Nonparametric estimation of the random effects distribution for the risk or rate ratio in rare events meta-analysis with the arm-based and contrast-based approaches.

Rare events are events which occur with low frequencies. These often arise in clinical trials or cohort studies where the data are arranged in binary contingency tables. In this article, we investigate the estimation of effect heterogeneity for the risk-ratio parameter in meta-analysis of rare events studies through two likelihood-based nonparametric mixture approaches: an arm-based and a contrast-based model. Maximum likelihood estimation is achieved using the EM algorithm. Special attention is given to the choice of initial values. Inspired by the classification likelihood, a strategy is implemented which repeatably uses random allocation of the studies to the mixture components as choice of initial values. The likelihoods under the contrast-based and arm-based approaches are compared and differences are highlighted. We use simulations to assess the performance of these two methods. Under the design of sampling studies with nested treatment groups, the results show that the nonparametric mixture model based on the contrast-based approach is more appropriate in terms of model selection criteria such as AIC and BIC. Under the arm-based design the results from the arm-based model performs well although in some cases it is also outperformed by the contrast-based model. Comparisons of the estimators are provided in terms of bias and mean squared error. Also included in the comparison is the mixed Poisson regression model as well as the classical DerSimonian-Laird model (using the Mantel-Haenszel estimator for the common effect). Using simulation, estimating effect heterogeneity in the case of the contrast-based method appears to behave better than the compared methods although differences become negligible for large within-study sample sizes. We illustrate the methodologies using several meta-analytic data sets in medicine.

On repeated diagnostic testing in screening for a medical condition: How often should the diagnostic test be repeated?

In screening large populations a diagnostic test is frequently used repeatedly. An example is screening for bowel cancer using the fecal occult blood test (FOBT) on several occasions such as at 3 or 6 days. The question that is addressed here is how often should we repeat a diagnostic test when screening for a specific medical condition. Sensitivity is often used as a performance measure of a diagnostic test and is considered here for the individual application of the diagnostic test as well as for the overall screening procedure. The latter can involve an increasingly large number of repeated applications, but how many are sufficient? We demonstrate the issues involved in answering this question using real data on bowel cancer at St Vincents Hospital in Sydney. As data are only available for those testing positive at least once, an appropriate modeling technique is developed on the basis of the zero-truncated binomial distribution which allows for population heterogeneity. The latter is modeled using discrete nonparametric maximum likelihood. If we wish to achieve an overall sensitivity of 90%, the FOBT should be repeated for 2 weeks instead of the 1 week that was used at the time of the survey. A simulation study also shows consistency in the sense that bias and standard deviation for the estimated sensitivity decrease with an increasing number of repeated occasions as well as with increasing sample size.

Modeling COVID-19 contact-tracing using the ratio regression capture-recapture approach.

Contact-tracing is one of the most effective tools in infectious disease outbreak control. A capture-recapture approach based upon ratio regression is suggested to estimate the completeness of case detection. Ratio regression has been recently developed as flexible tool for count data modeling and has proved to be successful in the capture-recapture setting. The methodology is applied here to Covid-19 contact tracing data from Thailand. A simple weighted straight line approach is used which includes the Poisson and geometric distribution as special cases. For the case study data of contact tracing for Thailand, a completeness of 83% could be found with a 95% confidence interval of 74%-93%.

The identity of two meta-analytic likelihoods and the ignorability of double-zero studies.

In meta-analysis, the conventional two-stage approach computes an effect estimate for each study in the first stage and proceeds with the analysis of effect estimates in the second stage. For counts of events as outcome, the risk ratio is often the effect measure of choice. However, if the meta-analysis includes many studies with no events the conventional method breaks down. As an alternative one-stage approach, a Poisson regression model and a conditional binomial model can be considered where no event studies do not cause problems. The conditional binomial model excludes double-zero studies, whereas this is seemingly not the case for the Poisson regression approach. However, we show here that both models lead to the same likelihood inference and double-zero studies (in contrast to single-zero studies) do not contribute in either case to the likelihood.

Novel Use of Capture-Recapture Methods to Estimate Completeness of Contact Tracing during an Ebola Outbreak, Democratic Republic of the Congo, 2018-2020.

Despite its critical role in containing outbreaks, the efficacy of contact tracing, measured as the sensitivity of case detection, remains an elusive metric. We estimated the sensitivity of contact tracing by applying unilist capture-recapture methods on data from the 2018-2020 outbreak of Ebola virus disease in the Democratic Republic of the Congo. To compute sensitivity, we applied different distributional assumptions to the zero-truncated count data to estimate the number of unobserved case-patients with any contacts and infected contacts. Geometric distributions were the best-fitting models. Our results indicate that contact tracing efforts identified almost all (n = 792, 99%) of case-patients with any contacts but only half (n = 207, 48%) of case-patients with infected contacts, suggesting that contact tracing efforts performed well at identifying contacts during the listing stage but performed poorly during the contact follow-up stage. We discuss extensions to our work and potential applications for the ongoing coronavirus pandemic.

Statistical methodology for estimating the mean difference in a meta-analysis without study-specific variance information.

Statistical inference for analyzing the results from several independent studies on the same quantity of interest has been investigated frequently in recent decades. Typically, any meta-analytic inference requires that the quantity of interest is available from each study together with an estimate of its variability. The current work is motivated by a meta-analysis on comparing two treatments (thoracoscopic and open) of congenital lung malformations in young children. Quantities of interest include continuous end-points such as length of operation or number of chest tube days. As studies only report mean values (and no standard errors or confidence intervals), the question arises how meta-analytic inference can be developed. We suggest two methods to estimate study-specific variances in such a meta-analysis, where only sample means and sample sizes are available in the treatment arms. A general likelihood ratio test is derived for testing equality of variances in two groups. By means of simulation studies, the bias and estimated standard error of the overall mean difference from both methodologies are evaluated and compared with two existing approaches: complete study analysis only and partial variance information. The performance of the test is evaluated in terms of type I error. Additionally, we illustrate these methods in the meta-analysis on comparing thoracoscopic and open surgery for congenital lung malformations and in a meta-analysis on the change in renal function after kidney donation. Copyright © 2017 John Wiley & Sons, Ltd.

Estimating risk and rate ratio in rare events meta-analysis with the Mantel-Haenszel estimator and assessing heterogeneity.

Meta-analysis of binary outcome data faces often a situation where studies with a rare event are part of the set of studies to be considered. These studies have low occurrence of event counts to the extreme that no events occur in one or both groups to be compared. This raises issues how to estimate validly the summary risk or rate ratio across studies. A preferred choice is the Mantel-Haenszel estimator, which is still defined in the situation of zero studies unless all studies have zeros in one of the groups to be compared. For this situation, a modified Mantel-Haenszel estimator is suggested and shown to perform well by means of simulation work. Also, confidence interval estimation is discussed and evaluated in a simulation study. In a second part, heterogeneity of relative risk across studies is investigated with a new chi-square type statistic which is based on a conditional binomial distribution where the conditioning is on the event margin for each study. This is necessary as the conventional Q-statistic is undefined in the occurrence of zero studies. The null-distribution of the proposed Q-statistic is obtained by means of a parametric bootstrap as a chi-square approximation is not valid for rare events meta-analysis, as bootstrapping of the null-distribution shows. In addition, for the effect heterogeneity situation, confidence interval estimation is considered using a nonparametric bootstrap procedure. The proposed techniques are illustrated at hand of three meta-analytic data sets.

Estimation of Effect Heterogeneity in Rare Events Meta-Analysis.

The paper outlines several approaches for dealing with meta-analyses of count outcome data. These counts are the accumulation of occurred events, and these events might be rare, so a special feature of the meta-analysis is dealing with low counts including zero-count studies. Emphasis is put on approaches which are state of the art for count data modelling including mixed log-linear (Poisson) and mixed logistic (binomial) regression as well as nonparametric mixture models for count data of Poisson and binomial type. A simulation study investigates the performance and capability of discrete mixture models in estimating effect heterogeneity. The approaches are exemplified on a meta-analytic case study investigating the acceptance of bibliotherapy.

Meta-analysis without study-specific variance information: Heterogeneity case.

The random effects model in meta-analysis is a standard statistical tool often used to analyze the effect sizes of the quantity of interest if there is heterogeneity between studies. In the special case considered here, meta-analytic data contain only the sample means in two treatment arms and the sample sizes, but no sample standard deviation. The statistical comparison between two arms for this case is not possible within the existing meta-analytic inference framework. Therefore, the main objective of this paper is to estimate the overall mean difference and associated variances, the between-study variance and the within-study variance, as specified as the important elements in the random effects model. These estimators are obtained using maximum likelihood estimation. The standard errors of the estimators and a quantification of the degree of heterogeneity are also investigated. A measure of heterogeneity is suggested which adjusts the original suggested measure of Higgins' I2 for within study sample size. The performance of the proposed estimators is evaluated using simulations. It can be concluded that all estimated means converged to their associated true parameter values, and its standard errors tended to be small if the number of the studies involved in the meta-analysis was large. The proposed estimators could be favorably applied in a meta-analysis on comparing two surgeries for asymptomatic congenital lung malformations in young children.

Does thoracoscopy have advantages over open surgery for asymptomatic congenital lung malformations? An analysis of 1626 resections.

AIM: The apparent incidence of antenatally diagnosed congenital lung malformations (CLM) is rising (1 in 3000), and the majority undergo elective resection even if asymptomatic. Thoracoscopy has been popularized, but early series report high conversion rates and significant complications. We aimed to perform systematic review/meta-analysis of outcomes of thoracoscopic vs open excision of asymptomatic CLMs. METHODS: A systematic review according to PRISMA guidelines was performed. Data were extracted for all relevant studies (2004-2015) and Rangel quality scores calculated. Analysis was on 'intention to treat' basis for thoracoscopy and asymptomatic lung lesions. Meta-analysis was performed using the addon package METAN of the statistical package STATA14™; p<0.05 was considered significant. RESULTS: 36 studies were eligible, describing 1626 CLM resections (904 thoracoscopic, 722 open). There were no randomized controlled trials. Median quality score was 14/45 (IQR 6.5) 'poor'. 92/904 (10%) thoracoscopic procedures were converted to open. No deaths were reported. Meta-analysis showed that regarding thoracoscopic procedures, the total number of complications was significantly less (OR 0.63, 95% CI 0.43, 0.92; p<0.02, 12 eligible series, 912 patients, 404 thoracoscopic). Length of stay was 1.4days shorter (95%CI 2.40, 0.37;p<0.01). Length of operation was 37 min longer (95% CI 18.96, 54.99; p<0.01). Age, weight, and number of chest tube days were similar. There was heterogeneity (I2 30%, p=0.15) and no publication bias seen. CONCLUSIONS: A reduced total complication rate favors thoracoscopic excision over thoracotomy for asymptomatic antenatally diagnosed CLMs. Although operative time was longer, and open conversion may be anticipated in 1/10, the overall length of hospital stay was reduced by more than 1day. LEVEL OF EVIDENCE: 4 (based on lowest level of article analyzed in meta-analysis/systematic review).