Natural interpretations in Tobit regression models using marginal estimation methods

Examining the relationship between long working hours and the use of prescription sedatives among U.S. workers

OBJECTIVES

The prevalence of long working hours has been accompanied by a corresponding rise in sleep disorders. Sedative-hypnotic agents (SHAs), have been reported as the second most commonly misused drug class in the U.S. The key objective of this study was to examine the relationship between working hours on the use of sleep aids and medications with sedative properties.

METHODS

The 2010-2019 Medical Expenditure Panel Survey data was utilized. SHAs and medications with sedative related properties (MSRPs) were identified. Furthermore, we employed different regression models ranging from multivariable linear regression, Tobit regression, Heckman regression, and multivariable logistic regression, to ensure consistency, robustness, and reliability of associations.

RESULTS

Overall, a sample of 81,518 observations of full-time workers was analyzed. Working 56hours or more per week was significantly associated (p < 0.05) with an increased odds of using SHAs and MSRPs by 13% (Adjusted Odds Ratio, aOR =1.13, 95% Confidence Interval, CI=1.01:1.26) and 9% (aOR=1.09, 95% CI=1.03:1.16), respectively more than that among those who worked fewer hours. Females in our study had a higher likelihood (aOR=1.11, 95% CI=1.05:1.19) of using SHAs when compared to males. Also, professional services had the highest likelihood (aOR=1.31, 95% CI=1.14:1.50) of using SHAs.

CONCLUSION

We found that long working hours were significantly associated with an elevated use of SHAs and MSRPs among U.S. workers. Specifically, female workers and individuals working in professional services had the highest likelihood of using sleep medications.

Exposure assessment for Cox proportional hazards cure models with interval-censored survival data

Mixture cure models have been developed as an effective tool to analyze failure time data with a cure fraction. Used in conjunction with the logistic regression model, this model allows covariate-adjusted inference of an exposure effect on the cured probability and the hazard of failure for the uncured subjects. However, the covariate-adjusted inference for the overall exposure effect is not directly provided. In this paper, we describe a Cox proportional hazards cure model to analyze interval-censored survival data in the presence of a cured fraction and then apply a post-estimation approach by using model-predicted estimates difference to assess the overall exposure effect on the restricted mean survival time scale. For baseline hazard/survival function estimation, simple parametric models as fractional polynomials or restricted cubic splines are utilized to approximate the baseline logarithm cumulative hazard function, or, alternatively, the full likelihood is specified through a piecewise linear approximation for the cumulative baseline hazard function. Simulation studies were conducted to demonstrate the unbiasedness of both estimation methods for the overall exposure effect estimates over various baseline hazard distribution shapes. The methods are applied to analyze the interval-censored relapse time data from a smoking cessation study.

Physical Activity, Blood Pressure Control, and Health-Related Quality of Life Among Hypertensive Individuals: A Cross-Sectional Study in Jiangsu Province, China

Hypertension has become one of the most serious chronic diseases that threaten public health. Regulating self-management is considered a priority and in which physical activity plays a vital role. Based on the Fifth National Health Service Survey (NHSS, 2013), a total of 6079 patients with hypertension were investigated by stratified cluster random sampling. This study explored the relationships between blood pressure control and physical activity, and health-related quality of life (HRQoL). Tobit regression and generalized linear regression analysis were used to explore the relationships among participants' socioeconomic characteristics, health behaviors, and HRQoL. The results showed that 4712 respondents (77.51%) had no problems in any aspect, but the proportion of respondents with problems increased significantly with age (P for trend <.001). Blood pressure control was significantly correlated with the health utility value (P < .001). Patients who participated in physical activity and maintained normal daily blood pressure also showed higher health utility value. Physical activity was significantly related to blood pressure control and HRQoL. Therefore, regular physical activity is recommended for hypertensive residents to improve HRQoL.

A semiparametric modeling approach for analyzing clinical biomarkers restricted to limits of detection

Before biomarkers can be used in clinical trials or patients' management, the laboratory assays that measure their levels have to go through development and analytical validation. One of the most critical performance metrics for validation of any assay is related to the minimum amount of values that can be detected and any value below this limit is referred to as below the limit of detection (LOD). Most of the existing approaches that model such biomarkers, restricted by LOD, are parametric in nature. These parametric models, however, heavily depend on the distributional assumptions, and can result in loss of precision under the model or the distributional misspecifications. Using an example from a prostate cancer clinical trial, we show how a critical relationship between serum androgen biomarker and a prognostic factor of overall survival is completely missed by the widely used parametric Tobit model. Motivated by this example, we implement a semiparametric approach, through a pseudo-value technique, that effectively captures the important relationship between the LOD restricted serum androgen and the prognostic factor. Our simulations show that the pseudo-value based semiparametric model outperforms a commonly used parametric model for modeling below LOD biomarkers by having lower mean square errors of estimation.

Significant inefficiency in running community health systems: The case of health posts in Southwest Ethiopia

Background

Although much has been documented about the performance of the health extension program, there is a lack of information on how efficiently the program is running. Furthermore, the rising cost of health services and the absence of competition among publicly owned health facilities demands strong follow up of efficiency. Therefore, this study aimed to assess the technical efficiency of the health posts and determinants in Southwestern Ethiopia.

Methods and materials

We used data for one Ethiopian fiscal year (from July 2016 to June 2017) to estimate the technical efficiency of health posts. A total of 66 health posts were included in the analysis. We employed a two-stage data envelopment analysis to estimate technical efficiency. At the first stage, technical efficiency scores were calculated using data envelopment analysis program version 2.1. Predictors of technical efficiency were then identified at the second stage using Tobit regression, with STATA version 14.

Results

The findings revealed that 21.2% were technically efficient with a mean technical efficiency score of 0.6 (± 0.3), indicating that health posts could increase their service volume by 36% with no change made to the inputs they received. On the other hand, health posts had an average scale efficiency score of 0.8 (± 0.2) implying that the facilities have the potential to increase service volume by 16% with the existing resources. The regression model has indicated average waiting time for service has negatively affected technical efficiency.

Conclusion

More than three-quarters of health posts were found inefficient. The technical efficiency score of more than one-third of the health posts is even less than 50%. Community mobilization to enhance the uptake of health services at the health posts coupled with a possible reallocation of resources in less efficient health posts is a possible approach to improve the efficiency of the program.

A new statistical test for latent class in censored data due to detection limit

Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.

Statistical tests for latent class in censored data due to detection limit

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, the exact measures cannot be obtained. Instead, the measures are censored as only partial information that the levels are under the limit is known. Assuming the concentration levels are from a single population with a normal distribution or follow a normal distribution after some transformation, Tobit regression models, or censored normal regression models, are the standard approach for analyzing such data. However, in practice, it is often the case that the data can exhibit more censored observations than what would be expected under the Tobit regression models. One common cause is the heterogeneity of the study population, caused by the existence of a latent group of subjects who lack the substance measured. For such subjects, the measurements will always be under the limit. If a censored normal regression model is appropriate for modeling the subjects with the substance, the whole population follows a mixture of a censored normal regression model and a degenerate distribution of the latent class. While there are some studies on such mixture models, a fundamental question about testing whether such mixture modeling is necessary, i.e. whether such a latent class exists, has not been studied yet. In this paper, three tests including Wald test, likelihood ratio test and score test are developed for testing the existence of such latent class. Simulation studies are conducted to evaluate the performance of the tests, and two real data examples are employed to illustrate the tests.

A microRNA biomarker panel for the non-invasive detection of bladder cancer

The development of accurate, non-invasive urinary assays for bladder cancer would greatly facilitate the detection and management of a disease that has a high rate of recurrence and progression. In this study, we employed a discovery and validation strategy to identify microRNA signatures that can perform as a non-invasive bladder cancer diagnostic assay. Expression profiling of 754 human microRNAs (TaqMan low density arrays) was performed on naturally voided urine samples from a cohort of 85 subjects of known bladder disease status (27 with active BCa). A panel of 46 microRNAs significantly associated with bladder cancer were subsequently monitored in an independent cohort of 121 subjects (61 with active BCa) using quantitative real-time PCR (RT-PCR). Multivariable modeling identified a 25-target diagnostic signature that predicted the presence of BCa with an estimated sensitivity of 87% at a specificity of 100% (AUC 0.982). With additional validation, the monitoring of a urinary microRNA biomarker panel could facilitate the non-invasive evaluation of patients under investigation for BCa.

Urinary mRNA biomarker panel for the detection of urothelial carcinoma

The early detection of bladder cancer is important as the disease has a high rate of recurrence and progression. The development of accurate, non-invasive urinary assays would greatly facilitate detection. In previous studies, we have reported the discovery and initial validation of mRNA biomarkers that may be applicable in this context. In this study, we evaluated the diagnostic performance of proposed molecular signatures in an independent cohort.

Forty-four mRNA transcripts were monitored blindly in urine samples obtained from a cohort of 196 subjects with known bladder disease status (89 with active BCa) using quantitative real-time PCR (RT-PCR). Statistical analyses defined associations of individual biomarkers with clinical data and the performance of predictive multivariate models was assessed using ROC curves. The majority of the candidate mRNA targets were confirmed as being associated with the presence of BCa over other clinical variables. Multivariate models identified an optimal 18-gene diagnostic signature that predicted the presence of BCa with a sensitivity of 85% and a specificity of 88% (AUC 0.935). Analysis of mRNA signatures in naturally micturated urine samples can provide valuable information for the evaluation of patients under investigation for BCa. Additional refinement and validation of promising multi-target signatures will support the development of accurate assays for the non-invasive detection and monitoring of BCa.

Soluble human leukocyte antigen -G during pregnancy and infancy in Benin: Mother/child resemblance and association with the risk of malaria infection and low birth weight

Human leukocyte antigen (HLA) G is a tolerogenic molecule involved in the maternal-fetal immune tolerance phenomenon. Its expression during some infectious diseases leading to immune evasion has been established. A first study conducted in Benin has shown that the production of soluble HLA-G (sHLA-G) during the first months of life is strongly correlated with the maternal level at delivery and associated with low birth weight and malaria. However sHLA-G measurements during pregnancy were not available for mothers and furthermore, to date the evolution of sHLA-G in pregnancy is not documented in African populations. To extend these previous findings, between January 2010 and June 2013, 400 pregnant women of a malaria preventive trial and their newborns were followed up in Benin until the age of 2 years. Soluble HLA-G was measured 3 times during pregnancy and repeatedly during the 2 years follow-up to explore how sHLA-G evolved and the factors associated. During pregnancy, plasma levels of sHLA-G remained stable and increased significantly at delivery (p<0.001). Multigravid women seemed to have the highest levels (p = 0.039). In infants, the level was highest in cord blood and decreased before stabilizing after 18 months (p<0.001). For children, a high level of sHLA-G was associated with malaria infection during the follow-up (p = 0.02) and low birth weight (p = 0.06). The mean level of sHLA-G during infancy was strongly correlated with the mother’s level during pregnancy (<0.001), and not only at delivery. Moreover, mothers with placental malaria infection had a higher probability of giving birth to a child with a high level of sHLA-g (p = 0.006). High sHLA-G levels during pregnancy might be associated with immune tolerance related to placental malaria. Further studies are needed but this study provides a first insight concerning the potential role of sHLA-G as a biomarker of weakness for newborns and infants.

Estimating overall exposure effects for the clustered and censored outcome using random effect Tobit regression models

The random effect Tobit model is a regression model that accommodates both left- and/or right-censoring and within-cluster dependence of the outcome variable. Regression coefficients of random effect Tobit models have conditional interpretations on a constructed latent dependent variable and do not provide inference of overall exposure effects on the original outcome scale. Marginalized random effects model (MREM) permits likelihood-based estimation of marginal mean parameters for the clustered data. For random effect Tobit models, we extend the MREM to marginalize over both the random effects and the normal space and boundary components of the censored response to estimate overall exposure effects at population level. We also extend the 'Average Predicted Value' method to estimate the model-predicted marginal means for each person under different exposure status in a designated reference group by integrating over the random effects and then use the calculated difference to assess the overall exposure effect. The maximum likelihood estimation is proposed utilizing a quasi-Newton optimization algorithm with Gauss-Hermite quadrature to approximate the integration of the random effects. We use these methods to carefully analyze two real datasets. Copyright © 2016 John Wiley & Sons, Ltd.