Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers

Multiple test procedures of disease prevalence based on stratified partially validated series in the presence of a gold standard

This paper discusses the problem of disease prevalence in clinical studies, focusing on multiple comparisons based on stratified partially validated series in the presence of a gold standard. Five test statistics, including two Wald-type test statistics, the inverse hyperbolic tangent transformation test statistic, likelihood ratio test statistic, and score test statistic, are proposed to conduct multiple comparisons. To control the overall type I error rate, several adjustment procedures are developed, namely the Bonferroni, Single-step adjusted MaxT, Single-step adjusted MinP, Holm's Step-down, and Hochberg's step-up procedures, based on these test statistics. The performance of the proposed methods is evaluated through simulation studies in terms of the empirical type I error rate and empirical power. Simulation results show that the Single-step adjusted MaxT procedure and Single-step adjusted MinP procedure generally outperform the other three procedures, and these two test procedures based on all test statistics have satisfactory performance. Notably, the Single-step adjusted MinP procedure tends to exhibit higher empirical power than the Single-step adjusted MaxT procedure. Furthermore, the Step-down and Step-up procedures show greater power compared to the Bonferroni method. The study also observes that as the validated ratio increases, the empirical type I errors of all test procedures approach the nominal level while maintaining higher power. Two real examples are presented to illustrate the proposed methods.

Maternal mortality decline in Zimbabwe, 2007/2008 to 2018/2019: findings from mortality surveys using civil registration, vital statistics and health system data

Background

Sustainable Development Goal (SDG) 3.1 target is to reduce the global maternal mortality ratio (MMR) to less than 70 maternal deaths per 100 000 live births by 2030. In the Ending Preventable Maternal Mortality strategy, a supplementary target was added, that no country has an MMR above 140 by 2030. We conducted two cross-sectional reproductive age mortality surveys to analyse changes in Zimbabwe’s MMR between 2007–2008 and 2018–2019 towards the SDG target.

Methods

We collected data from civil registration, vital statistics and medical records on deaths of women of reproductive ages (WRAs), including maternal deaths from 11 districts, randomly selected from each province (n=10) using cluster sampling. We calculated weighted mortality rates and MMRs using negative binomial models, with 95% CIs, performed a one-way analysis of variance of the MMRs and calculated the annual average reduction rate (ARR) for the MMR.

Results

In 2007–2008 we identified 6188 deaths of WRAs, 325 pregnancy-related deaths and 296 maternal deaths, and in 2018–2019, 1856, 137 and 130, respectively. The reproductive age mortality rate, weighted by district, declined from 11 to 3 deaths per 1000 women. The MMR (95% CI) declined from 657 (485 to 829) to 217 (164 to 269) deaths per 100 000 live births at an annual ARR of 10.1%.

Conclusions

Zimbabwe’s MMR declined by an annual ARR of 10.1%, against a target of 10.2%, alongside declining reproductive age mortality. Zimbabwe should continue scaling up interventions against direct maternal mortality causes to achieve the SDG 3.1 target by 2030.

Confidence interval construction for proportion difference from partially validated series with two fallible classifiers

This article investigates the confidence interval (CI) construction of proportion difference for two independent partially validated series under the double-sampling scheme in which both classifiers are fallible. Several CIs based on the variance estimates recovery method of combining confidence limits from asymptotic, bootstrap, and Bayesian methods for two independent binomial proportions are developed under two models. Simulation results show that all CIs except for the bootstrap percentile-t CI and Bayesian credible interval with uniform prior under the independence model and all CIs under the dependence model generally perform well and are recommended. Two examples are used to illustrate the methodologies.

Homogeneity testing for binomial proportions under stratified double-sampling scheme with two fallible classifiers

This article investigates the homogeneity testing problem of binomial proportions for stratified partially validated data obtained by double-sampling method with two fallible classifiers. Several test procedures, including the weighted-least-squares test with/without log-transformation, logit-transformation and double log-transformation, and likelihood ratio test and score test, are developed to test the homogeneity under two models, distinguished by conditional independence assumption of two classifiers. Simulation results show that score test performs better than other tests in the sense that the empirical size is generally controlled around the nominal level, and hence be recommended to practical applications. Other tests also perform well when both binomial proportions and sample sizes are not small. Approximate sample sizes based on score test, likelihood ratio test and the weighted-least-squares test with double log-transformation are generally accurate in terms of the empirical power and type I error rate with the estimated sample sizes, and hence be recommended. An example from the malaria study is illustrated by the proposed methodologies.