Computing short-interval transition matrices of a discrete-time Markov chain from partially observed data

Markov chains constitute a common way of modelling the progression of a chronic disease through various severity states. For these models, a transition matrix with the probabilities of moving from one state to another for a specific time interval is usually estimated from cohort data. Quite often, however, the cohort is observed at specific times with intervals that may be greater than the interval of interest. The transition matrix computed then needs to be decomposed in order to estimate the desired interval transition matrix suited to the model. Although simple to implement, this method of matrix decomposition can yet result in an invalid short-interval transition matrix with negative or complex entries. In this paper, we present a method for computing short-interval transition matrices that is based on regularization techniques. Our method operates separately on each row of the invalid short-interval transition matrix aiming to minimize an appropriate distance measure. We test our method on various matrix structures and sizes, and evaluate its performance on a real-life transition model for HIV-infected individuals.     

Estimation of mortality rates for disease simulation models using Bayesian evidence synthesis.

PURPOSE: The authors propose a Bayesian approach for estimating competing risks for inputs to disease simulation models. This approach is suggested when modeling a disease that causes a large proportion of all-cause mortality, particularly when mortality from the disease of interest and other-cause mortality are both affected by the same risk factor. METHODS: The authors demonstrate a Bayesian evidence synthesis by estimating other-cause mortality, stratified by smoking status, for use in a simulation model of lung cancer. National (US) survey data linked to death registries (National Health Interview Survey [NHIS]--Multiple Cause of Death files) were used to fit cause-specific hazard models for 3 causes of death (lung cancer, heart disease, and all other causes), controlling for age, sex, race, and smoking status. Synthesis of NHIS data with national vital statistics data on numbers and causes of deaths was performed in WinBUGS (version 1.4.1, MRC Biostatistics Unit, UK). Correction for inconsistencies between the NHIS and vital statistics data is described. A published cohort study was a source of prior information for smoking-related mortality. RESULTS: Marginal posterior densities of annual mortality rates for lung cancer and other-cause death (further divided into heart disease and all other causes), stratified by 5-year age interval, race (white and black), gender, and smoking status (current, former, never), were estimated, specific to a time period (1987-1995). Overall, black current smokers experienced the highest mortality rates. CONCLUSIONS: Bayesian evidence synthesis is an effective method for estimation of cause-specific mortality rates, stratified by demographic factors.     

Markov chain Monte Carlo estimation of a multiparameter decision model: consistency of evidence and the accurate assessment of uncertainty.

Decision models are usually populated 1 parameter at a time, with 1 item of information informing each parameter. Often, however, data may not be available on the parameters themselves but on several functions of parameters, and there may be more items of information than there are parameters to be estimated. The authors show how in these circumstances all the model parameters can be estimated simultaneously using Bayesian Markov chain Monte Carlo methods. Consistency of the information and/or the adequacy of the model can also be assessed within this framework. Statistical evidence synthesis using all available data should result in more precise estimates of parameters and functions of parameters, and is compatible with the emphasis currently placed on systematic use of evidence. To illustrate this, WinBUGS software is used to estimate a simple 9-parameter model of the epidemiology of HIV in women attending prenatal clinics, using information on 12 functions of parameters, and to thereby compute the expected net benefit of 2 alternative prenatal testing strategies, universal testing and targeted testing of high-risk groups. The authors demonstrate improved precision of estimates, and lower estimates of the expected value of perfect information, resulting from the use of all available data.     

Estimation of test error rates, disease prevalence and relative risk from misclassified data: a review

We review methods for the analysis of categorical clinical and epidemiological data, in which the observations are subject to misclassification. Under certain conditions, it is possible to estimate error parameters such as sensitivity, specificity, relative risk, or predictive value, even though no definitive classification (gold standard) is available. The parameter estimates are obtained by modelling the data, using maximum likelihood, with or without some constraints. The models recognize that the true classification of an individual is unknown, and so are sometimes referred to as "latent class" models. The latent class approach provides a unified framework for various methods found in a dispersed literature, characterising each by the number of populations or subgroups in the data, and the number of observations made on each individual; the statistical degrees of freedom are implied by the sampling design. Data sets with less than three replicate observations per individual necessarily require constraints for parameter estimation to be possible. Data sets with three or more replicates lead directly to estimates of the misclassification rates, subject to some simple assumptions. Some more complex problems are also discussed, including data where the response variable has more than two levels, sequential and irregular designs and the effects of assumption violations.     

A stochastic model of malaria transition rates from longitudinal data: considering the risk of "lost to follow-up".

A model, using stochastic processes, is developed to estimate some epidemiological parameters of malaria in a homogeneous population from longitudinal data. Assessments of transition probabilities from one state of health to the other are made taking "lost to follow-up" as a competing risk. The model is based on the assumptions that individuals are transferred at constant rate between states, and only one transition is possible between two consecutive surveys. It shows a good fit to the observed data; the model is simple to understand and can easily be used if computer facilities are not available.     

Estimation of actual report rates using data from the survey of physicians, dentists and pharmacists

PURPOSES: Physicians, dentists and pharmacists are required to report to the Ministry of Health, Labour and Welfare every two years by law in Japan and the Survey of Physicians, Dentists and Pharmacists (SPDP) is carried out based on the information provided. Because report omissions are known to occur with the SPDP, we estimated the actual report rates. METHODS: The report rate is usually estimated by diving the number of persons reporting by the number of total registrants in each registration year, but the survival rate is not considered in this method. We therefore estimated the report rates of registrants after 1955, using data from the SPDP between the years 1982 and 2000, without considering the survival rate, and then estimated the report rates of registrants after 1955, using data from the 2000 SPDP, this time considering the survival rate. We also compared the report rates among physicians, dentists and pharmacists. RESULTS: In the year 2000 SPDP, the report rates (physicians, dentists and pharmacists) without considering the survival rate were 87.08%, 84.98% and 71.58%, respectively. The respective values considering the survival rate were 90.30%, 87.15% and 72.98%, respectively. The improvement in the report rate for pharmacists was less than those for physicians or dentists. With physicians and dentists, when the survival rates were taken into consideration, rates were more than 90% between 1965 and 2000, except for a temporary decline around 1990. With pharmacists, however, lower rates were observed in the earlier years of registration. The reasons for the differences in report rates for physicians, dentists and pharmacists were thought to be as follows: 1) There are more women pharmacists than physicians or dentists. 2) The survival rate of pharmacists is higher than for physicians or dentists. 3) The mean registration age of pharmacists is younger than that of physicians or dentists. CONCLUSIONS: Differences exist with report rates of physicians, dentists and pharmacists, and these appear due to variation in the gender ratio and age distribution.     

Estimation of incidence and recovery rates of Plasmodium falciparum parasitaemia from longitudinal data

A method is described of estimating the malaria incidence rate ĥ and the recovery rate r from longitudinal data. The method is based on the assumption that the phenomenon of patent parasitaemia can be represented by a reversible two-state catalytic model; it is applicable to all problems that can be represented by such a model.     

A chain of evidence with mixed comparisons: models for multi-parameter synthesis and consistency of evidence

Multi-parameter evidence synthesis is a generalization of meta-analysis in which several parameters are estimated jointly. Here this approach is applied to a common form of data structure in which mixed pairwise comparisons are made between treatments in a 'chain of evidence' structure. The data set investigated here, which first appeared in the confidence profile method literature, features three types of data relating to thrombolytic treatment following acute myocardial infarction. There is information on reperfusion (coronary patency) following treatment, information on survival in reperfused and non-reperfused patients (conditional survival), and independent information on the effect of treatment on survival without specifying reperfusion state (overall survival). The objective of this study is to explore models for combining these three types of evidence within a single model, and some of the evidence consistency issues that arise. Bayesian Markov chain Monte Carlo methods are used to fit two models. The first, proposed in the confidence profile literature, assumes there are no differences between studies in baseline effects (equal study effects). The second model assumes fixed treatment effects but allows for study differences in baseline reperfusion and conditional survival rates by assuming random study effects. The equal study effects model fits the data poorly, and cross-validation shows that the overall survival evidence is not consistent with the reperfusion and conditional survival evidence under this model. The evidence appears to be consistent within the more loosely structured random study effects model, but results are sensitive to prior assumptions about the between-study variance. The inconsistency between the three evidence types relates to overall survival, rather than to the effect of treatment on survival. Multi-parameter evidence synthesis, with suitable checks for evidence consistency, can be used to help determine whether chains of evidence 'add up' epidemiologically within an overall model, and to construct parameter distributions for an entire model simultaneously, consistent with all the available data.     

A theoretical model of adolescent suicide and some evidence from US data

Suicide rates for adolescents have doubled since 1970 and tripled since 1960, even as rates for other age groups have declined. Using a Becker-type model of household production and consumption, we demonstrate conditions under which utility maximizing parents allocate time away from time-intensive commodities like children's well-being, and towards market work and less time-intensive consumption commodities. This reallocation of time towards market work has mixed effects on children' mental health: higher money income tends to improve family and children's well-being, but the loss of parental time has an opposite effect on children's mental health and increases the risk of adolescent suicide. Empirical evidence using state panel regressions of adolescent suicide rates on economic, social and demographic variables is consistent with predictions based on our model; our results indicate that the favorable effect of higher incomes has more than offset the negative effect of lost parental time.     

Relinquishment of premarital births: evidence from national survey data.

According to 1982 and 1988 NSFG data, unmarried white women are far less likely than they were in the early 1970s to place their children for adoption. The levels of relinquishment among black women have remained low throughout this period, and relinquishment among Hispanic women may be virtually nonexistent. Multivariate analysis of the determinants of relinquishment among unmarried non-Hispanic white women suggests that having a well-educated mother, being in school at the time of conception, having no labor force experience, and being older are positively associated with placing a child for adoption. Sons were found to be less likely to be relinquished than daughters.     

Good practices that address continuity during transition from child to adult care: synthesis of the evidence

BACKGROUND: Effective transition to adult services is required by an increasing number of children with ongoing needs. AIM: To identify practices that promote continuity at transition between child and adult services. METHODS: Systematic examination of the evidence from two search strategies yielding 5319 items. RESULTS: Only three of the 126 appraised items had strong external validity. A large range of different practices, which focused on the service, the young person and the family, were identified. Practices within the service addressed structural, process and outcome components. CONCLUSION: Four transition models are proposed for testing.     

Health,health care,and the environment. Econometric evidence from German micro data

The paper develops and applies a Grossman-style health production model set up in discrete time to explain the impact of environmental pollution on the demand for both health and health care. In order to introduce the environment, our analysis takes changes in environmental conditions to influence the rate at which an individual's stock of health depreciates. While the theoretical part of our paper also contains a discussion of the full model, we restrict our empirical analysis to a submodel which is known as the pure investment model. This is because the other submodel, the pure consumption model, implies a rather implausible case of satiation with respect to the individual's preferences. Our empirical findings are based on data taken from the German Socio-economic Panel. The stock of health capital and environmental pollution are treated as latent variables and estimated using a Linear Covariance Structures model. The quality of the environment turns out to be an important determinant of health capital. From the point of view of health economics, improvements in environmental conditions can be interpreted as preventive measures. In terms of prevention, public policies designed to protect the environment also yield significant health effects. As regards health care demand the influence is not clearcut, i.e., one cannot necessarily expect a reduction in resource use.     

Participation,heterogeneity and dynamics in tobacco consumption: evidence from cohort data

In this paper we look at the behaviour of households as far as participation and rate of consumption of tobacco are concerned using cohort data from the Spanish Continuous Family Expenditure Survey during the period 1985–94. We test the results, in statistical and economic terms, from several estimators on samples with different levels of aggregation and offer evidence on the different behaviour of households according to several demographic characteristics. The results suggest that the effect of legislative measures cannot be identified when participation and consumption are not separately considered. Once we do so, these measures seem to affect participation alone. © 1998 John Wiley & Sons, Ltd.     

The effects of economic instability on infant, neonatal, and postneonatal mortality rates: evidence from Taiwan

This paper uses a panel data set comprising 23 cities for the years 1979-2002 in Taiwan and a fixed-effects model to find evidence of the effect of economic instability on infant, neonatal, and postneonatal mortality rates. In addition, the effects of income, demographic factors, and the availability of medical resources are also examined in relation to the mortalities. The most important finding is that infant, neonatal, and postneonatal mortality rates move counter-cyclically with the city unemployment rate in Taiwan. The provision of national health insurance is also found to have a positive impact on the health of infants in Taiwan. Finally, the impact of economic instability on the infant, neonatal, and postneonatal mortality rates is found to be the strongest in the eastern part of Taiwan, which is the region with the fewest health care resources. The analysis provides evidence of the effects of economic instability on the infant, neonatal, and postneonatal mortality rates in a developing country, which are comparable to those of other countries and may provide some important insights into this issue.     

Medical guidelines, physician density, and quality of care: evidence from German SHARE data

We use German SHARE data to study the relationship between district general practitioner density and the quality of preventive care provided to older adults. We measure physician quality of care as the degree of adherence to medical guidelines (for the management of risk factors for cardiovascular disease and the prevention of falls) as reported by patients. Contrary to theoretical expectations, we find only weak and insignificant effects of physician density on quality of care. Our results shed doubt on the notion that increasing physician supply will increase the quality of care provided in Germany's present health care system.     

The effectiveness of automobile safety regulation: evidence from the FARS data.

In a paper published in the August 1981 issue of this Journal, Leon Robertson attempts to measure the effects of the vehicle safety and occupant protection standards implemented in the 1960s. Data from the Fatal Accident Reporting System are used. Additional statistical analysis with these data reveals a multicollinearity problem that makes the prediction of the effects of regulation uncertain. There is also bias in regression results due to the inappropriate inclusion of truck data in the regressions. Regressions on the car data reveal a lifesaving effect of regulation that, at best, is one-fourth the value reported by Robertson.     

Taxation, smuggling and demand for cigarettes in Canada: evidence from time-series data

This study analyzes Canadian cigarette consumption and taxation between 1980 and 1994, a period in which there have been large price rises and declines, and a dramatic increase in the consumption of contraband tobacco products. We examine elasticities of legal cigarette sales and total sales (including contraband) with respect to the price of legal cigarettes and various other factors. The growth of the contraband market since 1987 appears to have created two classes of cigarette--taxed and untaxed--with responses to changes in the legal price that are respectively higher, and lower, than was previously the case. The sensitivity of total cigarette sales to the taxation instrument is much lower than it would appear from sales of taxed cigarettes alone.     

Alcohol and oesophageal cancer: an assessment of the evidence from routinely collected data.

Although various factors have been implicated in the aetiology of oesophageal cancer, one factor common to many countries is the consumption of alcoholic beverages. In England and Wales mrtality from oesophageal cancer declined rapidly during the early part of this century but both mortality and incidence have increased in recent years. The generation of males born in 1906 had lower mortality than any preceding or succeeding generation. It is suggested that ages 20 to 30 may be critical in the development of oesophageal cancer and that the 1906 cohort was less exposed to alcohol than other generations. The international analysis suggests that ethyl alcohol itself rather than any specific alcoholic beverage is associated with this cancer.