Probabilistic sensitivity analysis using Monte Carlo simulation. A practical approach

The data for medical decision analyses are often unreliable. Traditional sensitivity analysis--varying one or more probability or utility estimates from baseline values to see if the optimal strategy changes--is cumbersome if more than two values are allowed to vary concurrently. This paper describes a practical method for probabilistic sensitivity analysis, in which uncertainties in all values are considered simultaneously. The uncertainty in each probability and utility is assumed to possess a probability distribution. For ease of application we have used a parametric model that permits each distribution to be specified by two values: the baseline estimate and a bound (upper or lower) of the 95 percent confidence interval. Following multiple simulations of the decision tree in which each probability and utility is randomly assigned a value within its distribution, the following results are recorded: (a) the mean and standard deviation of the expected utility of each strategy; (b) the frequency with which each strategy is optimal; (c) the frequency with which each strategy "buys" or "costs" a specified amount of utility relative to the remaining strategies. As illustrated by an application to a previously published decision analysis, this technique is easy to use and can be a valuable addition to the armamentarium of the decision analyst.     

The quantile regression approach to efficiency measurement: insights from Monte Carlo simulations

In the health economics literature there is an ongoing debate over approaches used to estimate the efficiency of health systems at various levels, from the level of the individual hospital - or nursing home - up to that of the health system as a whole. The two most widely used approaches to evaluating the efficiency with which various units deliver care are non-parametric data envelopment analysis (DEA) and parametric stochastic frontier analysis (SFA). Productivity researchers tend to have very strong preferences over which methodology to use for efficiency estimation. In this paper, we use Monte Carlo simulation to compare the performance of DEA and SFA in terms of their ability to accurately estimate efficiency. We also evaluate quantile regression as a potential alternative approach. A Cobb-Douglas production function, random error terms and a technical inefficiency term with different distributions are used to calculate the observed output. The results, based on these experiments, suggest that neither DEA nor SFA can be regarded as clearly dominant, and that, depending on the quantile estimated, the quantile regression approach may be a useful addition to the armamentarium of methods for estimating technical efficiency.     

Measuring chemical sensitivity prevalence: a questionnaire for population studies.

Because no information exists on the prevalence of chemical sensitivity syndromes such as multiple chemical sensitivities, a questionnaire for use in population studies was developed and tested to assess the presence or absence of chemical sensitivity. Seven hundred five individuals attending clinics answered a questionnaire asking whether each of 122 common substances caused symptoms. Results showed that patients with multiple chemical sensitivities and asthma had average total scores that were significantly different from each other and from those of each of the other diagnostic categories. Higher total scores were also reported by female patients. The instrument described here may facilitate meaningful prevalence studies of multiple chemical sensitivities. It will also allow study of chemically induced symptoms in other conditions such as asthma.     

Bayesian proportional hazards model with time-varying regression coefficients: a penalized Poisson regression approach

One can fruitfully approach survival problems without covariates in an actuarial way. In narrow time bins, the number of people at risk is counted together with the number of events. The relationship between time and probability of an event can then be estimated with a parametric or semi-parametric model. The number of events observed in each bin is described using a Poisson distribution with the log mean specified using a flexible penalized B-splines model with a large number of equidistant knots. Regression on pertinent covariates can easily be performed using the same log-linear model, leading to the classical proportional hazard model. We propose to extend that model by allowing the regression coefficients to vary in a smooth way with time. Penalized B-splines models will be proposed for each of these coefficients. We show how the regression parameters and the penalty weights can be estimated efficiently using Bayesian inference tools based on the Metropolis-adjusted Langevin algorithm.     

Measuring the benefits of clinical decision support: return on investment.

In an effort to provide high quality care in a more cost-effective manner, health care providers have found it necessary to implement a series of decision support strategies designed to improve outcomes of care. While each of these strategies has measurable benefits, they each come along with additional costs. This article will describe a methodology for measuring the costs and direct and indirect benefits from decision support activities.     

Measuring familial aggregation by using odds-ratio regression models.

Detection of familial aggregation of a disease is important for studying possible genetic and environmental factors contributing to disease etiology. Accurate quantification of familial aggregation can provide guidance for subsequent, more sophisticated genetic studies. This article presents a statistical model and method for detecting both inter- and intra-class aggregation of a binary trait with family data. The method used here is based on the logistic regression model which incorporates effects of individual covariates while measuring familial aggregation of risk as the odds ratios among classes of relatives. An estimation equation approach is presented where the joint distribution of binary traits among family members need not be fully specified. Data from a genetic epidemiologic study on liver cancer in Shanghai are analyzed for illustration, and reveal strong aggregation of risk even after adjusting for covariates. Effects of non-random sampling and ascertainment bias are also discussed.     

Measuring maternal mortality: sense and sensitivity

The majority of maternal deaths in developing countries arepreventable. The long overdue recognition of this tragic fact,together with the mounting evidence of the sheer magnitude ofthe problem, has strengthened the need to interpret these deathsfrom the perspective of the family. The conventional measuresof maternal mortality disguise the impact of these family tragediessince they inadequately reflect the influence of the level andpattern of fertility and the lifetime risk of childbearing.These inadequacies have important programme implications. Usingdata from a selection of developing countries, the paper showsthat women in their prime reproductive period contribute thegreatest number of maternal deaths. These women also have thegreatest number of young, dependent children whose own survivaland well-being may be seriously compromised by the death oftheir mother. In many developing countries, maternal healthcare is often targeted on women outside the prime childbearingperiod who, whilst having the highest risk of dying once theyare pregnant, also have a much lower chance of being pregnantin the first place and will have relatively fewer dependentchildren. This strategy limits the potential reduction in thenumber of maternal deaths and overlooks the wider familial repercussionsof these tragic events.     

Measuring inpatient and outpatient costs: a cost-function approach

In this article, the authors estimate a multiple-output cost function for a sample of 2,235 hospitals during the period 1984-88 to disaggregate total costs into inpatient and outpatient components. The results suggest that outpatient cost growth is roughly proportional to that of inpatient cost, despite much higher relative growth in revenues and utilization on the outpatient side. The stability in the outpatient/inpatient cost ratio implies that the increase in the outpatient-to-inpatient utilization ratio was offset by a decline in their relative unit costs.     

Measuring reproductive morbidity: a community-based approach, Jordan

Our objective in this study was to determine the prevalence of reproductive and related nonreproductive morbidities in a group of reproductive-aged women living in Jordan. The study was designed as a two-phase survey. The first phase consisted of a structured personal interview and the second phase was a follow-up physical examination. Three hundred seventeen women aged 18-49 years were randomly selected and answered the questionnaire in the first phase of the study. Two hundred sixty agreed to both the general physical and pelvic examination. The main outcome measures were selected reproductive and related nonreproductive morbidities. Results show reproductive tract infections were diagnosed in 55% of the women, a presumed chlamydia trachomatis genital infection in 40%, and genital prolapse in 22%. As for related nonreproductive morbidities, 14% were diagnosed with a urinary tract infection (UTI), 24% with urinary incontinence, and 40% with anemia. Our results of the study support the idea that in this community, women's health is at risk throughout their reproductive years, not only when they are pregnant or postpartum. We suggest further research in other Jordanian communities as well as solutions addressed to the health care community.     

Predicting sediment toxicity using logistic regression: a concentration-addition approach

The question posed in this article is how useful the chemical concentration measurements for predicting the outcome of sediment toxicity tests are. Using matched data on sediment toxicity and sediment chemical concentrations from a number of studies, we investigated several approaches for predicting toxicity based on multiple logistic regression with concentration-addition models. Three models were found to meet criteria for acceptability. The first model uses individual chemicals selected using stepwise selection. The second uses derived variables to reflect combined metal contamination, polycyclic aromatic hydrocarbon (PAH) contamination, and the interaction between metals and PAHs. The third and final model is a separate species model with derived variables. Overall, these models suggest that toxicity may be correctly predicted approximately 77% of the time, although prediction is better for samples identified as nontoxic than for those known to be toxic.     

Statistical evidence for GLM regression parameters: a robust likelihood approach

When a likelihood ratio is used to measure the strength of evidence for one hypothesis over another, its reliability (i.e. how often it produces misleading evidence) depends on the specification of the working model. When the working model happens to be the 'true' or 'correct' model, the probability of observing strong misleading evidence is low and controllable. But this is not necessarily the case when the working model is misspecified. Royall and Tsou (J. R. Stat. Soc., Ser. B 2003; 65:391-404) show how to adjust working models to make them robust to misspecification. Likelihood ratios derived from their 'robust adjusted likelihood' are just as reliable (asymptotically) as if the working model were correctly specified in the first place. In this paper, we apply and extend these ideas to the generalized linear model (GLM) regression setting. We provide several illustrations (both from simulated data and real data concerning rates of parasitic infection in Philippine adolescents), show how the required adjustment factor can be obtained from standard statistical software, and draw some connections between this approach and the 'sandwich estimator' for robust standard errors of regression parameters. This substantially broadens the availability and the viability of likelihood methods for measuring statistical evidence in regression settings.     

A Bayesian approach to a general regression model for ROC curves.

A fully Bayesian approach to a general nonlinear ordinal regression model for ROC-curve analysis is presented. Samples from the marginal posterior distributions of the model parameters are obtained by a Markov-chain Monte Carlo (MCMC) technique--Gibbs sampling. These samples facilitate the calculation of point estimates and credible regions as well as inferences for the associated areas under the ROC curves. The analysis of an example using freely available software shows that the use of noninformative vague prior distributions for all model parameters yields posterior summary statistics very similar to the conventional maximum-likelihood estimates. Clinically important advantages of this Bayesian approach are: the possible inclusion of prior knowledge and beliefs into the ROC analysis (via the prior distributions), the possible calculation of the posterior predictive distribution of a future patient outcome, and the potential to address questions such as: "What is the probability that a certain diagnostic test is better in one setting than in another?"     

Comprehensive decision analytical modelling in economic evaluation: a Bayesian approach

Decision analytical models are widely used in economic evaluation of health care interventions with the objective of generating valuable information to assist health policy decision-makers to allocate scarce health care resources efficiently. The whole decision modelling process can be summarised in four stages: (i) a systematic review of the relevant data (including meta-analyses), (ii) estimation of all inputs into the model (including effectiveness, transition probabilities and costs), (iii) sensitivity analysis for data and model specifications, and (iv) evaluation of the model. The aim of this paper is to demonstrate how the individual components of decision modelling, outlined above, may be addressed simultaneously in one coherent Bayesian model (sometimes known as a comprehensive decision analytical model) and evaluated using Markov Chain Monte Carlo simulation implemented in the specialist software WinBUGS. To illustrate the method described, it is applied to two illustrative examples: (1) The prophylactic use of neurominidase inhibitors for the prevention of influenza. (2) The use of taxanes for the second-line treatment of advanced breast cancer.The advantages of integrating the four stages outlined into one comprehensive decision analytical model, compared to the conventional 'two-stage' approach, are discussed.     

A Bayesian approach to sensitivity analysis.

Sensitivity analysis has traditionally been applied to decision models to quantify the stability of a preferred alternative to parametric variation. In the health literature, sensitivity measures have traditionally been based upon distance metrics, payoff variations, and probability measures. We advocate a new approach based on information value and argue that such an approach is better suited to address the decision-maker's real concerns. We provide an example comparing conventional sensitivity analysis to one based on information value. This article is a US government work and is in the public domain in the United States.     

Measuring health status: information for primary care decision making

Primary Care Trusts (PCTs), charged with improving the health of their population, need to measure the extent to which patients actually benefit from the health care that is provided for them. One way of achieving this is to measure health status of patients over time. The study described here reports on the feasibility of administering the EQ-5D in general practitioner (GP) surgeries and identifies how the results might be used by practices and PCTs to improve the health of their populations. The study took place in an opportunistic sample of 1942 patients attending GP surgeries. One year later, patients who had provided contact details were sent another EQ-5D together with a request for additional information about their use of health care services in the intervening time period. A total of 770 patients completed this follow-up questionnaire. There were significant age effects associated with variation in self-reported health status and also associated with top-level Read diagnostic codes in some groups of patients. The results showed that EQ-5D could be used by individual GP practices to identify patients with specific health problems. This knowledge can also be used by PCTs and other primary care organisations, to better target scarce health resources.     

Scale and scope economies in nursing homes: a quantile regression approach

Nursing homes vary widely between facilities with very few beds and facilities with several hundred beds. Previous studies, which estimate nursing home scale and scope economies, do not account for this heterogeneity and implicitly assume that all nursing homes face the same cost structure. To account for heterogeneity, this paper uses quantile regression to estimate cost functions for skilled and intermediate care nursing homes. The results show that the parameters of nursing home cost functions vary significantly by output mix and across the cost distribution. Estimates show that product-specific scale economies systematically increase across the cost distribution for both skilled and intermediate care facilities, with diseconomies of scale in the lower deciles and no significant scale economies in the higher deciles. As for ray scale economies, estimates show economies of scale in the lower deciles and diseconomies of scale or no significant scale economies at higher deciles. The estimates also show that scope economies exist in the lower cost deciles and that no scope economies exist in the higher cost deciles. Additionally, the degree of scope economies monotonically decreases across the deciles.     

Measuring health indicators and allocating health resources: a DEA-based approach

This paper suggests new empirical DEA models for the measurement of health indicators and the allocation of health resources. The proposed models were developed by first suggesting a population-based health indicator. By introducing the suggested indicator into DEA models, a new approach that solves the problem of health resource allocation has been developed. The proposed models are applied to an empirical study of Taiwan’s health system. Empirical findings show that the suggested indicator can successfully accommodate the differences in health resource demands between populations, providing more reliable performance information than traditional indicators such as physician density. Using our models and a commonly used allocation mechanism, capitation, to allocate medical expenditures, it is found that the proposed model always obtains higher performance than those derived from capitation, and the superiority increases as allocated expenditures rise.