Forecasting the Health Transition and Medical Expenditure of the Future Elderly in China: A Longitudinal Study Based on Markov Chain and Two Part Model

Set in the rapid development of population aging, this study focuses on the relationship between health and medical expenditure of the elderly population. Taking the health and medical expenditure of the elderly as the research object, this study analyzes the characteristics and the intrinsic relationship between them. Based on the future elderly model, this study calculates the transition probability of the elderly's self-assessment health state using the Health Transition Model and estimates the medical expenditure of the elderly by the Two-Part Model. Based on the above, this study predicts the trend of the population size and medical expenditure of the elderly in the next 15 years (2020–2035). Based on the results, the policy suggestions are put forward. To begin with, strengthening health management and health services for the elderly in the construction of healthy China. Next, building a comprehensive system of health care for the elderly in government, society, family, and individual. Then, establishing a long-term care service system as soon as possible. In addition, it is better to establish lifelong health consciousness and cultivate healthy accomplishment behavior. Finally, it is necessary to promote gender mainstreaming in the health field.

mSHAP: SHAP Values for Two-Part Models

Two-part models are important to and used throughout insurance and actuarial science. Since insurance is required for registering a car, obtaining a mortgage, and participating in certain businesses, it is especially important that the models that price insurance policies are fair and non-discriminatory. Black box models can make it very difficult to know which covariates are influencing the results, resulting in model risk and bias. SHAP (SHapley Additive exPlanations) values enable interpretation of various black box models, but little progress has been made in two-part models. In this paper, we propose mSHAP (or multiplicative SHAP), a method for computing SHAP values of two-part models using the SHAP values of the individual models. This method will allow for the predictions of two-part models to be explained at an individual observation level. After developing mSHAP, we perform an in-depth simulation study. Although the kernelSHAP algorithm is also capable of computing approximate SHAP values for a two-part model, a comparison with our method demonstrates that mSHAP is exponentially faster. Ultimately, we apply mSHAP to a two-part ratemaking model for personal auto property damage insurance coverage. Additionally, an R package (mshap) is available to easily implement the method in a wide variety of applications.

Studying dietary intake in daily life through multilevel two-part modelling: a novel analytical approach and its practical application

Background Understanding which factors influence dietary intake, particularly in daily life, is crucial given the impact diet has on physical as well as mental health. However, a factor might influence whether but not how much an individual eats and vice versa or a factor’s importance may differ across these two facets. Distinguishing between these two facets, hence, studying dietary intake as a dual process is conceptually promising and not only allows further insights, but also solves a statistical issue. When assessing the association between a predictor (e.g. momentary affect) and subsequent dietary intake in daily life through ecological momentary assessment (EMA), the outcome variable (e.g. energy intake within a predefined time-interval) is semicontinuous. That is, one part is equal to zero (i.e. no dietary intake occurred) and the other contains right-skewed positive values (i.e. dietary intake occurred, but often only small amounts are consumed). However, linear multilevel modelling which is commonly used for EMA data to account for repeated measures within individuals cannot be applied to semicontinuous outcomes. A highly informative statistical approach for semicontinuous outcomes is multilevel two-part modelling which treats the outcome as generated by a dual process, combining a multilevel logistic/probit regression for zeros and a multilevel (generalized) linear regression for nonzero values. Methods A multilevel two-part model combining a multilevel logistic regression to predict whether an individual eats and a multilevel gamma regression to predict how much is eaten, if an individual eats, is proposed. Its general implementation in R, a widely used and freely available statistical software, using the R-package brms is described. To illustrate its practical application, the analytical approach is applied exemplary to data from the Eat2beNICE-APPetite-study. Results Results highlight that the proposed multilevel two-part model reveals process-specific associations which cannot be detected through traditional multilevel modelling. Conclusions This paper is the first to introduce multilevel two-part modelling as a novel analytical approach to study dietary intake in daily life. Studying dietary intake through multilevel two-part modelling is conceptually as well as methodologically promising. Findings can be translated to tailored nutritional interventions targeting either the occurrence or the amount of dietary intake.

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.

Does the amount of formal care affect informal care? Evidence among over-60s in France

This paper investigates the causal effect of the amount of formal care used on the informal care received by formal care users. We use an original instrument for formal care volume based on local disparities (NUTS 3 level, 96 units) in the price of formal care. Using the French CARE survey, we use a two-part model to assess the effect of formal care on the extensive and the intensive margin of informal care. An increase in the amount of formal care is found to be associated with a small decrease in the probability of using informal care. Heterogeneity tests show that this negative effect is mainly driven by help for daily activities provided by women. At the intensive margin, informal care is not significantly affected by the amount of formal care. Reforms increasing subsidies for formal care can thus be suspected to have a limited effect on informal care arrangements.

Bayesian Analysis of Nonnegative Data Using Dependency-Extended Two-Part Models

This article is motivated by the challenge of analysing an agricultural field experiment with observations that are positive on a continuous scale or zero. Such data can be analysed using two-part models, where the distribution is a mixture of a positive distribution and a Bernoulli distribution. However, traditional two-part models do not include any dependencies between the two parts of the model. Since the probability of zero is anticipated to be high when the expected value of the positive part is low, and the other way around, this article introduces dependency-extended two-part models. In addition, these extensions allow for modelling the median instead of the mean, which has advantages when distributions are skewed. The motivating example is an incomplete block trial comparing ten treatments against weed. Gamma and lognormal distributions were used for the positive response, although any density on the support of real numbers can be accommodated. In a cross-validation study, the proposed new models were compared with each other and with a baseline model without dependencies. Model performance and sensitivity to choice of priors were investigated through simulation. A dependency-extended two-part model for the median of the lognormal distribution performed best with regard to mean square error in prediction. Supplementary materials accompanying this paper appear online.

Use of diffusive and empirical models to predict drying rate of acerola seeds (Malpighia sp.)

The thin layer drying process of acerola seeds was analyzed using a flat plate geometry diffusion model, Page's model, and a two-part model proposed based on the diffusion equation. These models were fitted to experimental drying kinetics data of acerola seeds for an air flow speed of 1.5 m/s, at temperatures of 40, 50, 60 and 70°C, using non-linear regression by Levenberg-Marquardt method. The diffusion model was used to determine the diffusion coefficients and activation energy. The predicted and experimental results were compared using the determination coefficient (R2) and mean square error (MSE) of the estimates as criteria. The results showed that the diffusion model is not suitable for predicting the drying rate of acerola seeds, while Page’s equation and the two-part proposed model can be safely used to predict the drying rates.

Obama and the use of force: a discursive institutionalist analysis of Libya and Syria

What factors explain variation in decisions to use force in American foreign policy? Consider the Obama administration’s decision to intervene in Libya. Upon assuming office, Obama outlined a foreign policy marked by a self-professed doctrine, ‘don’t do stupid shit’. In short, Obama sought to avoid the unnecessary use of military force, but when the threat of mass atrocity emerged, despite strong protests from senior advisers, he became drawn into the 2011 Libya intervention. By contrast, following chemical weapon attacks in Syria in 2013, Obama reneged on upholding his so-called ‘red-line’, pursuing diplomatic measures even though support for a military response was strong. But what explains this variation? Rationalist perspectives across the board have tended to overrate interpretive efficiency. Yet, such assumptions obscure the capacity for interests to be interpreted in different ways. To redress this issue, I build on discursive institutionalist insights, developing a model to show how principled and cognitive ideas act as weapons in institutional debates, serving to repress or displace information. To show how agents come to rely on principled or cognitive ideas, I develop a three-part model offering two mechanisms – cognitive repression and normative displacement – by which agents displace and repress certain types of information, depending on the ‘form’ in which that information is presented. This enables a more comprehensive understanding of how different interpretations lead to policy variation at critical moments of decision.