Diagnostics for regression models with semicontinuous outcomes.

Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely employed to understand the relationship between semicontinuous outcomes and covariates. Given the potential detrimental consequences of model misspecification, after fitting a regression model, it is of prime importance to check the adequacy of the model. However, due to the point mass at zero, standard diagnostic tools for regression models (eg, deviance and Pearson residuals) are not informative for semicontinuous data. To bridge this gap, we propose a new type of residuals for semicontinuous outcomes that is applicable to general regression models. Under the correctly specified model, the proposed residuals converge to being uniformly distributed, and when the model is misspecified, they significantly depart from this pattern. In addition to in-sample validation, the proposed methodology can also be employed to evaluate predictive distributions. We demonstrate the effectiveness of the proposed tool using health expenditure data from the US Medical Expenditure Panel Survey.

Understanding Pathways into Care-homes using Data (UnPiCD study): a two-part model to estimate inpatient and care-home costs using national linked health and social care data.

BACKGROUND: Pathways into care-homes have been under-researched. Individuals who move-in to a care-home from hospital are clinically distinct from those moving-in from the community. However, it remains unclear whether the source of care-home admission has any implications in term of costs. Our aim was to quantify hospital and care-home costs for individuals newly moving-in to care homes to compare those moving-in from hospital to those moving-in from the community. METHODS: Using routinely-collected national social care and health data we constructed a cohort including people moving into care-homes from hospital and community settings between 01/04/2013-31/03/2015 based on records from the Scottish Care-Home Census (SCHC). Individual-level data were obtained from Scottish Morbidity Records (SMR01/04/50) and death records from National Records of Scotland (NRS). Unit costs were identified from NHS Scotland costs data and care-home costs from the SCHC. We used a two-part model to estimate costs conditional on having incurred positive costs. Additional analyses estimated differences in costs for the one-year period preceding and following care-home admission. RESULTS: We included 14,877 individuals moving-in to a care-home, 8,472 (57%) from hospital, and 6,405 (43%) from the community. Individuals moving-in to care-homes from the community incurred higher costs at £27,117 (95% CI £ 26,641 to £ 27,594) than those moving-in from hospital with £24,426 (95% CI £ 24,037 to £ 24,814). Hospital costs incurred during the year preceding care-home admission were substantially higher (£8,323 (95% CI£8,168 to £8,477) compared to those incurred after moving-in to care-home (£1,670 (95% CI£1,591 to £1,750). CONCLUSION: Individuals moving-in from hospital and community have different needs, and this is reflected in the difference in costs incurred. The reduction in hospital costs in the year after moving-in to a care-home indicates the positive contribution of care-home residency in supporting those with complex needs. These data provide an important contribution to inform capacity planning on care provision for adults with complex needs and the costs of care provision.

Two-part joint model for a longitudinal semicontinuous marker and a terminal event with application to metastatic colorectal cancer data.

Joint models for a longitudinal biomarker and a terminal event have gained interests for evaluating cancer clinical trials because the tumor evolution reflects directly the state of the disease. A biomarker characterizing the tumor size evolution over time can be highly informative for assessing treatment options and could be taken into account in addition to the survival time. The biomarker often has a semicontinuous distribution, i.e., it is zero inflated and right skewed. An appropriate model is needed for the longitudinal biomarker as well as an association structure with the survival outcome. In this article, we propose a joint model for a longitudinal semicontinuous biomarker and a survival time. The semicontinuous nature of the longitudinal biomarker is specified by a two-part model, which splits its distribution into a binary outcome (first part) represented by the positive versus zero values and a continuous outcome (second part) with the positive values only. Survival times are modeled with a proportional hazards model for which we propose three association structures with the biomarker. Our simulation studies show some bias can arise in the parameter estimates when the semicontinuous nature of the biomarker is ignored, assuming the true model is a two-part model. An application to advanced metastatic colorectal cancer data from the GERCOR study is performed where our two-part model is compared to one-part joint models. Our results show that treatment arm B (FOLFOX6/FOLFIRI) is associated to higher SLD values over time and its positive association with the terminal event leads to an increased risk of death compared to treatment arm A (FOLFIRI/FOLFOX6).

Heterogeneous effects of other-regarding interventions on household recycling: A field experimental study.

Behavioral interventions that address other-regarding motivations (i.e., other-regarding interventions) are gaining momentum as promising tools to stimulate household recycling. However, previous studies have shown considerable variability in the impact of such strategies, and the factors that moderate treatment effects remain poorly studied. Using a field experiment with 7195 households in Quzhou, China, this study investigated treatment effect heterogeneity systematically based on intervention types, treatment durations, personal motivations, and social networks. Three strategies were examined, including biospheric and altruistic appeals and personalized normative feedback. We found that normative feedback outperformed other strategies in inducing household participation in recycling, that the influences of all strategies attenuated over time, and that the feedback effect was greater among recipients with weaker biospheric or altruistic concerns and those embedded within stronger neighbor networks. However, no significant treatment effects were found on the amount of waste recycled. These findings improve the understanding of the heterogeneous impact of other-regarding interventions, with important implications for the design of recycling policies. Future studies need to explore additional moderators and the effects of treatment combinations.

Production loss and sick leave caused by antibiotic resistance: a register-based cohort study.

BACKGROUND: Adverse economic consequences of antibiotic resistance, both in health care systems and in society at large, have been estimated to emerge and significantly affect the global economy. To date, most studies of the societal costs of antibiotic resistance have had a macroeconomic perspective, using the number of attributable deaths as a quantifier for production loss. In contrast, there have been few studies of the consequences of antibiotic resistance in terms of the length of sick leave and hence the impact of morbidity on production loss. The aim of our study was to estimate the production loss from ill health caused by antibiotic resistance. METHOD: To estimate additional production loss due to antibiotic resistance, we used Swedish register-based cohort data to determine days of long-term sick leave (LTSL) for episodes of infection caused by resistant and susceptible bacteria respectively. We collected patient data for four common infection types (bloodstream infection, urinary tract infection, skin and soft tissue infection, and pneumonia), as well as, antibiotic susceptibility test data, and total days of LTSL. We used a two-part model to estimate the number of LTSL days attributable to resistance, and controlled for comorbidities and demographic variables such as age and gender. RESULTS: The results show that antibiotic resistance adds an additional 8.19 days of LTSL compared with a similar infection caused by susceptible bacteria, independent of infection type and resistance type. Furthermore, the results suggest that production loss due to temporary sick leave caused by antibiotic resistance in a working-age population amounts to about 7% of total health care costs attributable to antibiotic resistance in Sweden. CONCLUSION: Estimating the effect of antibiotic resistance in terms of temporary production loss is important to gain a better understanding of the economic consequences of antibiotic resistance in society and, by extension, enable more effective resource allocation to combat further emergence of resistance. Society's economic costs of antibiotic resistance are, however, probably much greater than those of sick leave due to disease alone.

How to analyze work productivity loss due to health problems in randomized controlled trials? A simulation study.

BACKGROUND: An increasing number of randomized controlled trials (RCTs) have measured the impact of interventions on work productivity loss. Productivity loss outcome is inflated at zero and max loss values. Our study was to compare the performance of five commonly used methods in analysis of productivity loss outcomes in RCTs. METHODS: We conducted a simulation study to compare Ordinary Least Squares (OLS), Negative Binominal (NB), two-part models (the non-zero part following truncated NB distribution or gamma distribution) and three-part model (the middle part between zero and max values following Beta distribution). The main number of observations each arm, Nobs, that we considered were 50, 100 and 200. Baseline productivity loss was included as a covariate. RESULTS: All models performed similarly well when baseline productivity loss was set at the mean value. When baseline productivity loss was set at other values and Nobs = 50 with ≤5 subjects having max loss, two-part models performed best if the proportion of zero loss> 50% in at least one arm and otherwise, OLS performed best. When Nobs = 100 or 200, the three-part model performed best if the two arms had equal scale parameters for their productivity loss outcome distributions between zero and max values. CONCLUSIONS: Our findings suggest that when treatment effect at any given values of one single covariate is of interest, the model selection depends on the sample size, the proportions of zero loss and max loss, and the scale parameter for the productivity loss outcome distribution between zero and max loss in each arm of RCTs.

Household expenditure for immunization among children in India: a two-part model approach.

BACKGROUND: Despite the Indian government's Universal Immunization Program (UIP), the progress of full immunization coverage is plodding. The cost of delivering routine immunization varies widely across facilities within country and across country. However, the cost an individual bears on child immunization has not been focussed. In this context, this study tries to estimate the expenditure on immunization which an individual bears and the factors affecting immunization coverage at the regional level. METHODS: Using the 75th round of National Sample Survey Organization data, the present paper attempts to check the individual expenditure on immunization and the factors affecting immunization coverage at the regional level. Descriptive statistics and multivariate regression analysis were used to fulfil the study objectives. The two-part model has been employed to inspect the determinants of expenditure on immunization. RESULTS: The overall prevalence of full immunization was 59.3 % in India. Full immunization was highest in Manipur (75.2 %) and lowest in Nagaland (12.8 %). The mean expenditure incurred on immunization varies from as low as Rs. 32.7 in Tripura to as high as Rs. 1008 in Delhi. Children belonging to the urban area [OR: 1.04; CI: 1.035, 1.037] and richer wealth quintile [OR: 1.14; CI: 1.134-1.137] had higher odds of getting immunization. Moreover, expenditure on immunization was high among children from the urban area [Rs. 273], rich wealth quintile [Rs. 297] and who got immunized in a private facility [Rs. 1656]. CONCLUSIONS: There exists regional inequality in immunization coverage as well as in expenditure incurred on immunization. Based on the findings, we suggest looking for the supply through follow-up and demand through spreading awareness through mass media for immunization.

Assessing Drivers' Trust of Automated Vehicle Driving Styles With a Two-Part Mixed Model of Intervention Tendency and Magnitude.

OBJECTIVE: This study examines how driving styles of fully automated vehicles affect drivers' trust using a statistical technique-the two-part mixed model-that considers the frequency and magnitude of drivers' interventions. BACKGROUND: Adoption of fully automated vehicles depends on how people accept and trust them, and the vehicle's driving style might have an important influence. METHOD: A driving simulator experiment exposed participants to a fully automated vehicle with three driving styles (aggressive, moderate, and conservative) across four intersection types (with and without a stop sign and with and without crossing path traffic). Drivers indicated their dissatisfaction with the automation by depressing the brake or accelerator pedals. A two-part mixed model examined how automation style, intersection type, and the distance between the automation's driving style and the person's driving style affected the frequency and magnitude of their pedal depression. RESULTS: The conservative automated driving style increased the frequency and magnitude of accelerator pedal inputs; conversely, the aggressive style increased the frequency and magnitude of brake pedal inputs. The two-part mixed model showed a similar pattern for the factors influencing driver response, but the distance between driving styles affected how often the brake pedal was pressed, but it had little effect on how much it was pressed. CONCLUSION: Eliciting brake and accelerator pedal responses provides a temporally precise indicator of drivers' trust of automated driving styles, and the two-part model considers both the discrete and continuous characteristics of this indicator. APPLICATION: We offer a measure and method for assessing driving styles.

A model-based approach for clustering of multivariate semicontinuous data with application to dietary pattern analysis and intervention.

Semicontinuous data, characterized by a sizable number of zeros and observations from a continuous distribution, are frequently encountered in health research concerning food consumptions, physical activities, medical and pharmacy claims expenditures, and many others. In analyzing such semicontinuous data, it is imperative that the excessive zeros be adequately accounted for to obtain unbiased and efficient inference. Although many methods have been proposed in the literature for the modeling and analysis of semicontinuous data, little attention has been given to clustering of semicontinuous data to identify important patterns that could be indicative of certain health outcomes or intervention effects. We propose a Bernoulli-normal mixture model for clustering of multivariate semicontinuous data and demonstrate its accuracy as compared to the well-known clustering method with the conventional normal mixture model. The proposed method is illustrated with data from a dietary intervention trial to promote healthy eating behavior among children with type 1 diabetes. In the trial, certain diabetes friendly foods (eg, total fruit, whole fruit, dark green and orange vegetables and legumes, whole grain) were only consumed by a proportion of study participants, yielding excessive zero values due to nonconsumption of the foods. Baseline foods consumptions data in the trial are used to explore preintervention dietary patterns among study participants. While the conventional normal mixture model approach fails to do so, the proposed Bernoulli-normal mixture model approach has shown to be able to identify a dietary profile that significantly differentiates the intervention effects from others, as measured by the popular healthy eating index at the end of the trial.

Association of household income with home-based rehabilitation and home help service utilization among long-term home care service users.

BACKGROUND: To examine the association of household income with home-based rehabilitation and home help services in terms of service utilization and expenditures. METHODS: A secondary data analysis of cross-sectional design was conducted using long-term care (LTC) insurance claims data, medical claims data, and three types of administrative data. The subjects comprised LTC insurance beneficiaries in Kashiwa city, Japan, who used long-term home care services in the month following care needs certification. Household income was the independent variable of interest, and beneficiaries were categorized into low-income or middle/high-income groups based on their insurance premiums. Using a two-part model, the odds ratios (ORs) and 95% confidence intervals (CIs) for the utilization of home-based rehabilitation and home help services in the month following care needs certification were estimated using logistic regression analysis, and the risk ratios (RRs) of service expenditures were estimated using a generalized linear model for gamma-distributed data with a log-link function. RESULTS: Among 3770 subjects, 681 (18.1%) used home-based rehabilitation and 1163 (30.8%) used home help services. There were 1419 (37.6%) low-income subjects, who were significantly less likely to use (OR: 0.813; 95%CI: 0.670-0.987) and spend on (RR: 0.910; 95%CI: 0.829-0.999) home-based rehabilitation services than middle/high-income subjects. Conversely, low-income subjects were significantly more likely to use (OR: 1.432; 95%CI: 1.232-1.664) but less likely to spend on (RR: 0.888; 95%CI: 0.799-0.986) home help services than middle/high-income subjects. CONCLUSION: Household income was associated with the utilization of long-term home care services. To improve access to these services, the LTC insurance system should examine ways to decrease the financial burden of low-income beneficiaries and encourage service utilization.

What contributes to medical debt? Evidence from patients in rural China.

BACKGROUND: Rural households in developing countries usually have severe medical debt due to high out-of-pocket (OOP) payments, which contributes to bankruptcy. China implemented the critical illness insurance (CII) in 2012 to decrease patients' medical expenditure. This paper aimed to explore the medical debt of rural Chinese patients and its influencing factors. METHODS: A questionnaire survey of health expenditures and medical debt was conducted in two counties of Central and Western China in 2017. Patients who received CII were used as the sample on the basis of multi-stage stratified cluster sampling. Descriptive statistics and multivariate analysis of variance were used in all data. A two-part model was used to evaluate the occurrence and extent of medical debt. RESULTS: A total of 826 rural patients with CII were surveyed. The percentages of patients incurring medical debt exceeded 50% and the median debt load was 20,000 Chinese yuan (CNY, 650 CNY = US$100). Financial assistance from kin (P < 0.001) decreased the likelihood of medical debt. High inpatient expenses (IEs, P < 0.01), CII reimbursement ratio (P < 0.001), and non-direct medical costs (P < 0.001) resulted in increased medical debt load. CONCLUSIONS: Medical debt is still one of the biggest problems in rural China. High IEs, CII reimbursement ratio, municipal or high-level hospitals were the risk determinants of medical debt load. Financial assistance from kin and household income were the protective factors. Increasing service capability of hospitals in counties could leave more patiemts in county-level and township hospitals. Improving CII with increased reimbursement rate may also be issues of concern.

The Winners and the Losers: Tax Incidence of Gambling in Finland.

Gambling markets have grown rapidly for the last few decades. As a result, gambling is also a very important and common source of tax income for many governments these days. This raises a question about the overall fairness of the gambling taxation systems. In this paper, we aim to study the tax incidence of gambling in Finland. First, we analyse who are the expected payers of the gambling taxes and second, who are expected to be the receivers of the gambling-tax based contributions. In the first part of the study, we analyse the demographic incidence of gambling taxation by using the Finnish gambling 2015 population survey combined with registry based variables. Our data contains 3776 individuals. In the second part of the study, we use data of county level gambling-taxation based contributions to different organisations to analyse how the gambling expenditures are distributed back to citizens in a form of public spending. This study shows that different socio-demographic factors have diverse association with the decisions whether or how much to gamble. The results also suggest that more disadvantaged, i.e. lower income, less educated and rural area living, individuals are expected to be the "losers" of the Finnish gambling taxation system. In other words, the Finnish gambling system is found to be regressive by nature.

Analysis of longitudinal semicontinuous data using marginalized two-part model.

BACKGROUND: Connective tissue growth factor (CTGF), is a secreted matricellular factor that has been linked to increased risk of cardiovascular disease in diabetic subjects. Despite the biological role of CTGF in diabetes, it still remains unclear how CTGF expression is regulated. In this study, we aim to identify the clinical parameters that modulate plasma CTGF levels measured longitudinally in type 1 diabetic patients over a period of 10 years. A number of patients had negligible measured values of plasma CTGF that formed a point mass at zero, whereas others had high positive values of CTGF that were measured on a continuous scale. The observed combination of excessive zero and continuous positively distributed non-zero values in the CTGF outcome is referred to as semicontinuous data. METHODS: We propose a novel application of a marginalized two-part model (mTP) extended to accommodate longitudinal semicontinuous data in which the marginal mean is expressed in terms of the covariates and estimates of their effect on the mean responses are generated. The continuous component is assumed to follow distributions that stem from the generalized gamma family whereas the binary measure is analyzed using logistic model and both have correlated random effects. Other approaches including the one- and two-part with uncorrelated and correlated random effects models were also applied and their estimates were all compared. RESULTS: Our results using the mTP model identified intensive glucose control treatment and smoking as clinical factors that were associated with decreased and increased odds of observing non-zero CTGF values respectively. In addition, hemoglobin A1c, systolic blood pressure, and high density lipoprotein were all shown to be significant risk factors that contribute to increasing CTGF levels. These findings were consistently observed under the mTP model but varied with the distributions for the other models. Accuracy and precision of the mTP model was further validated using simulation studies. CONCLUSION: The mTP model identified new clinical determinants that modulate the levels of CTGF in diabetic subjects. Applicability of this approach can be extended to other biomarkers measured in patient populations that display a combination of negligible zero and non-zero values.

Determinants of cigarette smoking and smoking intensity among adult males in Ghana.

BACKGROUND: In spite of the adverse health and financial implications of smoking, it still remains one of the leading causes of preventable diseases and deaths in the world. Key to discouraging the habit of smoking is knowledge of the drivers of smoking. In Ghana, though smoking behaviours are relatively more associated with adult males than youth and adolescents, studies on smoking behaviours of adult males are scant. This study, therefore, investigates the determinants of cigarette smoking and smoking intensity among adult males in Ghana. METHODS: Data were obtained from the most recent Ghana Demographic and Health Survey (DHS) conducted in 2014. Based on the 2014 GDHS, a negative binomial-logit hurdle model was estimated to explore the socioeconomic and demographic characteristics associated with cigarette consumption and smoking intensity among adult males in Ghana. To ensure robustness, separate estimations were performed for the respective logit and negative binomial models used in the two-part model. RESULTS: We find that men in lower socioeconomic category (poor and low education) have a higher likelihood to smoke. Also, age proved significant in explaining smoking behaviors in Ghana. Moreover, religion and region of residence are reported to affect cigarette consumption decision. Furthermore, we find that among the men who smoke, those between the ages of 44 and 60 years and have attained approximately primary education have a higher likelihood to smoke greater quantities of cigarette daily. Also, the smokers who reside in the Upper East and Upper West regions are reported to smoke more intensely than their counterparts in the Greater Accra region. CONCLUSION: Since smoking remains one of the major causes of diseases and deaths the world over, the current study provides recent empirical evidence based on a nationally representative sample for public health policies geared towards smoking reduction and ultimately cessation. This study suggests that public policies that promote higher educational attainment and improved incomes (wealth) are crucial in smoking reduction and cessation in Ghana.

Joint modeling of zero-inflated panel count and severity outcomes.

Panel counts are often encountered in longitudinal, such as diary, studies where individuals are followed over time and the number of events occurring in time intervals, or panels, is recorded. This article develops methods for situations where, in addition to the counts of events, a mark, denoting a measure of severity of the events, is recorded. In many situations there is an association between the panel counts and their marks. This is the case for our motivating application that studies the effect of two hormone therapy treatments in reducing counts and severities of vasomotor symptoms in women after hysterectomy/ovariectomy. We model the event counts and their severities jointly through the use of shared random effects. We also compare, through simulation, the power of testing for the treatment effect based on such joint modeling and an alternative scoring approach, which is commonly employed. The scoring approach analyzes the compound outcome of counts times weighted severity. We discuss this approach and quantify challenges which may arise in isolating the treatment effect when such a scoring approach is used. We also show that the power of detecting a treatment effect is higher when using the joint model than analysis using the scoring approach. Inference is performed via Markov chain Monte Carlo methods.

Two-year post-discharge costs of care among patients treated with transcatheter or surgical aortic valve replacement in Germany.

BACKGROUND: This study presents data on post-discharge costs of care among patients treated with transcatheter or surgical aortic valve replacement over a two year period. METHODS: Based on a prospective clinical trial, post-discharge utilization of health services and status of assistance were collected for 151 elderly patients via 2250 monthly telephone interviews, valued using standardized unit costs and analysed using two-part regression models. RESULTS: At month 1 post-discharge, total costs of care are substantially elevated (monthly mean: €3506.7) and then remain relatively stable over the following 23 months (monthly mean: €622.3). As expected, the majority of these costs are related to in-hospital care (~98% in month 1 post-discharge and ~72% in months 2-24). Patients that died during follow-up were associated with substantially higher cost estimates of in-hospital care than those surviving the two-year study period, while patients' age and other patient characteristics were of minor relevance. Estimated costs of outpatient care are lower at month 1 than during the rest of the study period, and not affected by the event of death during follow-up. The estimated costs of nursing care are, in contrast, much higher in year 2 than in year 1 and differ substantially by gender and type of procedure as well as by patients' age. Overall, these monthly cost estimates add up to €10,352 for the first and €7467.6 for the second year post-discharge. CONCLUSIONS: Substantial cost increases at month 1 post-discharge and in case of death during follow-up are the main findings of the study, which should be taken into account in future economic evaluations on the topic. Application of standardized unit costs in combination with monthly patient interviews allows for a far more precise estimate of the variability in post-discharge health service utilization in this group of patients than the ones given in previous studies. TRIAL REGISTRATION: German Clinical Trial Register Nr. DRKS00000797 .

Estimating the prevalence of atrial fibrillation from a three-class mixture model for repeated diagnoses.

Atrial fibrillation (AF) is an abnormal heart rhythm characterized by rapid and irregular heartbeat, with or without perceivable symptoms. In clinical practice, the electrocardiogram (ECG) is often used for diagnosis of AF. Since the AF often arrives as recurrent episodes of varying frequency and duration and only the episodes that occur at the time of ECG can be detected, the AF is often underdiagnosed when a limited number of repeated ECGs are used. In studies evaluating the efficacy of AF ablation surgery, each patient undergoes multiple ECGs and the AF status at the time of ECG is recorded. The objective of this paper is to estimate the marginal proportions of patients with or without AF in a population, which are important measures of the efficacy of the treatment. The underdiagnosis problem is addressed by a three-class mixture regression model in which a patient's probability of having no AF, paroxysmal AF, and permanent AF is modeled by auxiliary baseline covariates in a nested logistic regression. A binomial regression model is specified conditional on a subject being in the paroxysmal AF group. The model parameters are estimated by the Expectation-Maximization (EM) algorithm. These parameters are themselves nuisance parameters for the purpose of this research, but the estimators of the marginal proportions of interest can be expressed as functions of the data and these nuisance parameters and their variances can be estimated by the sandwich method. We examine the performance of the proposed methodology in simulations and two real data applications.

[Medical cost attributable to hypertension among Chinese middle and old aged residents in 2011].

OBJECTIVE: To measure and calculate the medical cost attributable to hypertension among Chinese middle and old aged residents in 12 provinces( city or region)in 2011. METHODS: The data were collected in 2011 from China Health and Nutrition Survey. The sample was 45 years old and over of health male and female residents. To estimate the probability of medical usage and medical expenditure, and calculate the medical cost attributable to hypertension. RESULTS: The results showed that, in 2011, the estimate predict that the per capita medical expenditure for a single medical event was246. 8 yuan, the medical cost attributable to hypertension was 21. 2 yuan, which amounted to 8. 6% of the total personal medical cost. Hypertension showed a positive effect on the probability of medical usage to a large extent. Female respondents had lower medical cost. New Rural Cooperative Medical Scheme was linked with higher medical expenditure and the medical cost was higher in the north. CONCLUSION: To some extent, the probability of medical usage and medical expenditure are affected by hypertension. The whole society, families and individuals may also have certain economic burden due to hypertension.

Bayesian two-part spatial models for semicontinuous data with application to emergency department expenditures.

In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero and a continuous distribution of positive values. Examples include medical expenditures, in which the zeros represent patients who do not use health services, while the continuous distribution describes the level of expenditures among users. Semicontinuous data are customarily analyzed using two-part mixture models. In the spatial analysis of semicontinuous data, two-part models are especially appealing because they provide a joint picture of how health services utilization and associated expenditures vary across geographic regions. However, when applying these models, careful attention must be paid to distributional choices, as model misspecification can lead to biased and imprecise inferences. This paper introduces a broad class of Bayesian two-part models for the spatial analysis of semicontinuous data. Specific models considered include two-part lognormal, log skew-elliptical, and Bayesian non-parametric models. Multivariate conditionally autoregressive priors are used to link model components and provide spatial smoothing across neighboring regions, resulting in a joint spatial modeling framework for health utilization and expenditures. We develop a fully conjugate Gibbs sampling scheme, leading to efficient posterior computation. We illustrate the approach using data from a recent study of emergency department expenditures.

Modeling zero-modified count and semicontinuous data in health services research Part 1: background and overview.

Health services data often contain a high proportion of zeros. In studies examining patient hospitalization rates, for instance, many patients will have no hospitalizations, resulting in a count of zero. When the number of zeros is greater or less than expected under a standard count model, the data are said to be zero modified relative to the standard model. A similar phenomenon arises with semicontinuous data, which are characterized by a spike at zero followed by a continuous distribution with positive support. When analyzing zero-modified count and semicontinuous data, flexible mixture distributions are often needed to accommodate both the excess zeros and the typically skewed distribution of nonzero values. Various models have been introduced over the past three decades to accommodate such data, including hurdle models, zero-inflated models, and two-part semicontinuous models. This tutorial describes recent modeling strategies for zero-modified count and semicontinuous data and highlights their role in health services research studies. Part 1 of the tutorial, presented here, provides a general overview of the topic. Part 2, appearing as a companion piece in this issue of Statistics in Medicine, discusses three case studies illustrating applications of the methods to health services research. Copyright © 2016 John Wiley & Sons, Ltd.