Regression Models For Binary Responses Research Articles

A modified net reclassification improvement statistic

The continuous net reclassification improvement (NRI) statistic is a popular model change measure that was developed to assess the incremental value of new factors in a risk prediction model. Two prominent statistical issues identified in the literature call the utility of this measure into question: (1) it is not a proper scoring function and (2) it has a high false positive rate when testing whether new factors contribute to the risk model. For binary response regression models, these subjects are interrogated and a modification of the continuous NRI, guided by the likelihood-based score residual, is proposed to address these issues. Within a nested model framework, the modified NRI may be viewed as a distance measure between two risk models. An application of the modified NRI is illustrated using prostate cancer data.

Application of Binary Response Regression Models to Detect Factors Influencing the Occurrence of Infection in Dental Surgeries

Postoperative infection is common in dental surgery, for example, in the removal of the third molar. To control these and other postoperative complications, various studies have reported the use of some drug protocols, namely the prophylact and the preemptive ones, using drugs such as dexamethasone and betamethasone. In this work, we used the generalized linear model via logistic regression to verify whether, in addition to the medicaments mentioned, some covariates that are frequently used in dental surgeries influence the occurrence, or not, of postoperative infection in surgeries for removal of the third molar. One of the main reasons that led us to employ such a model is because the response variable (having or not having infection) presents values of the binary type, in addition to being one of the most applied models in the area of health, among them, the dentistry area. The application of descriptive methods and analysis of association via statistical tests were also used to choose other factors that influence the response variable infection in addition to medications. The AIC (Akaike Information Criterion) selection criterion, analysis of the difeerence in the deviations, and the analysis of residual using the half-normal plot for selection and the assumption of the proposed model were employed. The data set under analysis consists of 113 patients submitted to dental surgery in a specialized clinic in the city of Piracicaba, SP-Brazil between 2003 and 2018. Through the proposed model, some important information the covariates in relation to the patients submitted to dental surgery. One of the key information is that characteristics as Age and Dental extractions are associated with the inflammatory processes after surgery. This relationship indicates that the older the patient, the chance of having an infection after surgery increases. The analysis is similar to the Number of extractions.

Regression models for binary response applied to data on neonatal deaths in newborns

The present study presents binary data modeling regarding 1.6% of neonatal deaths in 3,448 newborns from an epidemiological and observational study with a cross-sectional design, involving the retrospective analysis of 4,293 medical records of high-risk pregnant women followed in a gestational outpatient clinic from September 2012 to September 2017. Different symmetric and asymmetric link functions were considered by means of Bayesian inference. The support of more accurate inferences regarding the parameters of the model will provide biological interpretations that are more reliable and consistent with the reality. The model that presented, significantly, the lowest value for the deviance information criterion (DIC = 398.8), was the binomial with power logit (PL) link function, whose median posterior value estimated and significant for the parameter asymmetry was l = 0.25 (0.14;1.17). This significance is observed in all other models of the power family, however with very different values ​​and significantly higher DIC values, indicating less parsimonious models. The Bayesian methodology proved to be flexible. Additionally, the results show that such model shows an accuracy = 97.4% and area under the ROC curve AUC = 89.4% in the prediction of neonatal deaths based on the weight of children at birth. Specifically, for 2.500g, a value predicted in the medical literature for low weight, the model predicts a probability of 1.43%.

Su1547 OUTCOMES OF PRECUT NEEDLE KNIFE FISTULOTOMY BASED ON THE ENDOSCOPIC MORPHOLOGY OF THE AMPULLA OF VATER AND OF THE SIZE OF BILE DUCT

Previous studies have suggested that the success and complications of precut needle knife fistulotomy (NKF) for achieving biliary access is largely dependent of the endoscopic morphology of the ampulla of Vater and also of the bile duct size. However, no study has addressed this topic. This study evaluated the outcomes of NKF on the basis of the morphology of the major papilla and of the size of the bile duct. This was a prospective multicenter study of all consecutive patients who were submitted to early NKF attempt for biliary access between August 2017 and August 2019. We evaluated the success rate and complications of NKF based on the following parameters: transverse and longitudinal measures of the papilla obtained using a visual method; diameter of the terminal CBD (t-CBD) measured 1 cm from the papilla using fluoroscopic images. Papilla were classified using a previously validated international classification of the major papilla into 7 categories. Outcomes were evaluated by a binary response regression models. We included 275 patients submitted to NKF, median age 75 years (17-97), 158 women(57.45%). NKF were performed in: 46 flat type papillas(16,67%), 102 prominent tubular non-pleated (37,21%), 74 prominent tubular pleated(26,74%), 27 prominent bulging(9,69%), 3 intradiverticular(1,09%) , 10 diverticular border(3,64%), 13 unclassified(4,65%). The cannulation rate was 97,07%. The post-ERCP complications rate were 9,09% (n= 25), with pancreatitis rate=6,18% (n=17) and no deaths. Cannulation success and complications were not significantly different among the seven papilla categories. In the regression model, cannulation and complications were not explained by the papilla morphology and the CBD diameter(Overall F-Test=0,46;p<0,80). The biliary cannulation and post-ERCP complications are not associated with papillary morphology or the distal size of CBD. The decision to use NKF for biliary access should not be conditioned by the papillary morphology.

Su1567 OUTCOMES OF NEEDLE KNIFE FISTULOTOMY AS AN INITIAL METHOD OF BILIARY CANNULATION

A previous feasibility study has suggested that needle knife fistulotomy (NFK) as an initial method for biliary access in patients with stones is associated with high levels of success and low rate of complications. This study evaluated the outcomes of NKF as an initial method for biliary access, in a large number of patients with any type of biliary pathology (tumors and stones), on the basis of success rate, complications and factors associated with success and complications. This was a prospective multicenter study of all consecutive patients who were submitted to NKF attempt as an initial method of biliary cannulation between August 2017 and November 2019 . We evaluated the success rate and complications of NKF based on the following parameters: morphology of the major papilla, biliary pathology, diameter of the terminal CBD (t-CBD) measured 1 cm from the papilla using fluoroscopic images while the patient was in a prone or supine. Papilla were classified using a previously validated international classification of the major papilla: flat type, prominent tubular non-pleated, prominent tubular pleated, prominent bulging, intradiverticular, diverticular border, unclassified papilla. Outcomes were evaluated a probit binary response regression models. We included 111 patients submitted to primary NKF, median age 70 years (17-97), 59 women (53,15%). In first ERCP, biliary cannulation rate=97.29% (108/111). The post-ERCP complications was 4,50% (n= 5), with pancreatitis rate of 3,60% (n=4) and no severe complications. Mean time to achieve cannulation was 6,25 min (sd 3,37) and mean ERCP duration=18,16 min (sd 5,58). In the regression model, complications were not explained by the papilla morphology, CBD diameter, biliary pathology (Overall F-Test=0,70;p=0,6725). When feasible NFK as initial method is associated with short time for gaining biliary access, high rate of success and low risk of complications, namely pancreatitis. The success of NFK is not related with the morphology of the papilla, t-CBD diameter, or underlying biliary pathology.

A data-driven bandwidth selection method for the smoothed maximum score estimator

Binary response regression models are useful in many economic and statistical applications. Horowitz (1992) proposes a semi-parametric estimation method, which is a smoothed version of, and has a faster convergence rate than, Manski’s maximum score estimator. The method for selecting the smoothing parameter (bandwidth) here is analogous to the plug-in method in kernel density estimation. It requires initial “pilot” values of the bandwidth to obtain the optimal bandwidth. However, this method has the disadvantage of not being fully data-driven. In this paper, we propose a data-driven bandwidth selection method by minimizing a cross-validated criterion function. Our simulation results show that the proposed method performs better than some existing methods.

On Group Comparisons With Logistic Regression Models

It is widely believed that regression models for binary responses are problematic if we want to compare estimated coefficients from models for different groups or with different explanatory variables. This concern has two forms. The first arises if the binary model is treated as an estimate of a model for an unobserved continuous response and the second when models are compared between groups that have different distributions of other causes of the binary response. We argue that these concerns are usually misplaced. The first of them is only relevant if the unobserved continuous response is really the subject of substantive interest. If it is, the problem should be addressed through better measurement of this response. The second concern refers to a situation which is unavoidable but unproblematic, in that causal effects and descriptive associations are inherently group dependent and can be compared as long as they are correctly estimated.

Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses

Association measures based on concordance, such as Kendall’s tau, Somers’ delta or Goodman and Kruskal’s gamma are often used to measure explained variations in regression models for binary outcomes. As responses only assume values in {0, 1}, these association measures are constrained, which makes their interpretation more difficult as a relatively small value may in fact strongly support the fitted model. In this paper, we derive the set of attainable values for concordance-based association measures in this setting so that the closeness to the best-possible fit can be properly assessed.

Log-Mean Linear Regression Models for Binary Responses with an Application to Multimorbidity

SummaryIn regression models for categorical data a linear model is typically related to the response variables via a transformation of probabilities called the link function. We introduce an approach based on two link functions for binary data named the log-mean and the log-mean linear methods. The choice of the link function plays a key role in the interpretation of the model, and our approach is especially appealing in terms of interpretation of the effects of covariates on the association of responses. Similarly to Poisson regression, the log-mean and log-mean linear regression coefficients of single outcomes are log-relative-risks, and we show that the relative risk interpretation is maintained also in the regressions of the association of responses. Furthermore, certain collections of zero log-mean linear regression coefficients imply that the relative risks for joint responses factorize with respect to the corresponding relative risks for marginal responses. This work is motivated by the analysis of a data set obtained from a case–control study aimed at investigating the effect of human immunodeficiency virus infection on multimorbidity, i.e. simultaneous presence of two or more non-infectious comorbidities in one patient.

Quantile regression with group lasso for classification

Applications of regression models for binary response are very common and models specific to these problems are widely used. Quantile regression for binary response data has recently attracted attention and regularized quantile regression methods have been proposed for high dimensional problems. When the predictors have a natural group structure, such as in the case of categorical predictors converted into dummy variables, then a group lasso penalty is used in regularized methods. In this paper, we present a Bayesian Gibbs sampling procedure to estimate the parameters of a quantile regression model under a group lasso penalty for classification problems with a binary response. Simulated and real data show a good performance of the proposed method in comparison to mean-based approaches and to quantile-based approaches which do not exploit the group structure of the predictors.

ICTs and maternal healthcare utilization. Evidence from Ghana

Purpose – Traditionally, the role of technology on health services has been argued from the supply side. The purpose of this paper is to use a demand side perspective to examine the effect of Information and Communication Technologies (ICTs) on the use of maternal health services in Ghana. Design/methodology/approach – Study used data from the 2008 Ghana Demographic and Health Surveys and binary response regression models to examine the effect of women's access to ICTs on maternal healthcare utilization in Ghana. Three variables on maternal healthcare utilization were employed: use of contraception, antenatal care and place of delivery. Findings – Results from the study show that the effect of the use of technology is both positive and significant. In particular, among the other ICTs (i.e. landline phone, listening to radio, watch television, color television in household, computer in household), the coefficients of mobile phone ownership tends to be consistently significant across all four reproductive health services. Therefore, ICTs have a good capacity to influence women's demand of health information. This needs to be taken into account when designing maternal health policies and interventions. Originality/value – This is one of the few papers examining the effect of ICTs on utilization of maternal health services from the demand side compared to the popular supply side argument often found in the literature.

On the Economic Meaning of Interaction Term Coefficients in Non-Linear Binary Response Regression Models

We show that it is perfectly correct to use just the interaction term, along with its standard error, to draw inferences about interactive effects in binary response regression models. This point is currently in dispute among applied econometricians, some of whom insist that simply relying on the interaction term is incorrect, since the cross partial derivative of the probability of occurrence with respect to interacted covariates can, for some observations, have the sign opposite to that of the interaction term coefficient. We show that this sign flip results from a mechanical saturation effect that is of no importance to researchers who recognize that small changes in probability are more important near the boundaries than near the center. For such researchers, the interaction term coefficient (which is the cross partial derivative of the logit or probit function of the probability) provides a more meaningful measure of interactive effects than does the cross partial derivative of the probability itself. We introduce an alternative cross partial derivative of the probability for which these sign changes cannot occur. Finally, we demonstrate some simple and intuitive ways of interpreting the economic meaning of interaction term coefficients.

Quantifying the Impact of Unobserved Heterogeneity on Inference from the Logistic Model

While consequences of unobserved heterogeneity such as biased estimates of binary response regression models are generally known; quantifying these and awareness of situations with more serious impact on inference is however, remarkably lacking. This study examines the effect of unobserved heterogeneity on estimates of the standard logistic model. An estimate of bias was derived for the maximum likelihood estimator , and simulated data was used to investigate a range of situations that influence size of bias due to unobserved heterogeneity. It was found that the position of the probabilities, along the logistic curve, and the variance of the unobserved heterogeneity, were important determinants of size of bias.

Selecting variables in non‐parametric regression models for binary response. An application to the computerized detection of breast cancer

In many biomedical applications, interest lies in being able to distinguish between two possible states of a given response variable, depending on the values of certain continuous predictors. If the number of predictors, p, is high, or if there is redundancy among them, it then becomes important to decide on the selection of the best subset of predictors that will be able to obtain the models with greatest discrimination capacity. With this aim in mind, logistic generalized additive models were considered and receiver operating characteristic (ROC) curves were applied in order to determine and compare the discriminatory capacity of such models. This study sought to develop bootstrap-based tests that allow for the following to be ascertained: (a) the optimal number q < or = p of predictors; and (b) the model or models including q predictors, which display the largest AUC (area under the ROC curve). A simulation study was conducted to verify the behaviour of these tests. Finally, the proposed method was applied to a computer-aided diagnostic system dedicated to early detection of breast cancer.

Assessing Ordinal Logistic Regression Models via Nonparametric Smoothing

A nonparametric local linear smoothing technique for testing goodness-of-fit of ordinal logistic regression models with continuous and categorical covariates is presented. This proposed test statistic is a generalization of Lin and Chen's statistic (2005) to ordinal response data. The extension of logistic regression models for binary responses to ordinal responses is usually involved by modeling cumulative logits. The expectation and variance of the proposed test statistic are derived, and the sampling distribution of the test statistic, which approximates a scaled chi-square distribution is evaluated by simulation. The power comparison between the proposed test and methods of Pulkstenis and Robinson (2004) are also provided. The simulations reveal that the proposed test has greater power to detect the omitted interaction term, incorrectly functional form of continuous covariates, or misspecification of the complimentary log-log link function for various sample sizes. The proposed testing procedure is illustrated by a numerical study.

Measurement error model for misclassified binary responses

The article considers regression models for binary response in a situation when the response is subject to classification error. It is also assumed that some of the covariates are unobservable, but measurements on its surrogates are available. Likelihood based analysis is developed to fit the model. A sensitivity analysis is also carried out through simulation to ascertain the effect of ignoring classification error and/or measurement error on the estimation of regression parameters. At the end, the methodology developed in this paper is illustrated through an example.

Graphics for studying logistic regression models

In this article we focus on logistic regression models for binary responses. An existing result shows that the log-odds can be modelled depending on the log of the ratio between the conditional densities of the predictors given the response variable. This suggests that relevant statistical information could be extracted investigating the inverse problem. Thus, we present different methods for studying the log-density ratio through graphs, which allow us to select which predictors are needed, and how they should be included in a logistic regression model. We also discuss data analysis examples based on real datasets available in literature in order to provide further insights into the methodology proposed.

The Binary Regression Quantile Plot: Assessing the Importance of Predictors in Binary Regression Visually

We present a graphical measure of assessing the explanatory power of regression models with a binary response. The binary regression quantile plot and an area defined by it are used for the visual comparison and ordering of nested binary response regression models. The plot shows how well various models explain the data. Two data sets are analyzed and the area representing the fit of a model is shown to agree with the usual likelihood ratio test.

Inferences for case-control and semiparametric two-sample density ratio models

SUMMARY We consider inference in general binary response regression models under retrospective sampling plans. Prentice & Pyke (1979) discovered that inference for the odds-ratio parameter in a logistic model can be based on a prospective likelihood even though the sampling scheme is retrospective. We show that the estimating function obtained from the prospective likelihood is optimal in a class of unbiased estimating functions. Also we link casecontrol sampling with a two-sample biased sampling problem, where the ratio of two densities is assumed to take a known parametric form. Connections between this model and the Cox proportional hazards model are pointed out. Large and small sample size behaviour of the proposed estimators is studied.

Bayesian Residual Analysis for Binary Response Regression Models

In a binary response regression model, classical residuals are difficult to define and interpret due to the discrete nature of the response variable. In contrast, Bayesian residuals have continuous-valued posterior distributions which can be graphed to learn about outlying observations. Two definitions of Bayesian residuals are proposed for binary regression data. Plots of the posterior distributions of the basic ‘observed –fitted’ residuals can be helpful in outlier detection. Alternatively, the notion of a tolerance random variable can be used to define latent data residuals that are functions of the tolerance random variables and the parameters. In the probit setting, these residuals are attractive in that a priori they are a sample from a standard normal distribution, and therefore the corresponding posterior distributions are easy to interpret. These residual definitions are illustrated in examples and contrasted with classical outlier detection methods for binary data.