A Bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data

Estimation of Risk Factors Affecting Screening Outcomes of Prostate Cancer Using the Bayesian Ordinal Logistic Model

Prostate cancer occurs when cells in the prostate gland grow out of control. Almost all prostate cancers are adenocarcinomas. The survival rate for prostate cancer patients depends on the screening outcome, which can be either no prostate cancer, early detection, and late detection or advanced stage detection. The main objective of this study was to estimate the risk factors affecting the screening outcome of prostate cancer. With ordinal outcomes, a generalized Bayesian ordinal logistic model was considered in the analysis. The generalized Bayesian ordinal logistic model helped in estimation of coefficient parameters of the risk factors affecting each level of prostate cancer-screening outcomes. In the study, positive coefficients, that is, ${\beta }_k>0$ , indicated that the higher values on the explanatory variable increased the chances of the respondent being in a higher category of the dependent variable than the current one, while the negative coefficients, that is, ${\beta }_k<0$ , signified that the higher values on the explanatory variable increased the likelihood of being in the current or lower category of prostate cancer. For instance, from the analysis, positive or negative outcomes of prostate cancer showed that an increase in weight lowered the chances of an individual having the disease.

Using marginal standardisation to estimate relative risk without dichotomising continuous outcomes

Background

Although criticisms regarding the dichotomisation of continuous variables are well known, applying logit model to dichotomised outcomes is the convention because the odds ratios are easily obtained and they approximate the relative risks (RRs) for rare events.

Methods

To avoid dichotomisation when estimating RR, the marginal standardisation method that transforms estimates from logit or probit model to RR estimate is extended to include estimates from linear model in the transformation. We conducted a simulation study to compare the statistical properties of the estimates from: (i) marginal standardisation method between models for continuous (i.e., linear model) and dichotomised outcomes (i.e., logit or probit model), and (ii) marginal standardisation method and distributional approach (i.e., marginal mean method) applied to linear model. We also compared the diagnostic test for probit, logit and linear models. For the real dataset analysis, we applied these analytical approaches to assess the management of inpatient hyperglycaemia in a pilot intervention study.

Results

Although the RR estimates from the marginal standardisation method were generally unbiased for all models in the simulation study, the marginal standardisation method for linear model provided estimates with higher precision and power than logit or probit model, especially when the baseline risks were at the extremes. When comparing approaches that avoid dichotomisation, RR estimates from these approaches had comparable performance. Assessing the assumption of error distribution was less powerful for logit or probit model via link test when compared with diagnostic test for linear model. After accounting for multiple thresholds representing varying levels of severity in hyperglycaemia, marginal standardisation method for linear model provided stronger evidence of reduced hyperglycaemia risk after intervention in the real dataset analysis although the RR estimates were similar across various approaches.

Conclusions

When compared with approaches that do not avoid dichotomisation, the RR estimated from linear model is more precise and powerful, and the diagnostic test from linear model is more powerful in detecting mis-specified error distributional assumption than the diagnostic test from logit or probit model. Our work describes and assesses the methods available to analyse data involving studies of continuous outcomes with binary representations.

Electronic supplementary material

The online version of this article (10.1186/s12874-019-0778-9) contains supplementary material, which is available to authorized users.

Wealth inequality as a predictor of HIV-related knowledge in Nigeria

Introduction

Considering the high state-level heterogeneity of HIV prevalence and socioeconomic characteristics in Nigeria, it is a relevant setting for studies into the socioeconomic correlates of HIV-related knowledge. Although the relationship between absolute poverty and HIV transmission has been studied, the role of wealth inequality in the dynamics of the HIV epidemic has yet to be investigated in Nigeria. The current study, therefore, investigates wealth inequality and other sociodemographic covariates as predictors of HIV-related knowledge, in order to identify subgroups of the Nigerian population that would benefit from HIV preventive interventions.

Methods

This study used the nationally representative 2013 Nigerian Demographic and Health Survey (NDHS). HIV-related knowledge was computed as a total score based on HIV-related knowledge indicators in the NDHS, dichotomised using the sample median as the cut-off. Wealth inequality and other relevant sociodemographic variables were introduced into a logistic regression model based on their significance in bivariate analyses. ORs derived from the model were interpreted to identify risk groups for low HIV-related knowledge after adjusting for confounding factors.

Results

The regression model indicated that individuals with lower literacy levels were almost twice as likely as literate respondents to have low HIV-related knowledge (adjusted OR (AOR): 1.95, 95% CI 1.85 to 2.05, P<0.001), and individuals in the upper wealth quintile were less than half as likely than those in the lower wealth quintile to have low HIV-related knowledge (AOR: 0.40, 95% CI 0.35 to 0.46, P<0.001). Women were also more than twice as likely as men to have low HIV-related knowledge at each level of wealth inequality. In addition, women were 80% less likely to have low mother-to-child transmission knowledge than men, but had over 1.5 times higher odds of having poor knowledge of HIV risk reduction measures. Ethnicity, religious affiliation, relationship status and residing in rural areas were additional significant predictors of HIV-related knowledge.

Conclusion

HIV-related knowledge in this sample is generally low among women, those with low literacy levels, the poor, the unemployed, those residing in rural areas, those with traditional religious beliefs and those living in states with the highest wealth inequality ratios. The identification of these risk groups for low HIV-related knowledge facilitates the implementation of future evidence-based interventions among these groups in order to potentially reduce HIV transmission.

Risk of using logistic regression to illustrate exposure-response relationship of infectious diseases

Background

In most biological experiments, especially infectious disease, the exposure-response relationship is interrelated by a multitude of factors rather than many independent factors. Little is known about the suitability of ordinary, categorical exposures, and logarithmic transformation which have been presented in logistic regression models to assess the likelihood of an infectious disease as a function of a risk or exposure. This study aims to examine and compare the current approaches.

Methods

A simulated human immunodeficiency virus (HIV) population, dynamic infection data for 100,000 individuals with 1% initial prevalence and 2% infectivity, was created. Using the Monte Carlo method (computational algorithm) to repeat random sampling to obtain numerical results, linearity between log odds and exposure, and suitability in practice were examined in the three model approaches.

Results

Despite diverse population prevalence, the linearity was not satisfied between log odds and raw exposures. Logarithmic transformation of exposures improved the linearity to a certain extent, and categorical exposures satisfied the linear assumption (which was important for modelling). When the population prevalence was low (assumed < 10%), performances of the three models were significantly different. Comparing to ordinary logistic regression, the logarithmic transformation approach demonstrated better accuracy of estimation except that at the two inflection points: likelihood of infection increased from slowly to sharply, then slowly again. The approach using categorical exposures had better estimations around the real values, but the measurement was coarse due to categorization.

Conclusions

It is not suitable to directly use ordinary logistic regression to explore the exposure-response relationship of HIV as an infectious disease. This study provides some recommendations for practical implementations including: 1) utilize categorical exposure if a large sample size and low population prevalence are provided; 2) utilize a logarithmic transformed exposure if the sample size is insufficient or the population prevalence is too high (such as 30%).

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2334-14-540) contains supplementary material, which is available to authorized users.