Two-part Random Effects Research Articles

Urnal of Data Science 13(2015), 1-20 Assessing Effects of An Intervention on Bottle-Weaning and Reducing Daily Milk Intake from Bottles in Toddlers Using Two-Part Random Effects Models

urnal of Data Science 13(2015), 1-20 Assessing Effects of An Intervention on Bottle-Weaning and Reducing Daily Milk Intake from Bottles in Toddlers Using Two-Part Random Effects Models

Nonparametric Bayesian functional two-part random effects model for longitudinal semicontinuous data analysis.

Longitudinal semicontinuous data, characterized by repeated measures of a large portion of zeros and continuous positive values, are frequently encountered in many applications including biomedical, epidemiological, and social science studies. Two-part random effects models (TPREM) have been used to investigate the association between such longitudinal semicontinuous data and covariates accounting for the within-subject correlation. The existing TPREM is, however, limited to incorporate a functional covariate, which is often available in a longitudinal study. Moreover, the existing TPREM typically assumes the normality of subject-specific random effects, which can be easily violated when there exists a subgroup structure. In this article, we propose a nonparametric Bayesian functional TPREM to assess the relationship between the longitudinal semicontinuous outcome and various types of covariates including a functional covariate. The proposed model also relaxes the normality assumption for the random effects through a Dirichlet process mixture of normals, which allows for identifying an underlying subgroup structure. The methodology is illustrated through an application to social insurance expenditure data collected by the Korean Welfare Panel Study and a simulation study.

Risk factors of child mortality in Ethiopia: Application of multilevel two-part model

The child mortality rate is an essential measurement of socioeconomic growth and the quality of life in Ethiopia which is one among the six countries that account for half of the global under-five deaths. Therefore, this study aimed to identify the potential risk factors for child mortality in Ethiopia. Data for the study was drawn from the Ethiopian Demographic and Health Survey data conducted in 2016. A two-part random effects regression model was employed to identify the associated predictors of child mortality. The study found that 53.3% of mothers did not face any child death, while 46.7% lost at least one. Vaccinated child (IRR = 0.735, 95%CI: 0.647, 0.834), were currently using contraceptive (IRR = 0.885, 95%CI: 0.814, 0.962), who had antenatal care visit four or more times visit (IRR = 0.841, 95%CI: 0.737,0.960), fathers whose level of education is secondary or above(IRR = 0.695, 95%CI: 0.594, 0.814), mothers who completed their primary school(IRR = 0.785, 95%CI: 0.713, 0.864), mothers who have birth interval greater than 36 months (IRR = 0.728, 95%CI: 0.676, 0.783), where the age of the mother at first birth is greater than 16 years(IRR = 0.711, 95%CI: 0.674, 0.750) associated with the small number of child death. While multiple births (IRR = 1.355, 95%CI: 1.249, 1.471, four and above birth order (IRR = 1.487, 95%CI: 1.373, 1.612) and had working father (IRR = 1.125, 95%CI: 1.049, 1.206) associated with a higher number of child death. The variance components for the random effects showed significant variation of child mortality between enumeration areas. Policies and programs aimed at addressing enumeration area variations in child mortality need to be formulated and their implementation must be strongly pursued. Efforts are also needed to extend educational programmers aimed at educating mothers on the benefits of the antenatal checkup before first birth, spacing their birth interval, having their child vaccinated, and selecting a safe place of delivery to reduce child mortality.

Nonfarm employment and household food security: evidence from panel data for rural Cambodia

Nonfarm employment has been increasingly important in improving food security of rural households in the developing world. In this paper, we (1) determine the factors explaining the participation in nonfarm employment and nonfarm income of rural households by employing a two-part random effects econometric model, and (2) examine the effects of nonfarm employment on rural household food security indicators by combining the propensity score matching with the difference-in-differences approach. We used a panel dataset of 561 households in 30 villages of Stung Treng province in Cambodia collected in 2013 and 2014. Our sample was divided into two groups, households with nonfarm employment, and households without nonfarm employment. Our findings show that (1) nonfarm employment contributed about 32% to total annual household income for the whole sample and 57% for the households with nonfarm employment; (2) participation in nonfarm employment and nonfarm income were significantly influenced by the education level of household heads, numbers of motorbikes and mobile phones, conditions of roads to the villages, farmland size, number of income shocks, and the distance from home to the nearest market; (3) there was no significant difference in terms of food availability between households with and households without nonfarm employment but the former have improved food access, utilization, and stability. We suggest that promoting rural education, improving road conditions, and empowering rural households to cope with income shocks would contribute to developing nonfarm employment and consequently improve food security of rural households.

Grandparents' Financial Contributions to Grandchildren in Rural China: The Role of Remittances, Household Structure, and Patrilineal Culture.

This investigation examined predictors of monetary transfers made by grandparents for the benefit of their grandchildren in rural China. Predictors included family factors related to financial supply (remittances received from the parents of grandchildren), household demand (living in a skipped-generation household), and patrilineal culture (targeting sons and grandsons). The 2015 wave of the Longitudinal Study of Older Adults in Anhui Province was used to study financial transfers made by 831 grandparents to grandchildren in the families of 1,633 parents. Two-part random-effects regression was used to predict whether a transfer was made and the value of transfers, given that one occurred. Grandparents provided higher value transfers to grandchildren whose parents provided greater remittances and with whom they coresided in skipped-generation households. The likelihood of making a transfer fully followed the male lineage, and was greatest to grandson-only families in which parents were first-born sons. Results show that economic, household, and cultural factors are independently associated with the largesse of grandparents. We conclude that grandparents' economic contributions to grandchildren in rural China are shaped by family demands in a highly mobile society, intergenerational interdependence, and a persistent patrilineal gender system that reaches to the level of grandchildren.

A collection of marginalized two-part random-effects models for analyzing medical expenditure panel data: Impact of the New Cooperative Medical Scheme on healthcare expenditures in China

Marginalized two-part random-effects generalized Gamma models have been proposed for analyzing medical expenditure panel data with excessive zeros. While these models provide marginal inference on expected healthcare expenditures, the usual unilateral specification of heteroscedastic variance on one of the two shape parameters for the generalized Gamma distribution in these models fails to encompass important special cases within the generalized gamma modeling framework. In this article, we construct marginalized two-part random-effects models that employ the log-normal, log-skew-normal, generalized Gamma, Weibull, Gamma, and inverse Gamma distributions to delineate the spectrum of nonzero healthcare expenditures in the second part of the models. These marginalized models supply additional choices for analyzing healthcare expenditure panel data with excessive zeros. We review the concepts of marginal effect and incremental effect, and summarize how these effects are estimated. For studies whose primary goal is to make inference on marginal effect or incremental effect of an independent variable with respect to healthcare expenditures, we advocate empirical mean square error criterion and information criteria to choose among candidate models. Then, we use the proposed models in an empirical analysis to examine the impact of the New Cooperative Medical Scheme on healthcare expenditures among older adults in rural China.

Two-Part and Related Regression Models for Longitudinal Data.

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has been particular interest in the use of these models for the analysis of repeated measures of an outcome variable over time. The aim of this review is to consider motivations for the use of such models in this context and to highlight the central issues that arise with their use. We examine two-part models for semicontinuous and zero-heavy count data, and we also consider models for count data with a two-part random effects distribution.

Estimating marginal and incremental effects in the analysis of medical expenditure panel data using marginalized two-part random-effects generalized Gamma models: Evidence from China healthcare cost data.

Conditional two-part random-effects models have been proposed for the analysis of healthcare cost panel data that contain both zero costs from the non-users of healthcare facilities and positive costs from the users. These models have been extended to accommodate more flexible data structures when using the generalized Gamma distribution to model the positive healthcare expenditures. However, a major drawback with the extended model, which is inherited from the conditional models, is that it is fairly difficult to make direct marginal inference with respect to overall healthcare costs that includes both zeros and non-zeros, or even on positive healthcare costs. In this article, we first propose two types of marginalized two-part random-effects generalized Gamma models (m2RGGMs): Type I m2RGGMs for the inference on positive healthcare costs and Type II m2RGGMs for the inference on overall healthcare costs. Then, the concepts of marginal effect and incremental effect of a covariate on overall and positive healthcare costs are introduced, and estimation of these effects is carefully discussed. Especially, we derive the variance estimates of these effects by following the delta methods and Taylor series approximations for the purpose of making marginal inference. Parameter estimates of Type I and Type II m2RGGMs are obtained through maximum likelihood estimation. An empirical analysis of longitudinal healthcare costs collected in the China Health and Nutrition Survey is conducted using the proposed methodologies.

Estimation of intervention effect using paired interval-censored data with clumping below lower detection limit.

Outcome variables that are semicontinuous with clumping at zero are commonly seen in biomedical research. In addition, the outcome measurement is sometimes subject to interval censoring and a lower detection limit (LDL). This gives rise to interval-censored observations with clumping below the LDL. Level of antibody against influenza virus measured by the hemagglutination inhibition assay is an example. The interval censoring is due to the assay's technical procedure. The clumping below LDL is likely a result of the lack of prior exposure in some individuals such that they either have zero level of antibodies or do not have detectable level of antibodies. Given a pair of such measurements from the same subject at two time points, a binary 'fold-increase' endpoint can be defined according to the ratio of these two measurements, as it often is in vaccine clinical trials. The intervention effect or vaccine immunogenicity can be assessed by comparing the binary endpoint between groups of subjects given different vaccines or placebos. We introduce a two-part random effects model for modeling the paired interval-censored data with clumping below the LDL. Based on the estimated model parameters, we propose to use Monte Carlo approximation for estimation of the 'fold-increase' endpoint and the intervention effect. Bootstrapping is used for variance estimation. The performance of the proposed method is demonstrated by simulation. We analyze antibody data from an influenza vaccine trial for illustration.

Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany

Linear-mixed models are frequently used to obtain model-based estimators in small area estimation (SAE) problems. Such models, however, are not suitable when the target variable exhibits a point mass at zero, a highly skewed distribution of the nonzero values and a strong spatial structure. In this paper, a SAE approach for dealing with such variables is suggested. We propose a two-part random effects SAE model that includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of units. To account for the skewness of the distribution of the positive values of the response variable, a Gamma model is adopted. To fit the model, to get small area estimates and to evaluate their precision, a hierarchical Bayesian approach is used. The study is motivated by a real SAE problem. We focus on estimation of the per-farm average grape wine production in Tuscany, at subregional level, using the Farm Structure Survey data. Results from this real data application and those obtained by a model-based simulation experiment show a satisfactory performance of the suggested SAE approach.

A Bayesian Two Part Model Applied to Analyze Risk Factors of Adult Mortality with Application to Data from Namibia

Despite remarkable gains in life expectancy and declining mortality in the 21st century, in many places mostly in developing countries, adult mortality has increased in part due to HIV/AIDS or continued abject poverty levels. Moreover many factors including behavioural, socio-economic and demographic variables work simultaneously to impact on risk of mortality. Understanding risk factors of adult mortality is crucial towards designing appropriate public health interventions. In this paper we proposed a structured additive two-part random effects regression model for adult mortality data. Our proposal assumed two processes: (i) whether death occurred in the household (prevalence part), and (ii) number of reported deaths, if death did occur (severity part). The proposed model specification therefore consisted of two generalized linear mixed models (GLMM) with correlated random effects that permitted structured and unstructured spatial components at regional level. Specifically, the first part assumed a GLMM with a logistic link and the second part explored a count model following either a Poisson or negative binomial distribution. The model was used to analyse adult mortality data of 25,793 individuals from the 2006/2007 Namibian DHS data. Inference is based on the Bayesian framework with appropriate priors discussed.

Small Area Estimation for Zero-Inflated Data

The commonly used method of small area estimation (SAE) under a linear mixed model may not be efficient if data contain substantial proportion of zeros than would be expected under standard model assumptions (hereafter zero-inflated data). The authors discuss the SAE for zero-inflated data under a two-part random effects model that account for excess zeros in the data. Empirical results show that proposed method for SAE works well and produces an efficient set of small area estimates. An application to real survey data from the National Sample Survey Office of India demonstrates the satisfactory performance of the method. The authors describe a parametric bootstrap method to estimate the mean squared error (MSE) of the proposed estimator of small areas. The bootstrap estimates of the MSE are compared to the true MSE in simulation study.

Analyzing repeated measures semi-continuous data, with application to an alcohol dependence study

Two-part random effects models (Olsen and Schafer,(1) Tooze et al.(2)) have been applied to repeated measures of semi-continuous data, characterized by a mixture of a substantial proportion of zero values and a skewed distribution of positive values. In the original formulation of this model, the natural logarithm of the positive values is assumed to follow a normal distribution with a constant variance parameter. In this article, we review and consider three extensions of this model, allowing the positive values to follow (a) a generalized gamma distribution, (b) a log-skew-normal distribution, and (c) a normal distribution after the Box-Cox transformation. We allow for the possibility of heteroscedasticity. Maximum likelihood estimation is shown to be conveniently implemented in SAS Proc NLMIXED. The performance of the methods is compared through applications to daily drinking records in a secondary data analysis from a randomized controlled trial of topiramate for alcohol dependence treatment. We find that all three models provide a significantly better fit than the log-normal model, and there exists strong evidence for heteroscedasticity. We also compare the three models by the likelihood ratio tests for non-nested hypotheses (Vuong(3)). The results suggest that the generalized gamma distribution provides the best fit, though no statistically significant differences are found in pairwise model comparisons.

Two-part random effects growth modeling to identify risks associated with alcohol and cannabis initiation, initial average use and changes in drug consumption in a sample of adult, male twins

AimsOur aim was to profile alcohol and cannabis initiation and to characterize the effects of developmental and environmental risk factors on changes in average drug use over time. DesignWe fitted a two-part random effects growth model to identify developmental and environmental risks associated with alcohol and cannabis initiation, initial average use and changes in average use. Participants1796 males aged 24–63 from the Virginia Adult Twin Study of Psychiatric and Substance Use Disorders. MeasurementsData from three interview waves included self-report measures of average alcohol and cannabis use between ages 15 and 24, genetic risk of problem drug use, childhood environmental risks, personality, psychiatric symptoms, as well as personal, family and social risk factors. FindingsAverage alcohol and cannabis use were correlated at all ages. Genetic risk of drug use based on family history, higher sensation seeking, and peer group deviance predicted both alcohol and cannabis initiation. Higher drug availability predicted cannabis initiation while less parental monitoring and drug availability were the best predictors of how much cannabis individuals consumed over time. ConclusionThe liability to initiate alcohol and cannabis, average drug use as well as changes in drug use during teenage years and young adulthood is associated with known risk factors.

Analysis of zero-inflated clustered count data: A marginalized model approach

Min and Agresti (2005) proposed random effect hurdle models for zero-inflated clustered count data with two-part random effects for a binary component and a truncated count component. In this paper, we propose new marginalized models for zero-inflated clustered count data using random effects. The marginalized models are similar to Dobbie and Welsh’s ( 2001) model in which generalized estimating equations were exploited to find estimates. However, our proposed models are based on a likelihood-based approach. A Quasi-Newton algorithm is developed for estimation. We use these methods to carefully analyze two real datasets.

A Bayesian Two-Part Latent Class Model for Longitudinal Medical Expenditure Data: Assessing the Impact of Mental Health and Substance Abuse Parity

In 2001, the U.S. Office of Personnel Management required all health plans participating in the Federal Employees Health Benefits Program to offer mental health and substance abuse benefits on par with general medical benefits. The initial evaluation found that, on average, parity did not result in either large spending increases or increased service use over the four-year observational period. However, some groups of enrollees may have benefited from parity more than others. To address this question, we propose a Bayesian two-part latent class model to characterize the effect of parity on mental health use and expenditures. Within each class, we fit a two-part random effects model to separately model the probability of mental health or substance abuse use and mean spending trajectories among those having used services. The regression coefficients and random effect covariances vary across classes, thus permitting class-varying correlation structures between the two components of the model. Our analysis identified three classes of subjects: a group of low spenders that tended to be male, had relatively rare use of services, and decreased their spending pattern over time; a group of moderate spenders, primarily female, that had an increase in both use and mean spending after the introduction of parity; and a group of high spenders that tended to have chronic service use and constant spending patterns. By examining the joint 95% highest probability density regions of expected changes in use and spending for each class, we confirmed that parity had an impact only on the moderate spender class.

Effect of toltrazuril treatment in nursing piglets naturally infected with Isospora suis

Isospora suis is an important parasitic infection in intensive pig production worldwide, responsible for significant economic losses. In this study the efficacy of toltrazuril treatment against isosporosis was evaluated, under field conditions and throughout the nursing period, in reducing (i) the mean time to onset of diarrhoea and oocyst excretion, (ii) the odds of diarrhoea and, (iii) the odds and level of oocyst excretion, adjusting for the heterogeneity of I. suis infection among litters and across time. In a 300-sow farrow-to-finish commercial operation, twenty-five litters were randomly allocated to receive toltrazuril (thirteen litters) or no treatment (twelve litters). The course of infection was followed in all piglets by coprological examination from day 6 after farrowing until weaning. Parametric shared frailty models, generalised linear mixed models and a two-part random effects model were used in the analyses. Treated piglets had longer mean time to onset of oocyst excretion, lower odds of excreting oocysts and lower mean amount of excreted oocysts on any day during the nursing period. Diarrhoea was less likely to occur in treated piglets. Variance partition coefficients revealed that almost half of the variation in the odds of oocyst excretion and diarrhoea was ascribed to unknown or unmeasured factors that operate at higher than the piglet levels of aggregation. Thus, beyond toltrazuril treatment, control of isosporosis in commercial pig farms can be improved by identification and quantification of these factors.

A flexible two-part random effects model for correlated medical costs

In this paper, we propose a flexible “two-part” random effects model ( Olsen and Schafer, 2001; Tooze et al., 2002) for correlated medical cost data. Typically, medical cost data are right-skewed, involve a substantial proportion of zero values, and may exhibit heteroscedasticity. In many cases, such data are also obtained in hierarchical form, e.g., on patients served by the same physician. The proposed model specification therefore consists of two generalized linear mixed models (GLMM), linked together by correlated random effects. Respectively, and conditionally on the random effects and covariates, we model the odds of cost being positive (Part I) using a GLMM with a logistic link and the mean cost (Part II) given that costs were actually incurred using a generalized gamma regression model with random effects and a scale parameter that is allowed to depend on covariates (cf., Manning et al., 2005). The class of generalized gamma distributions is very flexible and includes the lognormal, gamma, inverse gamma and Weibull distributions as special cases. We demonstrate how to carry out estimation using the Gaussian quadrature techniques conveniently implemented in SAS Proc NLMIXED. The proposed model is used to analyze pharmacy cost data on 56,245 adult patients clustered within 239 physicians in a mid-western U.S. managed care organization.

Influence of smoking and alcohol consumption on admissions and duration of hospitalization

Previous studies have linked smoking and alcohol consumption to a considerable disease burden and large healthcare expenditures. However, findings from studies based on individual level data are sparse and inconclusive. Our objective was to assess the association between alcohol consumption, smoking and patterns of hospitalization, defined as admission and duration of hospitalization. The study was based on 12 698 men and women, aged 20 years or more, enrolled in the Copenhagen City Heart Study. We related smoking and alcohol to hospital admission from any cause, smoking- and alcohol-related diseases and duration of hospitalization in a two-part random effects model. Smoking status was strongly associated with admission and duration of hospitalization. For smoking-related admissions, odds ratios (OR) of 2.77 (95% CI 2.13-3.59) in men and 6.30 (95% CI 4.80-8.26) in women were observed among smokers of >20 g/day compared to never-smokers. For any admission (excl. smoking-related causes), corresponding ORs were 1.32 (95% CI 1.15-1.51) and 1.80 (95% CI 1.58-2.06), respectively. In men, a U-shaped association between alcohol consumption and risk of admission was found, both regarding any admission and admissions due to alcohol-related diseases. Alcohol was associated with alcohol-related admissions in women but not with duration of hospitalization. Smoking was associated with increased risk of hospital admission and duration of hospitalization. A U-shaped relation was observed for alcohol consumption and risk of hospitalization in men, but no effect on duration was observed. In women, however, alcohol consumption was only vaguely associated with admission and duration of hospitalization.

Growth in alcohol use in at-risk adolescent boys: Two-part random effects prediction models

Background Alcohol use frequently onsets and shows rapid growth during the adolescent years, but few studies have examined growth in two indicators, namely in use and in volume given use, with prediction from key risk factors measured across the adolescent years. Methods Based on a dynamic developmental systems framework, we predicted that the general risk pathway associated with the development of antisocial behavior (namely poor parental practices and antisocial behavior/deviant peer association) would be associated with both indicators of use in Grade 6. Specific proximal social influences, namely alcohol use by parents and peers, were also hypothesized, with growth in peer use of alcohol expected to be predictive of growth. Predictors were assessed by youth, parent, and teacher reports, with alcohol use and volume assessed yearly by youth self-reports. Models were tested separately for the 3-year middle school period and the 4-year high school period. Hypotheses were tested for the Oregon Youth Study sample of approximately 200 at-risk boys. Results Findings indicated that alcohol use by both parents and peers were associated with initial levels of alcohol use and volume, but increases in peer use predicted growth in these indicators. Parental monitoring showed a protective effect on growth in volume in high school. Conclusion Alcohol use by members of the adolescent's social network is critical to initiation of use, and peer use is critical to growth. With these predictors specific to alcohol use in the model, none of the general risk factors for antisocial behavior were significant.