Notes on the Construction of Geometric Representations of Confidence Intervals of Ratios using Stata, Gauss and Eviews (original) (raw)
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Medical Decision Making, 1998
Predictions of cost over well-defined time horizons are frequently required in the analysis of clinical trials and social experiments, for decision models investigating the cost-effectiveness of interventions, and for macro-level estimates of the resource impact of disease. With rare exceptions, cost predictions used in such applications continue to take the form of deterministic point estimates. However, the growing availability of large administrative and clinical data sets offers new opportunities for a more general approach to disease cost forecasting: the estimation of multivariable cost functions that yield predictions at the individual level, conditional on intervention(s), patient characteristics, and other factors. This raises the fundamental question of how to choose the "best" cost model for a given application. The central purpose of this paper is to demonstrate how to evaluate competing models on the basis of predictive validity. This concept is operationalized according to three alternative criteria: 1) root mean square error (RMSE), for evaluating predicted mean cost; 2) mean absolute error (MAE), for evaluating predicted median cost; and 3) a logarithmic scoring rule (log score), an information-theoretic index for evaluating the entire predictive distribution of cost. To illustrate these concepts, the authors conducted a split-sample analysis of data from a national sample of Medicare-covered patients hospitalized for ischemic stroke in 1991 and followed to the end of 1993. Using test and training samples of about 500,000 observations each, they investigated five models: single-equation linear models, with and without log transform of cost; two-part (mixture) models, with and without log transform, to directly address the problem of zero-cost observations: and a Cox proportional-hazards model stratified by time interval. For deriving the predictive distribution of cost, the log transformed two-part and proportional-hazards models are superior. For deriving the predicted mean or median cost, these two models and the commonly used log-transformed linear model all perform about the same. The untransformed models are dominated in every instance. The approaches to model selection illustrated here can be applied across a wide range of settings.
Journal of the Royal Statistical Society: Series A (Statistics in Society), 2015
We conduct a quasi-Monte-Carlo comparison of the recent developments in parametric and semiparametric regression methods for healthcare costs, both against each other and against standard practice. The population of English National Health Service hospital in-patient episodes for the financial year 2007-2008 (summed for each patient) is randomly divided into two equally sized subpopulations to form an estimation set and a validation set. Evaluating out-of-sample using the validation set, a conditional density approximation estimator shows considerable promise in forecasting conditional means, performing best for accuracy of forecasting and among the best four for bias and goodness of fit. The best performing model for bias is linear regression with square-root-transformed dependent variables, whereas a generalized linear model with square-root link function and Poisson distribution performs best in terms of goodness of fit. Commonly used models utilizing a log-link are shown to perform badly relative to other models considered in our comparison.
Confidence Intervals for Estimates of Elasticities
This chapter presents the econometric methods that are used in health economics to model individuals health care costs. These methods are used for prediction, projection and forecasting, in the context of risk adjustment, resource allocation, technology assessment and policy evaluation. The chapter reviews the literature on the comparative performance of the methods, especially in the context of forecasting individual health care costs, and concludes with an empirical case study.
Comparing Cost-of-Illness Estimates from Alternative Approaches: An Application to Diabetes
Health Services Research, 2009
Objective. To compare disease cost estimates from two commonly used approaches. Data Source. Pooled Medical Expenditure Panel Survey (MEPS) data for 1998-2003. Study Design. We compared regression-based (RB) and attributable fraction (AF) approaches for estimating disease-attributable costs with an application to diabetes. The RB approach used results from econometric models of disease costs, while the AF approach used epidemiologic formulas for diabetes-attributable fractions combined with the total costs for seven conditions that result from diabetes. Data Extraction. We used SAS version 9.1 to create a dataset that combined data from six consecutive years of MEPS. Principal Findings. The RB approach produced higher estimates of diabetes-attributable medical spending ($52.9 billion in 2004 dollars) than the AF approach ($37.1 billion in 2004 dollars). RB model estimates may in part be higher because of the challenges of implementing the two approaches in a similar manner, but may also be higher because they capture the costs of increased treatment intensity for those with the disease. Conclusions. We recommend using the RB approach for estimating disease costs whenever individual-level data on health care spending are available and when the presence of the disease affects treatment costs for other conditions, as in the case of diabetes.
Healthcare Cost Regressions: Going Beyond the Mean to Estimate the Full Distribution
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Understanding the data generating process behind healthcare costs remains a key empirical issue. Although much research to date has focused on the prediction of the conditional mean cost, this can potentially miss important features of the full distribution such as tail probabilities. We conduct a quasi-Monte Carlo experiment using the English National Health Service inpatient data to compare 14 approaches in modelling the distribution of healthcare costs: nine of which are parametric and have commonly been used to fit healthcare costs, and five others are designed specifically to construct a counterfactual distribution. Our results indicate that no one method is clearly dominant and that there is a trade-off between bias and precision of tail probability forecasts. We find that distributional methods demonstrate significant potential, particularly with larger sample sizes where the variability of predictions is reduced. Parametric distributions such as log-normal, generalised gamma...
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IJCRT , 2022
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Cost Prediction of Health Insurance
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Value in health : the journal of the International Society for Pharmacoeconomics and Outcomes Research, 2017
The validation of health economic (HE) model outcomes against empirical data is of key importance. Although statistical testing seems applicable, guidelines for the validation of HE models lack guidance on statistical validation, and actual validation efforts often present subjective judgment of graphs and point estimates. To discuss the applicability of existing validation techniques and to present a new method for quantifying the degrees of validity statistically, which is useful for decision makers. A new Bayesian method is proposed to determine how well HE model outcomes compare with empirical data. Validity is based on a pre-established accuracy interval in which the model outcomes should fall. The method uses the outcomes of a probabilistic sensitivity analysis and results in a posterior distribution around the probability that HE model outcomes can be regarded as valid. We use a published diabetes model (Modelling Integrated Care for Diabetes based on Observational data) to v...
Keep it simple? Predicting primary health care costs with clinical morbidity measures
Models of the determinants of individuals' primary care costs can be used to set capitation payments to providers and to test for horizontal equity. We compare the ability of eight measures of patient morbidity and multimorbidity to predict future primary care costs and examine capitation payments based on them. The measures were derived from four morbidity descriptive systems: 17 chronic diseases in the Quality and Outcomes Framework (QOF); 17 chronic diseases in the Charlson scheme; 114 Expanded Diagnosis Clusters (EDCs); and 68 Adjusted Clinical Groups (ACGs). These were applied to patient records of 86,100 individuals in 174 English practices. For a given disease description system, counts of diseases and sets of disease dummy variables had similar explanatory power. The EDC measures performed best followed by the QOF and ACG measures. The Charlson measures had the worst performance but still improved markedly on models containing only age, gender, deprivation and practice effects. Comparisons of predictive power for different morbidity measures were similar for linear and exponential models, but the relative predictive power of the models varied with the morbidity measure. Capitation payments for an individual patient vary considerably with the different morbidity measures included in the cost model. Even for the best fitting model large differences between expected cost and capitation for some types of patient suggest incentives for patient selection. Models with any of the morbidity measures show higher cost for more deprived patients but the positive effect of deprivation on cost was smaller in better fitting models.