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Capture-recapture method for estimating misclassification errors: application to the measurement of vaccine efficacy in randomized controlled trials.

BACKGROUND: The measure of efficacy is optimally performed by randomized controlled trials. However, low specificity of the judgement criteria is known to bias toward lower estimation, while low sensitivity increases the required sample size. A common technique for ensuring good specificity without a drop in sensitivity is to use several diagnostic tests in parallel, with each of them being specific. This approach is similar to the more general situation of case-counting from multiple data sources, and this paper explores the application of the capture-recapture method for the analysis of the estimates of efficacy. METHOD: An illustration of this application is derived from a study on the efficacy of pertussis vaccines where the outcome was based on > or =21 days of cough confirmed by at least one of three criteria performed independently for each subject: bacteriology, serology, or epidemiological link. Log-linear methods were applied to these data considered as three sources of information. RESULTS: The best model considered the three simple effects and an interaction term between bacteriology and epidemiological linkage. Among the 801 children experiencing > or =21 days of cough, it was estimated that 93 cases were missed, leading to a corrected total of 413 confirmed cases. The relative vaccine efficacy estimated from the same model was 1.50 (95% confidence interval: 1.24-1.82), similar to the crude estimate of 1.59 and confirming better protection afforded by one of the two vaccines. CONCLUSION: This method allows supporting analysis to interpret primary estimates of vaccine efficacy.

Adolescent↗

Estimation of PAHs dry deposition and BaP toxic equivalency factors (TEFs) study at Urban, Industry Park and rural sampling sites in central Taiwan, Taichung.

The concentrations of polycyclic aromatic hydrocarbons (PAHs) in gas phase and particle bound were measured simultaneously at industrial (INDUSTRY), urban (URBAN), and rural areas (RURAL) in Taichung, Taiwan. And the PAH concentrations, size distributions, estimated PAHs dry deposition fluxes and health risk study of PAHs in the ambient air of central Taiwan were discussed in this study. Total PAH concentrations at INDUSTRY, URBAN, and RURAL sampling sites were found to be 1650 +/- 1240, 1220 +/- 520, and 831 +/- 427 ng/m3, respectively. The results indicated that PAH concentrations were higher at INDUSTRY and URBAN sampling sites than the RURAL sampling sites because of the more industrial processes, traffic exhausts and human activities. The estimation dry deposition and size distribution of PAHs were also studied. The results indicated that the estimated dry deposition fluxes of total PAHs were 58.5, 48.8, and 38.6 microg/m2/day at INDUSTRY, URBAN, and RURAL, respectively. The BaP equivalency results indicated that the health risk of gas phase PAHs were higher than the particle phase at three sampling sites of central Taiwan. However, compared with the BaP equivalency results to other studies conducted in factory, this study indicated the health risk of PAHs was acceptable in the ambient air of central Taiwan.

Air Pollutants↗

Empirical Bayes methods for estimating hospital-specific mortality rates.

We present alternative methods for estimating hospital-level mortality rates to those used by the Health Care Finance Administration for Medicare patients. We use an empirical Bayes model to represent the different sources of variation in observed hospital-specific mortality rates and we use a logistic regression model to adjust for severity differences (in patient mix) across hospitals. In addition to providing a principled derivation of a standard error for the commonly used estimator, our fully model-based formulation produces much more accurate estimates and resolves the severe problem of multiple comparisons that arises when extreme estimates are used to identify exceptional hospitals. We estimate models for each of four disease conditions using the national Medicare mortality data base which does not contain patient severity descriptors, and mortality data from national samples which do include patient severity descriptors. We find substantial between-hospital variation in the unadjusted death rates from the national data base. Mortality rates differ substantially with patient severity in our models, but the sample sizes are too small to yield reliable estimates of the between-hospital variation in adjusted mortality rates.

Bayes Theorem↗

The meaning and use of the area under a receiver operating characteristic (ROC) curve.

A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.

Evaluation Studies as Topic↗

HMO enrollment: a study of market forces and regulations.

This paper investigates the influence of market forces and state regulations on enrollment in prepaid group practices (PGPs)--the dominant form of HMO. Using data at the metropolitan-area level, the paper estimates a lagged-adjustment model in two stages. The first stage estimates the determinants of the existence of a PGP of viable size. Using a technique appropriate for censored samples, the second stage estimates the determinants of enrollment given viability. The result of greatest relevance for policymakers is that restrictions on corporate employment of physicians hinder the growth of PGPs.

Certificate of Need↗

Evaluating the uncertainty of risk prediction in genetic counseling: a Bayesian approach.

A general method to obtain the exact point estimate and the measure of uncertainty of recurrence risks for genetic counseling is present. This method, which follows Bayesian estimation theory, can be applied without restrictions of sample size, class of risk function, or parameter dimension. As an illustration, the recurrence risks for isolated cases in two autosomal dominant disorders with incomplete penetrance (mandibulofacial and fontonasal dyostoses) are estimated.

Bayes Theorem↗

Genotypic correlation and regression in social groups: multiple alleles, multiple loci and subdivided populations.

Genotypic correlations and regressions can be estimated from multiallelic data sets either by weighting the allelic effects additively or by specifically weighting the genotypic interactions. Both methods can be extended to multiple loci, but they do not fully take into account the joint segregation patterns at the loci. These genotypic statistics have a great importance in sociobiological contexts, as they can be used for genetic descriptions of social structures. In this paper I examine the two estimation methods and show how the genotypic correlation and regression coefficients from genotypic interactions are connected to other statistics of standard population genetics; special emphasis is given to the sample-size correction when intracolony correlations from small samples were estimated. I also show how genotypic correlation and regression can be estimated in subdivided populations, both in continuous populations with isolation by distance and in populations divided into separate subpopulations. The latter analysis is an example of a more general hierarchic correlation analysis.

Alleles↗

Mixture models for estimating the size of a closed population when capture rates vary among individuals.

We develop a parameterization of the beta-binomial mixture that provides sensible inferences about the size of a closed population when probabilities of capture or detection vary among individuals. Three classes of mixture models (beta-binomial, logistic-normal, and latent-class) are fitted to recaptures of snowshoe hares for estimating abundance and to counts of bird species for estimating species richness. In both sets of data, rates of detection appear to vary more among individuals (animals or species) than among sampling occasions or locations. The estimates of population size and species richness are sensitive to model-specific assumptions about the latent distribution of individual rates of detection. We demonstrate using simulation experiments that conventional diagnostics for assessing model adequacy, such as deviance, cannot be relied on for selecting classes of mixture models that produce valid inferences about population size. Prior knowledge about sources of individual heterogeneity in detection rates, if available, should be used to help select among classes of mixture models that are to be used for inference.

Animal Identification Systems↗

Robustness of some estimators for the analysis of covariance structures.

A sampling experiment was designed to evaluate the robustness of some estimators used in the analysis of covariance structures to misspecification of the discrepancy function in finite samples. The estimators were studied under four distribution (a multivariate normal, an elliptical, a non-elliptically symmetric, and an asymmetric multivariate distribution, and eight sample size (75, 150, 300, 600, 1200, 2400, 4800, 9600) conditions. Parameters of the composite direct product model for a 6-variable MTMM matrix were estimated using the Maximum Wishart Likelihood (MWL), generalized least squares (GLS), asymptotically distribution free (ADF), and approximate ADF (DADF) estimators. Browne's elliptical correction (CMWL) to the test statistic and standard errors for scale-invariant models was also made for each sample. Each of the 32 distribution-sample size conditions was replicated 300 times. The accuracy of the parameter estimates and estimated standard errors and the distribution of the test statistic were studied. The theoretically predicted importance of information contained in higher-order moments of arbitrary distributions was confirmed. Robustness of the MWL and normal theory GLS estimators cannot be taken for granted. Elliptical corrections may be a practical solution to some data analytic problems.

Female↗

Confidence intervals, hypothesis tests, and sample sizes for the prevented fraction in cross-sectional studies.

The prevented fraction (PF) is the proportion of disease occurrence in a population averted due to a protective risk factor or public health intervention. The PF is not equivalent to the population attributable risk (AR). The AR is appropriate for epidemiologic studies of disease etiology, and for estimating the potential impact of modifying risk factor prevalence. The PF more directly measures the impact of public health interventions, however, and thus is an important evaluation tool. We derived the variance of the estimated PF by using maximum likelihood theory for cross-sectional studies. We used simulations to compare the performance of confidence intervals based on various transformations of the estimated PF. The logit transformation was the best choice when PF > or = 0.3, whereas the untransformed estimate was best when PF < 0.3. We present formulae for hypothesis testing and sample size calculations, discuss the issues of interaction and confounding and give two estimators adjusted for confounding.

Analysis of Variance↗

Transmission of encephalomyocarditis virus in pigs estimated from field data in Belgium by means of R0.

Transmission of encephalomyocarditis-virus (EMCV) has been estimated in experiments, but never using field data. In this field study, a farm in Belgium was selected where the presence of EMCV was confirmed by necropsy and virus isolation. Serology was used to estimate the transmission parameter R0. In one compartment with 630 pigs, 6 pens were fully sampled, in the remaining 38 pens, 2 randomly selected pigs were bled. The 151 pigs were bled twice and their serum was tested in a virus neutralisation test. Seroprevalence at the first and second sampling was 41 and 43% respectively, with a cut off value of 1:40. R0 was estimated for 2 scenarios, in- and excluding mortality based on the final sizes from the serological results of the second sampling. The R0 for the fully sampled pens was estimated between 0.6 and 1.7, the combined estimated R0 of these 6 pens was 1.36 (95%-CI 0.93-2.23). The median of the estimated R0 of the partially sampled pens was 1.3 and 1.4. Sampling two pigs per pen provided insight into the spread of the virus in the compartment, while the fully sampled pens provided an accurate estimation of R0. The low R0 strongly suggests that EMCV is not very effectively transmitted between pigs. The number of seropositive pigs in a pen and the spread in the compartment suggests that other routes of infection are more important, in this case most likely rodents. Preventing viral spread should therefore be focussed on rodent control instead of reduction of contact between pigs.

Animals↗

[Variabilities in chromosomal aberrations in human somatic cells].

Variabilities in the frequency of spontaneous chromosomal aberrations depend on subjective and objective factors, the stochastic nature of occurrence and recording of the aberrations. Due to the low frequency of spontaneous chromosomal aberrations, it is impossible to exactly assess their frequency on an individual basis. The low accuracy of estimating the individual frequency of spontaneous chromosomal aberrations while analyzing 100-1000 cells virtually allows the use of the individual average frequencies of chromosomal aberrations without taking into account the size of a sample to have an average group estimation of the frequency of chromosomal aberrations. The average frequencies of spontaneous chromosomal aberrations can be obtained to a rather high accuracy for individual groups when a sample comprises 50 to several hundreds of individuals. It is shown that the frequency of spontaneous chromosomal aberrations does not depend on sex and age. There is a significant variability in their frequency in relation to a season and to the year of a follow-up. Regular changes are found in the frequency of spontaneous chromosomal aberrations depending on the number of a month and on the year of a follow-up.

Age Factors↗

Lot quality assurance sampling (LQAS) for monitoring leprosy elimination in an endemic district in Tamilnadu.

This paper examines whether the health administration can use lot quality assurance sampling (LQAS) for identifying high prevalence areas for leprosy for initiating necessary corrective measures. The null hypothesis was that leprosy prevalence in the district was at or above ten per 10,000 and the alternative hypothesis was that it was at or below five per 10,000. A total of 25,500 individuals were to be examined with 17 as an acceptable maximum number of cases (critical value). Two-stage cluster sample design was adopted. The sample size need not be escalated as the estimated design effect was 1. During the first phase, the survey covered a population of 4,837 individuals out of whom 4,329 (89.5%) were examined. Thirty-five cases were detected and this number far exceeded the critical value. It was concluded that leprosy prevalence in the district should be regarded as having prevalence of more than ten per 10,000 and further examination of the population in the sample was discontinued. LQAS may be used as a tool by which one can identify high prevalence districts and target them for necessary strengthening of the programme. It may also be considered for certifying elimination achievement for a given area.

Cluster Analysis↗

In defense of matching.

This paper discusses the simplified situation of an epidemiologic study involving disease, exposure, and a single (possibly confounding) extraneous factor, all of which are dichotomous. The question is: In studying the association between disease and exposure, should the comparison group be selected by random sampling or by matching on the extraneous factor? An example is used to demonstrate the general principle that matching controls confounding in estimating the risk ratio in a follow-up study, but not in estimating the exposure odds ratio in a case-control study. Calculations based on a probability model show that, despite the possible reduction in sample size which may be associated with matching, matching will often lead to a more precise estimate of the effect measure than random sampling and is not likely to result in a significant loss in precision in situations of practical importance. Therefore, selection of the referent group by matching should be given serious consideration for both follow-up and case-control studies.

Epidemiologic Methods↗

A plant-transformation-competent BIBAC library from the Arabidopsis thaliana Landsberg ecotype for functional and comparative genomics.

The genome of the model plant Arabidopsis thaliana has been sequenced to near completion. To facilitate experimental determination of the function of every gene in the species, we constructed a large-insert library from the Landsberg ecotype using a plant-transformation-competent binary BAC vector, BIBAC2. The library contains 11,520 clones with an estimated average insert size of 162 kb. Of a sample of 102 clones, 17.6% had no inserts; further, in the library as a whole, 287 clones contained chloroplast DNA, and 25 contained mitochondrial DNA. Thus it is estimated that 9,295 clones originated from the nuclear genome, representing a 11.5 x coverage. The library was further characterized by screening with probes corresponding to 180-bp repeats, 5S rDNA, 18S-25S rDNA and 23 single-copy RFLP markers. The results showed that 92 clones contained 180-bp centromeric repeats, 78 contained 5S rDNA and 95 contained 18S-25S rDNA, approximately 1%, 0.8% and 1%, respectively, of the nuclear clones in the library. Screening the library with the 23 RFLP markers showed that each one hybridized to an average of seven clones. This library is the first large-insert DNA library for the widely studied Landsberg erecta strain. It will greatly facilitate gene identification by complementation screening, and will enhance analysis of the structure, organization and evolution of the A. thaliana genome.

Arabidopsis↗

Slopes of a receiver operating characteristic curve and likelihood ratios for a diagnostic test.

This paper clarifies two important concepts in clinical epidemiology: the slope of a receiver operating characteristic (ROC) curve and the likelihood ratio. It points out that there are three types of slopes in an ROC curve--the tangent at a point on the curve, the slope between the origin and a point on the curve, and the slope between two points on the curve. It also points out that there are three types of likelihood ratios that can be defined for a diagnostic test that produces results on a continuous scale--the likelihood ratio for a particular single test value, the likelihood ratio for a positive test result, and the likelihood ratio for a test result in a particular level or category. It further illustrates mathematically and empirically the following three relations between these various definitions of slopes and likelihood ratios: 1) the tangent at a point on the ROC curve corresponds to the likelihood ratio for a single test value represented by that point; 2) the slope between the origin and a point on the curve corresponds to the positive likelihood ratio using the point as a criterion for positivity; and 3) the slope between two points on the curve corresponds to the likelihood ratio for a test result in a defined level bounded by the two points. The likelihood ratio for a single test value is considered an important parameter for evaluating diagnostic tests, but it is not easily estimable directly from laboratory data because of limited sample size. However, by using ROC analysis, the likelihood ratio for a single test value can be easily measured from the tangent. It is suggested that existing ROC analysis software be revised to provide estimates for tangents at various points on the ROC curve.

Creatine Kinase↗

Diagnostic test accuracy and prevalence inferences based on joint and sequential testing with finite population sampling.

The two-test two-population model, originally formulated by Hui and Walter, for estimation of test accuracy and prevalence estimation assumes conditionally independent tests, constant accuracy across populations and binomial sampling. The binomial assumption is incorrect if all individuals in a population e.g. child-care centre, village in Africa, or a cattle herd are sampled or if the sample size is large relative to population size. In this paper, we develop statistical methods for evaluating diagnostic test accuracy and prevalence estimation based on finite sample data in the absence of a gold standard. Moreover, two tests are often applied simultaneously for the purpose of obtaining a 'joint' testing strategy that has either higher overall sensitivity or specificity than either of the two tests considered singly. Sequential versions of such strategies are often applied in order to reduce the cost of testing. We thus discuss joint (simultaneous and sequential) testing strategies and inference for them. Using the developed methods, we analyse two real and one simulated data sets, and we compare 'hypergeometric' and 'binomial-based' inferences. Our findings indicate that the posterior standard deviations for prevalence (but not sensitivity and specificity) based on finite population sampling tend to be smaller than their counterparts for infinite population sampling. Finally, we make recommendations about how small the sample size should be relative to the population size to warrant use of the binomial model for prevalence estimation.

Agglutination Tests↗

Modelling the effect of surveillance programmes on spread of bovine herpesvirus 1 between certified cattle herds.

For the eradication of an infectious agent, like bovine herpesvirus 1 (BHV-1), surveillance and certification can be used to reduce the transmission between herds. The goal of surveillance is that a certified herd that becomes infected is detected timely so that infection of several other certified herds is prevented. What counts is whether the reproduction ratio R, i.e. the average number of certified herds infected by one infected certified herd can be kept below 1. To support policy makers in making decisions about the minimal demands for a surveillance programme in an eradication campaign of BHV-1 in cattle, two mathematical models were investigated. With these models, the basic reproduction ratio between herds was calculated. The surveillance programmes were characterised with sample size, sampling frequency, test sensitivity, herd size, vaccination status, and contacts between herds. When R between herds is below 1, then the surveillance programme is sufficiently good to prevent spread of infection, provided that R is estimated well. In the model based on bulk milk testing sample size was replaced by a threshold at which bulk milk can be found positive. The R between herds was mainly influenced by the vaccination status, sampling frequency, and contacts between herds. Herd size moderately affected the outcome. Test sensitivity and sample size, however, were of minor importance. If herds of 50 cows became free of BHV-1 without vaccination, then spread of infection between herds might be prevented when animals within herds are sampled once a year (milk or blood samples). This frequency needs to be intensified, being twice a year, for larger herds and/or herds with extensive contacts with other herds. When bulk milk is sampled instead, sampling should be done at least every 5 months and more intensively, being each month, with larger herd sizes and more contacts between herds.

Animals↗