Cost-effectiveness of proton beam therapy vs. conventional radiotherapy for patients with brain tumors in Sweden: results from a non-randomized prospective multicenter study.

BACKGROUND: This study assessed the cost-effectiveness of proton beam therapy (PBT) compared to conventional radiotherapy (CRT) for treating patients with brain tumors in Sweden. METHODS: Data from a longitudinal non-randomized study performed between 2015 and 2020 was used, and included adult patients with brain tumors, followed during treatment and through a one-year follow-up. Clinical and demographic data were sourced from the longitudinal study and linked to Swedish national registers to get information on healthcare resource use. A cost-utility framework was used to evaluate the cost-effectiveness of PBT vs. CRT. Patients in PBT group (n = 310) were matched with patients in CRT group (n = 40) on relevant observables using propensity score matching with replacement. Costs were estimated from a healthcare perspective and included costs related to inpatient and specialized outpatient care, and prescribed medications. The health outcome was quality-adjusted life-years (QALYs), derived from the EORTC-QLQ-C30. Generalized linear models (GLM) and two-part models were used to estimate differences in costs and QALYs. RESULTS: PBT yielded higher total costs, 14,639 US$, than CRT, 13,308 US$, with a difference of 1,372 US$ (95% CI, -4,914-7,659) over a 58 weeks' time horizon. Further, PBT resulted in non-significantly lower QALYs, 0.746 compared to CRT, 0.774, with a difference of -0.049 (95% CI, -0.195-0.097). The probability of PBT being cost-effective was < 30% at any willingness to pay. CONCLUSIONS: These results suggest that PBT cannot be considered a cost-effective treatment for brain tumours, compared to CRT. TRIAL REGISTRATION: Not applicable.

Healthcare expenditures for people with substance use disorders in drug courts compared to their peers in traditional courts.

Individuals within the criminal justice system are at greater risk of substance use-related morbidity and mortality and have substantial healthcare needs. In this quasi-experimental study, we assessed utilization patterns of Massachusetts Medicaid Program (MassHealth) services and associated expenditures among drug court probationers compared to a propensity score-matched sample of traditional court probationers. Risk of reoffending, employment status, age, and living arrangement data were used to calculate propensity scores and match probationers between the two court types, producing a final sample of 271 in each court (N=542). Utilization of services and associated expenditures were analyzed using a two-part model to address the skewed distribution of the data and to control for residual differences after matching from the perspective of the payer (i.e., MassHealth). The largest categories of MassHealth spending were prescription pharmaceuticals, hospital inpatient visits, and physician visits. In the unadjusted analysis, drug court probationers exhibited greater MassHealth services utilization and expenditures than traditional court probationers. However, drug courts enrolled more females, more people at higher risk of reoffending, and more people with opioid use disorders. After controlling for differences between the two court types, the difference in MassHealth services utilization and associated expenditures did not reach statistical significance. Drug court probationers were more likely to engage with healthcare services but did not incur significantly greater expenditures than traditional court probationers after controlling for differences between the samples.

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.

Assessing adult physical activity and compliance with 2008 CDC guidelines using a Bayesian two-part measurement error model.

While there is wide agreement that physical activity is an important component of a healthy lifestyle, it is unclear how many people adhere to public health recommendations on physical activity. The Physical Activity Guidelines (PAG), published by the CDC, provides guidelines to American adults, but it is difficult to assess compliance with these guidelines. The PAG further complicates adherence assessment by recommending activity to occur in at least 10 min bouts. To better understand the measurement capabilities of various instruments to quantify activity, and to propose an approach to evaluate activity relative to the PAG, researchers at Iowa State University administered the Physical Activity Measurement Survey (PAMS) to over 1000 participants in four different Iowa counties. In this paper, we develop a two-part Bayesian measurement error model and apply it to the PAMS data in order to assess compliance with the PAG in the Iowa adult population. The model accurately accounts for the 10 min bout requirement put forth in the PAG. The measurement error model corrects biased estimates and accounts for day-to-day variation in activity. The model is also applied to the nationally representative National Health and Nutrition Examination Survey.

Relationships between the Physical Activity Intensity and the Medical Expenditure of Middle-Aged and Elderly People: Parsing from the CHARLS Database.

There are many studies on the impact of physical activity on health but few studies on the relationship between physical activity and medical expenditure among the elderly. Based on the China Health and Retirement Longitudinal Survey (CHARLS) database and selected 4456 valid samples, this paper used a two-part model to analyze the effects of high, moderate, and low physical activity intensity on medical expenditure. It is found that the intensity of physical activity was negatively correlated with medical expenditure, and the medical expenditure of the high physical activity intensity group was significantly lower than that of the low physical activity intensity group. For example, compared to people with no physical activity, the total medical expenditure decreased by 22.4%, 40.4%, and 62.5% per week in those with low, moderate, and high physical activity intensity. Thus, the government should provide more places for the elderly to exercise, planning special exercise areas for the elderly in community playgrounds, such as a dancing square, which will also help the elderly to increase their amount of exercise per week and develop a daily exercise habit.

Factors associated with the incidence and the expenditure of self-medication among middle-aged and older adults in China: A cross-sectional study.

Background: With the accelerated ageing of population and the growing prevalence of various chronic diseases in China, self-medication plays an increasingly important role in complementing the health care system due to its convenience and economy. Objective: This study aimed to investigate the incidence of self-medication and the amount of self-medication expenditure among middle-aged and older adults in China, and to explore factors associated with them. Methods: A total of 10,841 respondents aged 45 years and older from the China Health and Retirement Longitudinal Study (CHARLS) wave 4 which conducted in 2018 were included as the sample of this study. The two-part model was adopted to identify the association between the incidence of self-medication and the amount of self-medication expenditure and specific factors, respectively. Results: The incidence of self-medication among Chinese middle-aged and older adults was 62.30%, and the average total and out-of-pocket (OOP) pharmaceutical expenditure of self-medication of the self-medicated individuals were 290.50 and 264.38 Chinese yuan (CNY) respectively. Participants who took traditional Chinese medicine (TCM), self-reported fair, and poor health status, suffered from one and multiple chronic diseases had strongly higher incidence of self-medication. Older age and multiple chronic diseases were strongly associated with higher expenditure of self-medication. Those who took TCM had more self-medication expenditure, while those who drank alcohol had less. Conclusion: Our study demonstrated the great prevalence of self-medication among middle-aged and older adults in China and the large pharmaceutical expenditure that come with it, especially in the high-risk groups of self-medication identified in this paper. These findings enhanced our understanding of self-medication behaviors among Chinese middle-aged and older adults and may contribute to the formulation of targeted public health policy.

Projecting Long-Term Care Costs for Home and Community-Based Services in China from 2005 to 2050.

OBJECTIVES: The aim of this study was to estimate and project the trend in long-term care (LTC) costs for home and community-based services as a percentage of gross domestic product in China between 2005 and 2050. DESIGN: Longitudinal. SETTING AND PARTICIPANTS: We used 61,249 observations from 37,702 adults age ≥65 years from waves 2005, 2008, 2011, 2014, and 2018 of the Chinese Longitudinal Healthy Longevity Surveys. METHODS: LTC costs for home and community-based services consisted of the monetary value of time spent on LTC and the direct LTC cost. We used the age-sex-residence-specific weights provided by the Chinese Longitudinal Healthy Longevity Surveys to estimate the LTC costs from 2005 to 2018. We used a component-based model to project LTC costs, in which the 2-part model was used to estimate the average LTC costs and the multi-state Markov model approach was used to project the future population by age, sex, and disability state. RESULTS: The percentage of older adults with disabilities was projected to increase from 6.1% in 2005 to 7.5% in 2020 and 9.6% in 2050. The total LTC cost for home and community-based services were projected to increase from 0.3% of gross domestic product in 2005 to 0.7% in 2020 and to 6.4% in 2050. CONCLUSIONS AND IMPLICATIONS: Policymakers in China should take urgent actions to delay the onset of disabilities among older adults, which would curb the increasing LTC costs and maintain the sustainability of the LTC policies.

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.

Associations between use of specific social media sites and electronic cigarette use among college students.

OBJECTIVE: To examine dose-response associations between use of specific social media sites and the use of electronic cigarettes (e-cigarettes) and traditional cigarettes. METHODS: This was a cross-sectional study of 298 first-year college students enrolled in the fall 2019 semester at a large state university. Heckman selection and Probit model were used to estimate associations between use of specific social media sites and e-cigarette/traditional cigarette use. RESULTS: Each additional hour per day spent on Snapchat was associated with a 4.61% increase in the probability of lifetime e-cigarette use. In addition, among current e-cigarette users, more time spent on Snapchat was associated with more frequent e-cigarette use (marginal effects: 0.13, p = 0.001). Facebook, Twitter, Snapchat and Instagram were not associated with traditional cigarette smoking. CONCLUSION: Snapchat was the only major social media platform associated with both lifetime and current e-cigarette use.

Utilization and out-of-pocket expenses of primary care among the multimorbid elderly in China: A two-part model with nationally representative data.

Background: Multimorbidity has become an essential public health issue that threatens human health and leads to an increased disease burden. Primary care is the prevention and management of multimorbidity by providing continuous, comprehensive patient-centered services. Therefore, the study aimed to investigate the determinants of primary care utilization and out-of-pocket expenses (OOPE) among multimorbid elderly to promote rational utilization of primary care and reduce avoidable economic burdens. Methods: The study used data from CHARLS 2015 and 2018, which included a total of 4,384 multimorbid elderly aged 60 and above. Guided by Grossman theory, determinants such as education, gender, marriage, household economy, and so on were included in this study. A two-part model was applied to evaluate primary care utilization and OOPE intensity in multimorbid populations. And the robustness testing was performed to verify research results. Results: Primary care visits rate and OOPE indicated a decline from 2015 to 2018. Concerning primary outpatient care, the elderly who were female (OR = 1.51, P < 0.001), married (OR = 1.24, P < 0.05), living in rural areas (OR = 1.77, P < 0.001) and with poor self-rated health (OR = 2.23, P < 0.001) had a significantly higher probability of outpatient utilization, whereas those with middle school education (OR = 0.61, P < 0.001) and better household economy (OR = 0.96, P < 0.001) had a significantly less likelihood of using outpatient care. Rural patients (ß = -0.72, P < 0.05) may have lower OOPE, while those with better household economy (ß = 0.29, P < 0.05; ß = 0.58, P < 0.05) and poor self-rated health (ß = 0.62, P < 0.001) occurred higher OOPE. Regarding primary inpatient care, adults who were living in rural areas (OR = 1.48, P < 0.001), covered by Urban Employee Basic Medical Insurance (UEBMI) or Urban Rural Basic Medical Insurance (URBMI) (OR = 2.46, P < 0.001; OR = 1.81, P < 0.001) and with poor self-rated health (OR = 2.30, P < 0.001) had a significantly higher probability of using inpatient care, whereas individuals who were female (OR = 0.74, P < 0.001), with middle school education (OR = 0.40, P < 0.001) and better household economy (OR = 0.04, P < 0.001) had a significantly lower tendency to use inpatient care. Significantly, more OOPE occurred by individuals who were women (ß = 0.18, P < 0.05) and with better household economy (ß = 0.40, P < 0.001; ß = 0.62, P < 0.001), whereas those who were covered by URBMI (ß = -0.25, P < 0.05) and satisfied with their health (ß = -0.21, P < 0.05) had less OOPE. Conclusion: To prompt primary care visits and reduce economic burden among subgroups, more policy support is in need, such as tilting professional medical staff and funding to rural areas, enhancing awareness of disease prevention among vulnerable groups and so on.

Medical expenditure and its inequity for people with disabilities: Evidence from the CHARLS 2018 data.

Introduction: Disabilities may raise heavy medical expenses and rich-poor inequalities. However, data is lacking for the Chinese older populations. This study aimed to measure socioeconomic inequalities in medical expenses amongst the Chinese adult 45 years or older, and explored the main determinants among different disability categories. Method: Data from the 2018 China Health and Retirement Longitudinal Study (CHARLS) were used. Disabilities were divided into five categories: physical disabilities, intellectual disability, vision problems, hearing problems, and multiple disabilities. The two-part model was employed to identify the factors that are associated with medical expenditures. Socioeconomic inequalities were measured by the concentration index (CI), and the horizontal inequity index (HI) which adjusts for health needs. Decomposition analysis was further applied to evaluate the contribution of each determinant. Results: Two thousand four hundred nineteen people were included in this study. The CIs and HIs of the expenditure were both positive. Amongst the varied types of medical expenses, the highest CIs were found for self-treatment expenses (0.0262). Amongst the five categories of disabilities, the group with vision problem disability reported the highest CIs and HIs for outpatient expenses (CI = 0.0843, HI = 0.0751), self-treatment expenses (CI = 0.0958, HI = 0.1119), and total expenses (CI = 0.0622, HI = 0.0541). The group of intellectual disability reported the highest CI and HI (CI = 0.0707, HI = 0.0625). The decomposition analysis showed that income (80.32%), education (25.14%) and living in the rural areas (13.96%) were the main determinants of medical expenses for HI amongst all types of disabilities. Conclusion: For five types of disabilities, our data shows that medical expenses concentrated in the richer groups in China. Income, education, and rural areas factors were the main contributors to the economic-related inequalities. Health policies to improve the affordability of medical care are needed to decrease inequity of medical expenditures for people with disabilities.

Depression with Chronic Disease Is Associated with Increased Use of Medical Services and Medical Expenses in Hardcore Smokers.

We aimed to investigate the association of chronic disease and depression with medical service use and expenses in hardcore smokers and provide basic data for health management system of hardcore smokers. This was a secondary data study involving 1735 smokers. Propensity score matching (PSM) was conducted to match hardcore smokers with regular smokers, and a two part model (TPM) was used based on the matched groups. In the case of general smokers, subjects with both depression and chronic disease had a significant relation to medical service use. In the case of hardcore smokers, subjects without depression and with chronic disease or with both depression and chronic disease had increased the use of medical services. The depression and chronic disease of general smokers did not affect the use of medical services. In the case of hardcore smokers, subjects who do not have depression and have only chronic disease (ß = 0.20, p = 0.002) or with depression and chronic disease (ß = 0.20, p = 0.014) significantly related the use of medical services. Conclusion: It is necessary to establish a health management system that considers both emotional states and chronic disease for hardcore smokers.

A three-part regression calibration to handle excess zeroes, skewness and heteroscedasticity in adjusting for measurement error in dietary intake data.

Exposure measurement error (ME) biases exposure-outcome associations. Calibration dietary intake data used in the regression calibration (RC) response to adjust for ME are usually right-skewed, heteroscedastic and with excess zeroes. We proposed three-part RC models to handle these distributional complexities simultaneously, while correcting for ME in fish intake. We applied data from the National Health and Nutrition Examination Survey (NHANES), where long-term intake was measured with food frequency questionnaire (FFQ) in the main study and short-term intake with 24-hour recall (24HR) in the calibration study. In the three-part RC models, never consumers were modelled using two approaches: a zero distribution (Three-part RC-het-det), and logistic distribution (Three-part RC-het-prob); heteroscedasticity using an exponential distribution and right-skewness using generalized gamma distribution. The proposed models were compared with two-part RC model that ignores never consumers, and with methods that estimate intakes using FFQ and 24HR. The models were evaluated in a simulation study. With NHANES data, mean increase in the mercury level (in µ g / L ) was 1.20 using FFQ-method, 0.4 using 24HR-method, 1.87 using two-part RC and 2.02 using three-part RC-het-prob method. The three-part RC estimated the association with the least bias in the simulation study.

DAE-TPGM: A deep autoencoder network based on a two-part-gamma model for analyzing single-cell RNA-seq data.

Single-cell RNA sequencing (scRNA-seq) can reveal differences in genetic material at the single-cell level and is widely used in biomedical studies. However, the minute RNA content within individual cells often results in a high number of dropouts and introduces random noise of scRNA-seq data, concealing the original gene expression pattern. Therefore, data normalization is critical in the analysis pipeline to adjust for unexpected biological and technical effects, leading to a particular bimodal expression pattern exhibited in the semi-continuous normalized data. We further find the positive continuous expression presents a right-skewed distribution, which is still under-explored by mainstream dimensionality reduction and imputation methods. We introduced a deep autoencoder network based on a two-part-gamma model (DAE-TPGM) for joint dimensionality reduction and imputation of scRNA-seq data. DAE-TPGM uses a two-part-gamma model to capture the statistical characteristics of semi-continuous normalized data and adaptively explores the potential relationships between genes for promoting data imputation by deep autoencoder. Just as the classic application scenarios that use an autoencoder in dimensionality reduction, our personalized autoendoer can capture phenotypic information on the peripheral blood mononuclear cells (PBMC) better and clearly infer continuous phenotype information for hematopoiesis in mice. Compared with that of mainstream imputation methods such as MAGIC, SAVER, scImpute and DCA, the new model achieved substantial improvement on the recognition of cellular phenotypes in two real datasets, and the comprehensive analyses on synthetic "ground truth" data demonstrated that our method obtains competitive advantages over other imputation methods in discovering underlying gene expression patterns in time-course data.

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.

A quantitative analysis on the effect of COVID-19 in a private health insurance plan expenditure.

This paper explores the effect of COVID-19 on health care expenditure using data from a private Health Insurance Plan (HIP). As well known, at the beginning of the COVID-19 pandemic, governments had to rely on Non-Pharmaceutical Interventions against the spread of the virus. However, the stringency of lockdowns differed across space and time as governments had to adjust their strategy dynamically to the country-specific development of the crisis. These strategies have strongly changed the policyholders' behavior; however, after this period, a fundamental question is whether the policyholder behavior will return to a status quo (i.e. in traditional care delivery). We analyze these effects using a "pre-post" quantitative study using longitudinal data collected from 2017 to 2021. We consider as a consumption measure the health care expenditure amount within several types of health services, coming from a group of insured persons, followed overtime every quarter, and separating the effect per gender and age. Moving in this direction, the purpose of our contribution is to investigate if the traditional actuarial approach for assessing the loss cost, based on the Generalized Linear Models, could predict the effect on the health care expenditure due to COVID-19 and the capacity to which a HIP can anticipate these uncertainties. Our results provide a comprehensive picture of the different effects of COVID-19 on the health services offered by the HIP, as well as on the behavior ofpolicyholders during and after the pandemic period.

Shared parameter and copula models for analysis of semicontinuous longitudinal data with nonrandom dropout and informative censoring.

Analysis of longitudinal semicontinuous data characterized by subjects' attrition triggered by nonrandom dropout is complex and requires accounting for the within-subject correlation, and modeling of the dropout process. While methods that address the within-subject correlation and missing data are available, approaches that incorporate the nonrandom dropout, also referred to informative right censoring, in the modeling step are scarce due to the computational intensity and possible intractable integration needed for its implementation. Appreciating the complexity of this problem and the need for a new methodology that is feasible for implementation, we propose to extend a framework of likelihood-based marginalized two-part models to account for informative right censoring. The censoring process is modeled using two approaches: (1) Poisson censoring for the count of visits before dropout and (2) survival time to dropout. Novel consideration was given to the proposed joint modeling approaches for the semicontinuous and censoring components of the likelihood function which included (1) shared parameter, and (2) Clayton copula. The cross-part and within-part correlations were accounted for through a complex random effect structure that models correlated random intercepts and slopes. Feasibility of implementation, and accuracy of these approaches were investigated using extensive simulation studies and clinical application.

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).

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.