Joint modeling approaches for censored predictors due to detection limits with applications to metabolites data.

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, exact measures cannot be obtained, and thus are left censored. The problem becomes more challenging when the censored data come from heterogeneous populations consisting of exposed and non-exposed subjects. If the censored data come from non-exposed subjects, their measures are always zero and hence censored, forming a latent class governed by a distinct censoring mechanism compared with the exposed subjects. The exposed group's censored measurements are always greater than zero, but less than the detection limit. It is very often that the exposed and non-exposed subjects may have different disease traits or different relationships with outcomes of interest, so we need to disentangle the two different populations for valid inference. In this article, we aim to fill the methodological gaps in the literature by developing a novel joint modeling approach to not only address the censoring issue in predictors, but also untangle different relationships of exposed and non-exposed subjects with the outcome. Simulation studies are performed to assess the numerical performance of our proposed approach when the sample size is small to moderate. The joint modeling approach is also applied to examine associations between plasma metabolites and blood pressure in Bogalusa Heart Study, and identify new metabolites that are highly associated with blood pressure.

Study on the measurement of coupling and coordinated development level between China's internet and elderly care services and its influencing factors.

BACKGROUND: With the intensification of China's aging population, the demand for elderly care services has become increasingly prominent. At the same time, rapid development of internet technology provides more convenience and possibilities for the elderly. However, the coordinated development between the internet and elderly care services still faces challenges. This study aims to measure the level of coupling and coordinated development between the internet and elderly care services in China, and analyze the influencing factors, in order to provide reference for promoting elderly care services. METHODS: In this paper, the entropy method and coupling coordination degree model were used to measure the coupling coordination development index of the internet and elderly care services in China from 2012 to 2021. In addition, considering that the coordinated development between the two is affected by many factors, the Tobit model was used to analyze the main factors affecting the integration of the internet and elderly care services. RESULTS: (1) The coupling and coordination of the Internet and senior care services is in its infancy, but the coupling and coordination of the two is on the rise, and there is still a lot of room for development in the future. (2) In terms of time scale, the coupling coordination development level between the internet and elderly care services in China has gone through three stages of "disorder recession-transition coordination-coordinated development". (3) In terms of influencing factors, government management ability has a more positive impact on the development of the integration of the Internet and senior care services, financial support, scientific and technological investment and the level of innovation play a mild pulling role, while the level of informatization to a certain extent restricts the level of integration of the Internet and senior care services. CONCLUSION: In order to promote the coordinated development of China's Internet and senior care services, it is necessary to comprehensively understand the current situation and development space of China's Internet and senior care services coupling coordination degree, accurately grasp the dynamic trend of China's Internet and senior care services coupling and coordinated development, promote the stage of leapfrogging, and fully consider the influencing factors, so as to realize the optimal allocation of policies and resources. These measures will help to promote a more coordinated and sustainable development of the internet and elderly care services in China.

Identifying the causal effects of long-term exposure to PM2.5 and ground surface ozone on individual medical costs in China-evidence from a representative longitudinal nationwide cohort.

BACKGROUND: There is little evidence on whether PM2.5 and ground surface ozone have consistent effects on increased individual medical costs, and there is a lack of evidence on causality in developing countries. METHODS: This study utilized balanced panel data from 2014, 2016, and 2018 waves of the Chinese Family Panel Study. The Tobit model was developed within a counterfactual causal inference framework, combined with a correlated random effects and control function approach (Tobit-CRE-CF), to explore the causal relationship between long-term exposure to air pollution and medical costs. We also explored whether different air pollutants exhibit comparable effects. RESULTS: This study encompassed 8928 participants and assessed various benchmark models, highlighting the potential biases from failing to account for air pollution endogeneity or overlooking respondents without medical costs. Using the Tobit-CRE-CF model, significant effects of air pollutants on increased individual medical costs were identified. Specifically, margin effects for PM2.5 and ground-level ozone signifying that a unit increase in PM2.5 and ground-level ozone results in increased total medical costs of 199.144 and 75.145 RMB for individuals who incurred fees in the previous year, respectively. CONCLUSIONS: The results imply that long-term exposure to air pollutants contributes to increased medical costs for individuals, offering valuable insights for policymakers aiming to mitigate air pollution's consequences.

A threshold longitudinal Tobit quantile regression model for identification of treatment-sensitive subgroups based on interval-bounded longitudinal measurements and a continuous covariate.

Identification of a subgroup of patients who may be sensitive to a specific treatment is an important problem in precision medicine. This article considers the case where the treatment effect is assessed by longitudinal measurements, such as quality of life scores assessed over the duration of a clinical trial, and the subset is determined by a continuous baseline covariate, such as age and expression level of a biomarker. Recently, a linear mixed threshold regression model has been proposed but it assumes the longitudinal measurements are normally distributed. In many applications, longitudinal measurements, such as quality of life data obtained from answers to questions on a Likert scale, may be restricted in a fixed interval because of the floor and ceiling effects and, therefore, may be skewed. In this article, a threshold longitudinal Tobit quantile regression model is proposed and a computational approach based on alternating direction method of multipliers algorithm is developed for the estimation of parameters in the model. In addition, a random weighting method is employed to estimate the variances of the parameter estimators. The proposed procedures are evaluated through simulation studies and applications to the data from clinical trials.

What determines how green crop farming can get? Spatial factors or green awareness spillovers.

This study intends to examine if traditional local factors (seasonal weather conditions) and/or green awareness spillovers contribute to the spatial dependency of farmland allocated to organic farming after its uptake in Taiwan. To investigate the push and pull factors to improve the policy targeting on environmentally-friendly farming practices, we assess spatial autocorrelation of the adoption intensity of organic farming with exploratory analysis, and expand that by exploring how explanatory factors affect the adoption intensity using a spatial Tobit regression analysis, taking into consideration that the adoption intensity is a typical example of censored data. Based on township-level data of 323 townships constructed from 213,534 rice farm households drawn from the 2015 Agriculture Census, we find high-high clusters (hot spots) are mostly in the northern and the eastern parts of Taiwan, whereas the majority of low-low clusters (cold spots) locate in central and southern Taiwan. Such spatial aspects of organic adoption intensity suggest that a spatially targeted program in promoting environmental awareness is pertinent to fostering the development of organic agriculture. The results from the spatial lag Tobit regression estimation provide empirical evidence supporting the role of local weather conditions and green awareness spillovers in explaining the spatial patterns of organic agriculture in Taiwan. In light of the stylized fact that the majority of the rice farm households in Taiwan are small with 84% having farmland areas less than 1 ha, the findings provide practical references to policy practitioners in tailoring farm programs or policies in line with the notion of inclusive and sustainable development.

What were the spatiotemporal evolution characteristics and the influencing factors of urban land green use efficiency? A case study of the Yangtze River Economic Belt.

China's rapid urbanization has had a tremendous impact on the country's limited land resources, and one of the major issues of green development is how to utilize the limited land resources to maximize social, economic, and environmental advantages. From 2005 to 2019, the super epsilon-based measure model (EBM) was employed to assess the green land use efficiency of 108 prefecture-level and above cities in the Yangtze River Economic Belt (YREB), as well as investigate its spatial and temporal evolution and influential factors. The findings demonstrate that overall, urban land green use efficiency (ULGUE) in the YREB has been ineffective; in terms of city scale, megacities have the highest efficiency, followed by large cities and small and medium-sized cities; and at the regional level, downstream efficiency does have the greatest average value, followed by upstream efficiency and middle efficiency. The results of temporal and spatial evolution reveal that the number of cities with a high ULGUE is increasing in general but that their spatial characteristics are relatively dispersed. Population density, environmental regulation, industrial structure, technology input, and the intensity of urban land investment all have major beneficial effects on ULGUE, whereas urban economic development level and urban land use scale clearly have inhibitory effects. In light of the previous conclusions, some recommendations are made to continuously improve ULGUE.

Hospital efficiency measurement in the west of Iran: data envelopment analysis and econometric approach.

OBJECTIVE: Measuring hospital efficiency is one of the way how to use resources.The optimal hospital performance is the goals of healthcare policymakers. This study aimed to the current study was conducted to evaluate the efficiency the current study was conducted to evaluate the efficiency and assess the association between hospital size and hospital area population with technical efficiency in public hospitals. METHODS: In this descriptive-analytical study, the statistical population consisted of 15 public hospitals in the west of Iran. First, the data envelopment analysis (DEA) method was used to evaluate technical efficiency. inputs included staff and beds, and outputs consisted of the number of surgeries, the number of patients, and the average length of stay. Then, according to the public ownership of all hospitals, their educational and therapeutic activities, as well as their size and population were considered as the environmental factor affecting efficiency. Thus, regression was applied to measure their effects on efficiency. RESULTS: The average technical efficiency of the studied hospitals, the average management efficiency, and the average efficiency of the scale were 0.935, 0.961, and 0.987, respectively. Out of the total evaluated hospitals, six and nine hospitals had an efficiency of less than one and one, respectively. Moreover, the size of the hospital and the population as the environment variable were significant in the Tobit model. Our regression demonstrated that although the size of the hospital is positively associated with its technical efficiency, the hospital population negatively affects hospital efficiency. CONCLUSION: According to the size and area population of the hospitals, they decrease their inputs to maximize their efficacy by optimizing their surplus amounts. Tobit regression analysis concludes that hospital size and population covered by the hospital significant effect on hospitals' efficiency.

Willingness to pay to enhance pandemic preparedness in Mauritius.

OBJECTIVES: The objective of this study is to assess the determinants of willingness to pay to enhance pandemic preparedness in Mauritius. STUDY DESIGN: A contingent valuation method is used to estimate willingness to pay to pay for enhancing pandemic preparedness using a sample of working people in Mauritius. METHODS: A two-phase decision process analysis is carried out to model the willingness to pay to enhance pandemic preparedness. The first phase is to analyse the respondents' decision of whether or not to pay for enhancing pandemic preparedness using a Probit model. The second phase is to estimate the determinants of the amount of money respondents are willing to pay using a Tobit model. RESULTS: Income earners are willing to pay an average of Rs. 1,900 (approximately USD 50) per annum to enhance pandemic preparedness. 'Perceived Response Efficacy', 'Awareness of the Need and Responsibility for Paying', 'Subjective Obligation to Pay' and the 'Theory of Planned Behaviour' are found to affect both stages of of the decision-making process. Knowledge on COVID-19 is found to have a positive impact on the decision to pay and health responsibility attitude is found to have a negative impact on the amount people are willing to pay. CONCLUSIONS: On average, the government can potentially expect to mobilise an additional Rs. 1,047,470,000 (USD 27,565,000) from taxpayers to spend on enhancing pandemic preparedness in Mauritius. To increase willingness to pay for enhanced pandemic preparedness, the government can focus on improving knowledge on a pandemic, perceived response efficacy and awareness on need and responsibility of paying.

Joint Optimization of Kinematics and Anthropometrics for Human Motion Denoising.

In this paper, we propose a novel technique for human motion denoising by jointly optimizing kinematic and anthropometric constraints for a noisy skeleton data. Specifically, we are focused on depth-sensor-based motion capture (D-Mocap) data that are often prone to error, outliers and distortion. To capture human kinematics, we first propose a joint-level Tobit particle filter (TPF) that incorporates a unique observation model to characterize the censored measurement of D-Mocap data. A skeleton-level Differential Evolution (DE) algorithm is then integrated with the sequential Monte Carlo sampling in the TPF, allowing joint-level particles to be re-distributed and re-weighted according to the stability and consistency of skeletal bone lengths as well as the suitability of joint kinematics. This leads to an integrated TPF-DE algorithm that significantly improves the quality of D-Mocap data by making 3D joint trajectories more kinematically admissible and anthropometrically stable. Experimental results on both simulated and real-world D-Mocap show that the errors of joint positions and the bone lengths have been reduced by 30-60%, and the accuracy of joint angles has been improved by 40-60%. The proposed TPF-DE method outperforms the recent filtering-based and deep learning methods and demonstrate the synergy between the TPF and DE algorithms for effective human motion enhancement.

Econometric analysis of oncology patients' Health-Related Quality of Life determinants in Bulgaria.

OBJECTIVES: The present study investigates the determinants of oncology patients' Health-Related Quality of Life (HRQoL) in Bulgaria. Looking at some patients' characteristics, including control variables in the estimated model - demographics and the time from the disease onset, it studies the relevance of HRQoL diverse factors: some of them are related to the physical and psychological dimensions of the patients' illness experience, such as the levels of pain and anxiety/depression; some other concern more specifically the patients' therapeutic path, i.e., the feeling of participation in the therapy, their perceived uncertainty in illness (predictability and complexity), and the quality of the information received from the nurses and other medical personnel. METHODS: A questionnaire collecting information on HRQoL, uncertainty in illness and patients' experience with the hospital treatment has been administered to 306 oncology patients at four oncology centres in Bulgaria. Data has then been employed in the estimation of a Tobit model: the dependent variable selected has been the variation in the Visual Analogue Scale (VAS) score. The econometric model takes into account the characteristics of censoring in the dependent variable. RESULTS: Overall, the coefficients estimated, and the regression itself showed a good level of significance. Some dimensions of EuroQol-5D (EQ-5D) questionnaire - pain and anxiety/depression - have a significant impact on HRQoL, as well as some features of uncertainty in illness, as unpredictability and complexity. As expected, the longer the time elapsed from the diagnosis, the higher the reported HRQoL; the value of the information provided to the patients by the nurses as well as physicians is also relevant. CONCLUSIONS: This study presents an analysis of the impact of uncertainty in illness, feeling of participation in the therapy, and communication with the hospital personnel on oncological patients' HRQoL, which increases the scanty evidence referring to the patient-centred care in the Bulgarian hospital setting. Further deepening might concern a wider sample, including data collected at other medical centres and/or in other geographical areas in Bulgaria as well as in other European countries.

Analysis of the spatial characteristics and influencing factors of agricultural eco-efficiency: evidence from Anhui Province, China, during the period 2011-2018.

Sustainable agriculture is important for preserving environmental health and simultaneously gaining economic profits while maintaining social and economic equity. One way to evaluate sustainable agriculture is by studying agricultural eco-efficiency (AEE). Hence, this study constructed a data-driven method to evaluate and optimize AEE with the aim of providing a basis for improving the sustainable development of regional agriculture. Sixteen cities in Anhui Province, China, were considered in the study, and the variables used were agricultural resource inputs, environmental pollution, and agricultural economic development. Agricultural non-point source pollution (NPSP) emissions were considered the undesired output to build an AEE evaluation index system. Furthermore, a data envelopment analysis (DEA) model was established to analyse AEE from the static and dynamic perspectives. The spatial development and the temporal and spatial characteristics of AEE were also analysed. In addition, we applied a random effect (RE) panel Tobit model to quantitatively analyse the influencing factors of AEE from the input perspective and then proposed reasonable suggestions for improving the sustainable development of regional agriculture. Our findings show that the overall agricultural development in the 16 cities in Anhui Province has been continuously improving, even though there is an agglomeration of spatial development in some regions. In conclusion, this study provides suggestions and references for policy makers and agricultural practitioners regarding how to improve regional AEE and promote the sustainable development of the regional agricultural economy.

Temporal and spatial changes and influencing factors of low-carbon economy efficiency in China.

Low-carbon development has always been an important focus of China's economic transformation. In order to promote the development of low-carbon economy, this study used SBM-DEA model to evaluate China's provincial LCEE from 2005 to 2019, studied its temporal and spatial evolution law, used spatial autocorrelation to explore the correlation of China's provincial LCEE, and explored the key influencing factors of LCEE with Tobit model. The empirical results show that the LCEE of most provinces in China is declining, and there are significant differences among different regions in China. Because the eastern region of China can rely on its own human resources, capital environment, and economic foundation, the overall LCEE level is relatively high, while the central and western regions still have obvious deficiencies due to industrial conditions, geographical location, and other factors. LCEE has significant spatial correlation, and neighboring provinces have spillover effects on local LCEE. On this basis, the key factors that affect LCEE are determined. Urbanization level, traffic level, economic development level, financial development, investment in fixed assets, and energy consumption are the important factors that affect LCEE in China, but these influences vary from province to region. It is more reasonable for local governments to develop low-carbon economy according to their own conditions.

Semiparametric models and inference for the effect of a treatment when the outcome is nonnegative with clumping at zero.

The outcome in a randomized experiment is sometimes nonnegative with a clump of observations at zero and continuously distributed positive values. One widely used model for a nonnegative outcome with a clump at zero is the Tobit model, which assumes that the treatment has a shift effect on the distribution of a normally distributed latent variable and the observed outcome is the maximum of the latent variable and zero. We develop a class of semiparametric models and inference procedures that extend the Tobit model in two useful directions. First, we consider more flexible models for the treatment effect than the shift effect of the Tobit model; for example, our models allow for the treatment to have a larger in magnitude effect for upper quantiles. Second, we make semiparametric inferences using empirical likelihood that allow the underlying latent variable to have any distribution, unlike the original Tobit model that assumes the latent variable is normally distributed. We apply our approach to data from the RAND Health Insurance Experiment. We also extend our approach to observational studies in which treatment assignment is strongly ignorable.

[Influence of Social Capital on the Life Quality of Patients with Chronic Diseases-A Study Based on EQ-5D-5L Scale].

OBJECTIVE: To explore the influence of social capital on the quality of life of patients with chronic non-communicable diseases. METHODS: A multi-phase stratified cluster sampling method was adopted to select the survey respondents. Professionally trained surveyors made home visits in order to conduct face-to-face questionnaire surveys in person. European Quality of Life Five Dimension Five Level Scale (EQ-5D-5L) and a self-developed social capital scale were used to investigate the quality of life and social capital of the respondents. Factor analysis and Cronbach's α coefficient test were done to verify the reliability and validity of the self-developed social capital scale. The χ 2 test and robust Tobit regression model were used to analyze the impact of social capital on the quality of life of patients with chronic non-communicable diseases. RESULTS: The self-developed social capital scale showed excellent performance. The Cronbach's α coefficient was 0.728, the KMO value was 0.716, and the result of Bartlett's test of sphericity was statistically significant ( P<0.001), indicating that the data were well suited for factor analysis. The four common factors cumulatively explained 68.27% of the total variation. The health utility value of the survey respondents was 0.869±0.181. Those who could walk around, shower and dress themselves, and perform usual activities without any problem accounted for 75.70%, 80.10%, and 74.1% of the respondents, respectively. Those who had pain or discomfort and anxiety or depression, with no self-perceived problem were 43.40% and 58.90%, respectively. In the EQ-5D-5L scale, the self-rated health influencing factors of the physical health dimension were community safety and interpersonal network relationships. The influencing factors of social function health was community safety and mental health was affected by community safety, community trust and interpersonal network relationships. When community safety improved by one level, the health utility value of patients with chronic non-communicable diseases increased by 0.046, and when interpersonal network relationships improved by an additional level, their health utility value increased by 0.037. CONCLUSION: The main problem of the quality of life of patients with chronic non-communicable diseases was found in the mental health dimension. In the process of treating chronic non-communicable diseases, attention should also be given to psychological counseling. Community safety and interpersonal network relationships are the protective factors for self-rated health status. Providing a safe community environment and expanding interpersonal networks help improve the health of patients.

Evaluating the technical efficiency of care among long-term care facilities in Xiamen, China: based on data envelopment analysis and Tobit model.

BACKGROUND: The technical efficiency (TE) of care among the elderly in long-term care facilities (LTCF) have become increasingly crucial policy concerns faced by developing countries and Asia, especially China. The purpose of this study was to evaluate the TE and the quality of care and identify its influencing factors among LTCF. METHODS: A total of 32 registered LTCF in Xiamen of China were surveyed in 2016. The Banker-Charnes-Cooper (BCC) model and Slacks-Based Measure (SBM) model of Data Envelopment Analysis (DEA) were used to evaluate the TE of LTCF. The TE has been decomposed into pure technical efficiency and scale efficiency. Utilization of DEA with human, financial, and material resources as inputs and quantity, quality of nursing care as outputs allowed estimation of the relative TE of care in LTCF. In addition, this study applied SBM to measuring the efficiencies and slacks. Furthermore, Tobit model was performed to explore factors associated with TE. RESULTS: There were 7 public and 25 private LTCF respectively, with a total of 6729 beds and 3154 elderly people. 17 LTCF were technically efficient (53.1%). In the BCC model, the average TE was 0.963. The average pure technical efficiency and scale efficiency of LTCF were 0.979, 0.984, respectively. There were 5 LTCF with increasing returns to scale, 8 LTCF with decreasing returns to scale. In the SBM model, the average TE was 0.813, and it had the same effective decision-making unit with SBM model. Depending on TE score from high to low, the top eight are private LTCF, and the last four were public LTCF. The slack analysis showed that they can be reduced in 8 LTCF with decreasing returns to scale such as 53.31% administrative staffs, 67.73% medical staffs, 33.1% caregivers, 51.66% paramedical staffs and 4.1% beds on average. The TE of private LTCF was higher than that of public LTCF. The LTCF in urban were more effective than rural. The TE of LTCF raised by increasing of working hours, training frequency and institutional occupancy. CONCLUSIONS: The overall TE of LTCF in Xiamen of China was relatively high, especially in private institutions. However, LTCF still needs to further improve the utilization of physical resources and the management and training of human resources. The TE of LTCF was associated to their location, institutional nature, allocation of human resources and occupancy rate. It was needed to focus on promoting the efficiency and quality of LTCF in order to achieve sustainability.

How does 'park and ride' perform? An evaluation using longitudinal data.

The efficiency of park and ride (PnR) lots has not been investigated in serious depth in prior literature. This study examines the effect of various factors on the utilization rate of PnR lots with panel Tobit models. The examined factors consist of land use features, roadway design features, transit ridership, sociodemographic attributes, travel characteristics, policy tools, gasoline prices, and weather conditions. The data is drawn from PnR lots in King County, Washington. Results show that: (1) degree of mixed land use, road density, employment density, percentages of people aged between 18 and 34 and people over 65, the percentage of white people, the percentage of poor people, and transit ridership are positively associated with the utilization rate of PnR lots; (2) the percentage of drive lanes in total roadway miles, the percentage of males, and the mode share percentage of driving are negatively correlated with the utilization rate of PnR lots; (3) various policy interventions, including countermeasures for preserving transit after the economic recession, congestion reduction charge, and bus-rail integration, are all positively correlated with the utilization rate of PnR lots. Contextualized to US cities, PnR is a practical way to attract bus riders, especially young adults, senior citizens, and low-income people to public transit. Dense urban development is encouraged for the full utilization of PnR lots. Additionally, the integration between bus and rail appears to be an effective policy tool to promote PnR utilization.

Health related quality of life in patients with community-acquired pneumococcal pneumonia in France.

BACKGROUND: Community Acquired Pneumococcal Pneumonia is a lung infection that causes serious health problems and can lead to complications and death. The aim of this study was to observe and analyze health related quality of life after a hospital episode for patients with community acquired pneumococcal pneumonia in France. METHODS: A total of 524 individuals were enrolled prospectively in the study and were followed for 12 months after hospital discharge. Presence of streptococcus pneumoniae was confirmed by microbiological sampling. Quality of life was reported at four different points of time with the EQ-5D-3 L health states using the French reference tariff. Complete data on all four periods was available for 269 patients. We used descriptive and econometric analysis to assess quality of life over time during follow-up, and to identify factors that impact the utility indexes and their evolution through time. We used Tobit panel data estimators to deal with the bounded nature of utility values. RESULTS: Average age of patients was 63 and 55% of patients were men. Negative predictors of quality of life were the severity of the initial event, history of pneumonia, smokers, age and being male. On average, quality of life improved in the first 6 months after discharge and stabilized beyond. At month 1, mean utility index was 0.53 (SD: 0.34) for men and 0.45 (SD: 0.34) for women, versus mean of 0.69 (SD: 0.33) and 0.70 (SD: 0.35) at Month 12. "Usual activities" was the dimension the most impacted by the disease episode. Utilities for men were significantly higher than for women, although male patients were more severe. Individuals over 85 years old did not improve quality of life during follow-up, and quality of life did not improve or deteriorated for 34% of patients. We found that length of hospital stay was negatively correlated with quality of life immediately after discharge. CONCLUSION: This study provides with evidence that quality of life after an episode of community acquired pneumococcal pneumonia improves overall until the sixth month after hospital discharge, but older patients with previous history of pneumonia may not experience health gains after the initial episode.

Tobit regression for modeling mean survival time using data subject to multiple sources of censoring.

Mean survival time is often of inherent interest in medical and epidemiologic studies. In the presence of censoring and when covariate effects are of interest, Cox regression is the strong default, but mostly due to convenience and familiarity. When survival times are uncensored, covariate effects can be estimated as differences in mean survival through linear regression. Tobit regression can validly be performed through maximum likelihood when the censoring times are fixed (ie, known for each subject, even in cases where the outcome is observed). However, Tobit regression is generally inapplicable when the response is subject to random right censoring. We propose Tobit regression methods based on weighted maximum likelihood which are applicable to survival times subject to both fixed and random censoring times. Under the proposed approach, known right censoring is handled naturally through the Tobit model, with inverse probability of censoring weighting used to overcome random censoring. Essentially, the re-weighting data are intended to represent those that would have been observed in the absence of random censoring. We develop methods for estimating the Tobit regression parameter, then the population mean survival time. A closed form large-sample variance estimator is proposed for the regression parameter estimator, with a semiparametric bootstrap standard error estimator derived for the population mean. The proposed methods are easily implementable using standard software. Finite-sample properties are assessed through simulation. The methods are applied to a large cohort of patients wait-listed for kidney transplantation.

The effect of urbanization on carbon dioxide emissions efficiency in the Yangtze River Delta, China.

Cities have been one of the most important areas of CO2 emissions. It is increasingly important to research the effect of urbanization on CO2 emissions, especially in large emerging and developing economies, due to the indispensable need for understanding the effect of urbanization on CO2 emissions, evaluating carbon reduction tasks and providing the scientific basis for low-carbon urbanization. Utilizing a balanced panel dataset in the Yangtze River Delta (YRD), China, during the period of 2000-2010, this paper employed data envelopment analysis (DEA) window analysis and a spatial lag panel Tobit model to investigate the effect of urbanization on CO2 emissions efficiency (the ratio of the target CO2 emissions to the actual CO2 emissions). The results show that the average CO2 emissions efficiency was 0.959 in 2010, and CO2 emissions efficiency ranged from 0.816 to 1 and exhibited spatial clustering in the region. The larger potential of CO2 emissions reduction appeared in Zhenjiang and Yangzhou, indicating that more CO2 emissions reduction tasks should be allocated to these two cities. Urbanization has negative effects on improving CO2 emissions efficiency, and there is a U-curve relation between CO2 emissions efficiency and urbanization, indicating that CO2 emissions efficiency decreases at the early stage of urbanization, then increases when urbanization reach a high level. There is spatial spillover effect among the prefecture-level cities, suggesting that different prefecture-level governments should coordinate with each other to improve CO2 emissions efficiency in the whole area. Gross domestic product (GDP) per capita also plays a markedly positive role in improving CO2 emissions efficiency. This research highlights the effect of urbanization on CO2 emissions efficiency and the importance of improving CO2 emissions efficiency in developing countries.

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

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