ability) of logistic regression model. Although there are several approaches for the C-statistic, their performance in quantifying the subsequent improvement in predictive accuracy due to inclusion of novel risk factors or biomarkers in the model has been extremely criticized in literature. This paper proposed a model-based concordance-type index, CK, for use with logistic regression model. The CK and its asymptotic sampling distribution is derived following Gonen and Heller's approach for Cox PH model for survival data but taking necessary modifications for use with binary data. Unlike the existing C-statistics for logistic model, it quantifies the concordance probability by taking the difference in the predicted risks between two subjects in a pair rather than ranking them and hence is able to quantify the equivalent incremental value from the new risk factor or marker. The simulation study revealed that the CK performed well when the model parameters are correctly estimated for large sample and showed greater improvement in quantifying the additional predictive value from the new risk factor or marker than the existing C-statistics. Furthermore, the illustration using three datasets supports the findings from simulation study. [ABSTRACT FROM AUTHOR]