Estimating the costs for a group of geriatric patients using the Coxian phase-type distribution

Queue hurdle Coxian phase-type model for two-stage process of population-based cancer screening

The quality assurance of two-stage population-based cancer screening program is determined by arrival rate (attending screening), positive rate (determined by the criteria of screening test), the compliance and the waiting time (WT) for confirmatory diagnosis in those screened as positive. These parameters were correlated between the process of screening procedures and the effectiveness of screening program. To capture such an inter-dependence of these parameters and quantify the effectiveness of program, we proposed a Queue hurdle Coxian phase-type (QH-CPH) model to estimate the arrival rate of screenees with the Poisson Queue process and the compliance rate of confirmatory diagnosis with the hurdle model, and also to identify the hidden states of WT that is affected by the capacity of health care and relevant covariates (such as demographic features and geographic areas) with the Coxian phase-type (CPH) process. We applied the proposed QH-CPH model to Taiwanese nationwide colorectal cancer screening program data for estimating the arrival rate and the probability of not complying with colonoscopy and classifying the compliers into two hidden states, short-waiting phase and long-waiting phase for colonoscopy. Significant covariates responsible for three processes were also identified by using the proportional hazards regression forms. A simulation study was further performed to assess the joint effect of these parameters on WT through a series of scenarios. The proposed QH-CPH model can provide an insight into the optimal and the practical design on population-based cancer screening for health policy-makers given the limited health care resources and capacity.

An alternative formulation of Coxian phase-type distributions with covariates: Application to emergency department length of stay

In this article, we present a new methodology to model patient transitions and length of stay in the emergency department using a series of conditional Coxian phase-type distributions, with covariates. We reformulate the Coxian models (standard Coxian, Coxian with multiple absorbing states, joint Coxian, and conditional Coxian) to take into account heterogeneity in patient characteristics such as arrival mode, time of admission, and age. The approach differs from previous research in that it reduces the computational time, and it allows the inclusion of patient covariate information directly into the model. The model is applied to emergency department data from University Hospital Limerick in Ireland, where we find broad agreement with a number of commonly used survival models (parametric Weibull and log-normal regression models and the semiparametric Cox proportional hazards model).

Prediction of out-of-pocket health expenditures in Rwanda using machine learning techniques

Introduction

in Rwanda, the estimated out-of-pocket health expenditure has been increased from 24.46% in 2000 to 26% in 2015. Despite the existence of guideline in estimation of out-of-pocket health expenditures provided by WHO (2018), the estimation of out-of-pocket health expenditure still have difficulties in many countries including Rwanda.

Methods

the purpose of this paper was to figure out the best model which predicts the out-of-pocket health expenditures in Rwanda during the process of considering various techniques of machine learning by using the Rwanda Integrated Living Conditions Surveys (EICV5) of 14580 households (2018).

Results

our findings presented the model which predict the out-of-pocket health expenditures with higher accuracy and was found as treenet model. Furthermore, machine learning techniques were used to judge which predictor variable was important in our prediction process and comparison of the performance of the algorithms through train accuracy and test accuracy metric measures. Finally, the findings show that the tests of accuracy of the models were 50.16% for multivariate adaptive regression splines (MARS) model, 74% decision tree model, 87% for treenet model, 83% for random forest model, gradient boosting 81%, predictor total consumption played a significant role in the model for all tested models.

Conclusion

finally, we conclude that the total consumption of the household came out to be the most important variable which is consistently true to all the algorithms tested. The findings from our study have policy implications for policy makers in Rwanda and in the world generally. We recommend the government to significantly increase public spending on health. Domestic financial resources are key to moving closer to universal health coverage (UHC) and should be increased on a long-term basis. In addition, these results will be useful for the future to assess the out-of-pocket health expenditures dataset.

Feature Selection for Health Care Costs Prediction Using Weighted Evidential Regression

Although many authors have highlighted the importance of predicting people's health costs to improve healthcare budget management, most of them do not address the frequent need to know the reasons behind this prediction, i.e., knowing the factors that influence this prediction. This knowledge allows avoiding arbitrariness or people's discrimination. However, many times the black box methods (that is, those that do not allow this analysis, e.g., methods based on deep learning techniques) are more accurate than those that allow an interpretation of the results. For this reason, in this work, we intend to develop a method that can achieve similar returns as those obtained with black box methods for the problem of predicting health costs, but at the same time it allows the interpretation of the results. This interpretable regression method is based on the Dempster-Shafer theory using Evidential Regression (EVREG) and a discount function based on the contribution of each dimension. The method "learns" the optimal weights for each feature using a gradient descent technique. The method also uses the nearest k-neighbor algorithm to accelerate calculations. It is possible to select the most relevant features for predicting a patient's health care costs using this approach and the transparency of the Evidential Regression model. We can obtain a reason for a prediction with a k-NN approach. We used the Japanese health records at Tsuyama Chuo Hospital to test our method, which included medical examinations, test results, and billing information from 2013 to 2018. We compared our model to methods based on an Artificial Neural Network, Gradient Boosting, Regression Tree and Weighted k-Nearest Neighbors. Our results showed that our transparent model performed like the Artificial Neural Network and Gradient Boosting with an R2 of 0.44.

Understanding Dynamic Status Change of Hospital Stay and Cost Accumulation via Combining Continuous and Finitely Jumped Processes

The Coxian phase-type models and the joint models of longitudinal and event time have been extensively used in the studies of medical outcome data. Coxian phase-type models have the finite-jump property while the joint models usually assume a continuous variation. The gap between continuity and discreteness makes the two models rarely used together. In this paper, a partition-based approach is proposed to jointly model the charge accumulation process and the time to discharge. The key construction of our new approach is a set of partition cells with their boundaries determined by a family of differential equations. Using the cells, our new approach makes it possible to incorporate finite jumps induced by a Coxian phase-type model into the charge accumulation process, therefore taking advantage of both the Coxian phase-type models and joint models. As a benefit, a couple of measures of the "cost" of staying in each medical stage (identified with phases of a Coxian phase-type model) are derived, which cannot be approached without considering the joint models and the Coxian phase-type models together. A two-step procedure is provided to generate consistent estimation of model parameters, which is applied to a subsample drawn from a well-known medical cost database.

Using Prior Information on Parameters to Eliminate Dependence on Initial Values in Fitting Coxian Phase Type Distributions to Length of Stay Data in Healthcare Settings

Background: Modeling length of stay (LOS) data in healthcare settings using Coxian phase type (PH) distributions is becoming increasingly popular. However, dependence on initial values is a persistent difficulty in parameter estimations. This paper explores the utility of prior information on the parameters to address this difficulty. Methods: Maximum likelihood methods were used to estimate parameters of PH distributions that best fit simulated datasets with various sample sizes arising from PH distributions of various numbers of phases and parameters, using randomly generated initial values. Estimated values for the parameters resulting from different initial values were compared to the known values to assess the extent to which estimates depend on initial values; the impacts of sample sizes, existence of prior information, as well as the number of parameters with prior information were assessed. Results: Without prior information, parameter estimates depend on initial values for all PH distributions and all sample sizes. Prior information on one or more parameters led to more concentrated estimates, with higher number of parameters with prior information or larger sample sizes leading to more concentrated estimates. For example, with a sample size of 500, the estimates for a parameter with known value of 0.706 without prior information had a wide range of 1.523; using prior information for two parameters narrowed that range down to 0.156. For 3-phase PH distributions, prior information on 3 parameters appeared to be sufficient to eliminate dependence on initial values, even for small sample sizes. For 4-phase PH distributions, prior information on 5 parameters and a moderate sample size were needed to eliminate such dependence. Conclusions: Combination of prior information on parameters and sufficient sample sizes can eliminate dependence on initial values in fitting PH distributions to LOS data.

Review of statistical methods for analysing healthcare resources and costs

We review statistical methods for analysing healthcare resource use and costs, their ability to address skewness, excess zeros, multimodality and heavy right tails, and their ease for general use. We aim to provide guidance on analysing resource use and costs focusing on randomised trials, although methods often have wider applicability. Twelve broad categories of methods were identified: (I) methods based on the normal distribution, (II) methods following transformation of data, (III) single-distribution generalized linear models (GLMs), (IV) parametric models based on skewed distributions outside the GLM family, (V) models based on mixtures of parametric distributions, (VI) two (or multi)-part and Tobit models, (VII) survival methods, (VIII) non-parametric methods, (IX) methods based on truncation or trimming of data, (X) data components models, (XI) methods based on averaging across models, and (XII) Markov chain methods. Based on this review, our recommendations are that, first, simple methods are preferred in large samples where the near-normality of sample means is assured. Second, in somewhat smaller samples, relatively simple methods, able to deal with one or two of above data characteristics, may be preferable but checking sensitivity to assumptions is necessary. Finally, some more complex methods hold promise, but are relatively untried; their implementation requires substantial expertise and they are not currently recommended for wider applied work.

Modeling length of stay in hospital and other right skewed data: comparison of phase-type, gamma and log-normal distributions

OBJECTIVES

To present a relatively novel method for modeling length-of-stay data and assess the role of covariates, some of which are related to adverse events. To undertake critical comparisons with alternative models based on the gamma and log-normal distributions. To demonstrate the effect of poorly fitting models on decision-making.

METHODS

The model has the process of hospital stay organized into Markov phases/states that describe stay in hospital before discharge to an absorbing state. Admission is via state 1 and discharge from this first state would correspond to a short stay, with transitions to later states corresponding to longer stays. The resulting phase-type probability distributions provide a flexible modeling framework for length-of-stay data which are known to be awkward and difficult to fit to other distributions.

RESULTS

The dataset consisted of 1901 patients' lengths of stay and values for a number of covariates. The fitted model comprised six Markov phases, and provided a good fit to the data. Alternative gamma and log-normal models did not fit as well, gave different coefficient estimates, and statistical significance of covariate effects differed between the models.

CONCLUSIONS

Models that fit should generally be preferred over those that do not, as they will produce more statistically reliable coefficient estimates. Poor coefficient estimates may mislead decision-makers by either understating or overstating the cost of some event or the cost savings from preventing that event. There is no obvious way of identifying a priori when coefficient estimates from poorly fitting models might be misleading.