Negative log-binomial model with optimal robust variance to estimate the prevalence ratio, in cross-sectional population studies

Abstract

Background: Cross-sectional studies are useful for the estimation of prevalence of a particular event with concerns in specific populations, as in the case of diseases or other public health interests. Most of these studies have been carried out with binary binomial logistic regression model which estimates OR values that could be overestimated due to the adjustment of the model. Thus, the selection of the best multivariate model for cross-sectional studies is a priority to control the overestimation of the associations.

Methods: We compared the precision of the estimates of the prevalence ratio (PR) of the negative Log-binomial model (NLB) with Mantel-Haenszel (MH) and the regression models Cox, Log-Poisson, Log-binomial, and the OR of the binary logistic regression in population-based cross-sectional studies. The prevalence from a previous cross-sectional study carried out in Colombia about the association of mental health disorders with the consumption of psychoactive substances (e.g., cocaine, marijuana, cigarette, alcohol and risk of consumption of psychoactive substances) were used. The precision of the point estimates of the PR was evaluated for the NLB model with robust variance estimates, controlled with confounding variables, and confidence interval of 95%.

Results: The NLB model adjusted with robust variance showed accuracy in the measurements of crude PRs, standard errors of estimate and its corresponding confidence intervals (95%CI) as well as a high precision of the PR estimate and standard errors of estimate after the adjustment of the model by grouped age compared with the MH PR estimate. Obtained PRs and 95%CI entre NLB y MH were: cocaine consumption (2.931,IC95%: 0.723-11.889 vs. 2.913, IC95%: 0.786-12.845), marijuana consumption (3.444, IC95%: 1.856-6.391 vs. 3.407, IC95%: 1.848, 6.281), cigarette smoking (2.175,IC95%: 1.493, 3.167 vs. 2.209, IC95%: 1.518-3.214), alcohol consumption (1.243,IC95%: 1.158-1.334 vs. 1.241, IC95%: 1.157-1.332), and risk of consumption of psychoactive substances (1.086, IC95%: 1.047-1.127 vs. 1.086, IC95%: 1.047, 1.126). The NLB model adjusted with robust variance showed mayor precision when increasing the prevalence, then the other models with robust variance with respect to MH.

Conclusions: The NLB model with robust variance was shown as a powerful strategy for the estimation of PRs for cross-sectional population-based studies, as high precision levels were identified for point estimators, standard errors of estimate and its corresponding confidence intervals, after the adjustment of confounding variables. In addition, it does not represent convergence issues for high prevalence cases (as it occur with the Log-binomial model) and could be considered in cases of overdispersion and with greater precision and goodness of fit than the other models with robust variance, as it was shown with the data set of the cross-sectional study used in here.

Keywords: Cross-Sectional Studies; Logistic Models; Maximum Likelihood Estimation and Binomial Distribution; Odds Ratio; Prevalence Ratio.

Fig. 1

Comparison of the standard errors of estimation of the PR adjusted by age groups, between the models with robust variance and MH

Fig. 2

Comparison of the standard errors of estimation of PR adjusted for numerical age, between models with robust variance