Correcting the Variance of Effect Sizes Based on Binary Outcomes for Clustering.

Intraclass correlation coefficient and outcome prevalence are associated in clustered binary data

Clustered binary data analysis is a common task in various fields, such as social sciences and epidemiology. Restricted Pseudo Likelihood Estimation (PLE) is a widely used approach for analyzing clustered binary data, providing flexibility in handling complex dependencies within clusters. This study aims to evaluate the efficiency of Restricted Pseudo Likelihood Estimation in balanced and unbalanced clustered binary data models. Using simulated data, we compare the performance of PLE in balanced and unbalanced clustered binary data scenarios. We consider various factors such as the number of clusters, cluster sizes, and intra-cluster correlation. The preferred class of models for clustered binary data is the Hierarchical Generalized Linear Model (HGLM). This article compares the performance of a restricted pseudo-likelihood estimation method of the Hierarchical Generalized Linear Model (HGLM) with equal and unequal cluster sizes. Through comprehensive simulation experiments, we assess the accuracy and precision of PLE estimates in terms of parameter estimation, standard errors, and hypothesis testing. Our findings provide insights into the efficiency of Restricted Pseudo Likelihood Estimation (RPLE) in balanced and unbalanced clustered binary data models. The results highlight the advantages and limitations of PLE in different scenarios, aiding researchers in selecting appropriate modeling approaches for their specific data characteristics. The results can guide researchers in making informed decisions regarding the selection and application of PLE in their own studies, ultimately enhancing the validity and reliability of statistical analyses in the presence of clustered binary data.

A logistic regression with random effects model is commonly applied to analyze clustered binary data, and every cluster is assumed to have a different proportion of success. However, it could be of interest to obtain the proportion of success over clusters (i.e. the marginal proportion of success). Furthermore, the degree of correlation among data of the same cluster (intraclass correlation) is also a relevant concept to assess, but when using logistic regression with random effects it is not possible to get an analytical expression of the estimators for marginal proportion and intraclass correlation. In our paper, we assess and compare approaches using different kinds of approximations: based on the logistic-normal mixed effects model (LN), linear mixed model (LMM), and generalized estimating equations (GEE). The comparisons are completed by using two real data examples and a simulation study. The results show the performance of the approaches strongly depends on the magnitude of the marginal proportion, the intraclass correlation, and the sample size. In general, the reliability of the approaches get worsen with low marginal proportion and large intraclass correlation. LMM and GEE approaches arises as reliable approaches when the sample size is large.

A comparison of methods for the analysis of binomial clustered outcomes in behavioral research

IntroductionPain remains a problem for many with spinal cord injury (SCI), and there is a need for sound, randomized clinical trials examining the efficacy of existing and novel therapeutics. SCI-related pain is complex, as more than one type of pain is often experienced. The purpose of this report is to (i) demonstrate how to design and power calculation of a clinical trial of SCI pain using multiple pain sites per individual; (ii) discuss consequences of failing to adjust for this; and (iii) provide intraclass correlation (ICC) estimates for common pain outcome measures that may be used to power future clinical trials in SCI pain.MethodUsing an existing dataset from a past SCI pain clinical trial, the ICC was calculated for common pain outcome measures to illustrate appropriate corrections for powering, analyzing and interpreting results from multiple pain sites per individual. The problem associated with not accounting for multiple pain sites per individual and the effect on the Type I error rate is also shown.Results and DiscussionNot accounting for the ICC can lead to (1) incorrect power estimates in the design of a trial, and (2) an inflated Type I error rate with a higher likelihood of misinterpretation of outcomes.ConclusionsPowering for future SCI pain trials and statistical analysis of trial outcomes may be substantially compromised if methods do not account for the intra-individual associations between pain sites, ultimately affecting study interpretations and evidence-based practice. We present ICC estimates based on SCI pain data for purposes of estimating power for future trials.

Acetabular dysplasia is the one of main causes of hip displacement in patients with cerebral palsy (CP). Although several studies have shown a relationship between hip displacement and acetabular dysplasia, relatively few have evaluated the association between quantitative acetabular dysplasia and related factors, such as Gross Motor Function Classification System (GMFCS) level. We performed a morphometric analysis of the acetabulum in patients with CP using multiplanar reformation of computed tomography data. The three directional acetabular indices (anterosuperior, superolateral, and posterosuperior) were used to evaluate acetabular dysplasia. Consequently, linear mixed-effects models were used to adjust for related factors such as age, sex, GMFCS level, and migration percentage. A total of 176 patients (mean age 9y 5mo, range 2y 4mo-19y 6mo; 104 males, 72 females) with CP and 55 typically developing individuals (mean age 13y 6mo, range 2y 5mo-19y 10mo; 37 males, 18 females) in a comparison group were enrolled in this study. Statistical modelling showed that all three directional acetabular indices independently increased with GMFCS level (p<0.001) and migration percentage (p<0.001). Acetabular dysplasia was independently affected by both the amount of hip displacement and the GMFCS level. Thus, physicians should consider not only the migration percentage but also three-dimensional evaluation in patients at high GMFCS levels.

Clustered binary data are common in medical research and can be fitted to the logistic regression model with random effects which belongs to a wider class of models called the generalized linear mixed model. The likelihood-based estimation of model parameters often has to handle intractable integration which leads to several estimation methods to overcome such difficulty. The penalized quasi-likelihood (PQL) method is the one that is very popular and computationally efficient in most cases. The expectation–maximization (EM) algorithm allows to estimate maximum-likelihood estimates, but requires to compute possibly intractable integration in the E-step. The variants of the EM algorithm to evaluate the E-step are introduced. The Monte Carlo EM (MCEM) method computes the E-step by approximating the expectation using Monte Carlo samples, while the Modified EM (MEM) method computes the E-step by approximating the expectation using the Laplace's method. All these methods involve several steps of approximation so that corresponding estimates of model parameters contain inevitable errors (large or small) induced by approximation. Understanding and quantifying discrepancy theoretically is difficult due to the complexity of approximations in each method, even though the focus is on clustered binary data. As an alternative competing computational method, we consider a non-parametric maximum-likelihood (NPML) method as well. We review and compare the PQL, MCEM, MEM and NPML methods for clustered binary data via simulation study, which will be useful for researchers when choosing an estimation method for their analysis.

We consider analysis of clustered binary data from multiple observations for each subject in which any two observations from a subject are assumed to have a common correlation coefficient. In the weighted sign test on proportion in clustered binary data, three weighting schemes are considered: equal weights to observations, equal weights to clusters and the optimal weights that minimize the variance of the estimator. Since the distribution of cluster sizes may not be exactly specified before the trial starts, the sample size is usually determined using an average cluster size without taking into account any potential imbalance in cluster size even though cluster size usually varies among clusters. In this paper we investigate the relative efficiency (RE) of unequal versus equal cluster sizes for clustered binary data using the weighted sign test estimators. The REs are computed as a function of correlation among observations within each subject and the various cluster size distributions. The required sample size for unequal cluster sizes will not exceed the sample size for an equal cluster size multiplied by the maximum RE. It is concluded that the maximum RE for various cluster size distributions considered here does not exceed 1.50, 1.61 and 1.12 for equal weights to observations, equal weights to clusters and optimal weights, respectively. It suggests sampling 50%, 61% and 12% more clusters depending on the weighting schemes than the number of clusters computed using an average cluster size.

In practice, clustered binary responses are very prevalent, where binary data is naturally grouped by sampling techniques. Clusters are often unequal in size in some areas of studies, such as medicine, education and others. The most suitable models for binary data clusters of unbalanced sizes are the Hierarchical Generalized Linear Model (HGLM), where the random term over-dispersion counts; and it is k known as clustered binary data. Current techniques for estimating parameters in (HGLM) are many, but these techniques do not allow over dispersion to be distinct from cluster to cluster. Where clustered binary data resulted in over-variation, that reasonable to conclude the unequal size of clustered binary data may have been distinct variations for distinct clusters. By ignoring the chance of shifting over variability between clusters, test statistics may be inflated in the Type I error rates. In this paper, the binomial beta (BB) (HGLM) method has been altered to account for distinct variations across separate clusters. In order to explore whether the Adjusted Scale Binomial Beta (ASBB) method is more suitable than the (BB) technique for dealing with over-dispersion for unequal cluster binary data models, the author was used simulation, the adjusted method was compared to the original "existing" technique in terms of, Type I error rate, estimator standard errors and power. (ASBB) h-likelihood “adjusted” method was comparable to BB "existing" technique, as it has a less standard error and the Type I error was acceptable. Moreover, Type I error inflated in “exist method” (BB) h-likelihood.

Background: High prevalence of hearing loss and its physical, mental, and social impacts when unaddressed underscore a need for early identification. However, in-person hearing assessment may be inaccessible in certain countries and areas. As such, numerous smartphone-based and web-based applications (apps) have been developed to perform remote hearing assessment, and yet many of them remain unvalidated. Purpose: The purpose of this study was to evaluate the performance, ecological validity, and usability of two freely available smartphone-based hearing assessment apps-Hearing Test (Android) and Mimi Hearing Test (iOS)-alongside a web-based app, MDHearing Aid. Research Design: This is a cross-sectional validation study. Study Sample: This study included 60 adults with hearing thresholds no greater than 20 dBHL or any degree of sensorineural hearing loss. Data Collection and Analysis: Participants completed standard audiometric testing followed by assessments using three apps in a controlled laboratory setting. The assessments were repeated by participants at home the subsequent day. The mHealth App Usability Questionnaire (MAUQ) was administered to evaluate the apps' usability. Performance metrics included sensitivity, specificity, accuracy, and test-retest reliability. Intraclass correlation coefficient (ICC) estimates were calculated to measure the apps' accuracy, test-retest reliability, and ecological validity. Results: All apps had moderate to good sensitivity (0.67-1.00) and specificity (0.72-0.99). The Hearing Test app showed poor accuracy at lower frequencies (ICC: 0.24-0.53) and moderate to good accuracy above 1000 Hz (ICC: 0.74-0.83). The Mimi Hearing Test showed poor accuracy at lower frequencies (ICC: 0.27-0.50) and moderate to good accuracy above 2000 Hz (ICC: 0.68-0.85). The web-based MDHearing Aid test showed moderate to good accuracy across frequencies (ICC: 0.64-0.85). All apps had moderate to excellent test-retest reliability (ICC: 0.66-0.99) and showed poor ecological validity below 500 Hz (ICC: 0.20-0.51) and moderate to excellent ecological validity above 1000 Hz (ICC: 0.54-0.95). Usability was rated highly across all apps, with MAUQ scores ranging from 5.4 to 5.9 out of 7. Conclusions: The examined apps exhibit varied accuracy levels and generally reasonable sensitivity, specificity, test-retest reliability, ecological validity, and usability. With additional validation, the Hearing Test app may be useful for hearing screening and monitoring in adults. There is a necessity for further research to unlock the examined apps' full clinical potential.

Conditional logistic regression (CLR) is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster-specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance. CLR aggregates unmeasured cluster-specific factors into a cluster-specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within-cluster dependency. We propose an alternative, resampling-based method for analyzing clustered binary outcome data, within-cluster paired resampling (WCPR), which allows for within-cluster dependency not solely due to baseline heterogeneity. For example, dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors. When both CLR and WCPR are valid, our simulations suggest that the two methods perform comparably. When CLR is invalid, WCPR continues to have good operating characteristics. For illustration, we apply both WCPR and CLR to a periodontal data set where there is heterogeneity in response to exposure across clusters.

Prior research has focused primarily on empirically estimating design parameters for cluster-randomized trials (CRTs) of mathematics and reading achievement. Little is known about how design parameters compare across other educational outcomes. This article presents empirical estimates of design parameters that can be used to appropriately power CRTs in science education and compares them to estimates using mathematics and reading. Estimates of intraclass correlations (ICCs) are computed for unconditional two-level (students in schools) and three-level (students in schools in districts) hierarchical linear models of science achievement. Relevant student- and school-level pretest and demographic covariates are then considered, and estimates of variance explained are computed. Subjects: Five consecutive years of Texas student-level data for Grades 5, 8, 10, and 11. Science, mathematics, and reading achievement raw scores as measured by the Texas Assessment of Knowledge and Skills. Results: Findings show that ICCs in science range from .172 to .196 across grades and are generally higher than comparable statistics in mathematics, .163-.172, and reading, .099-.156. When available, a 1-year lagged student-level science pretest explains the most variability in the outcome. The 1-year lagged school-level science pretest is the best alternative in the absence of a 1-year lagged student-level science pretest. Science educational researchers should utilize design parameters derived from science achievement outcomes.

When participants in individually randomized group treatment trials are treated by multiple clinicians or in multiple group treatment sessions throughout the trial, this induces partially nested clusters which can affect the power of a trial. We investigate this issue in the Whole Health Options and Pain Education trial, a three-arm pragmatic, individually randomized clinical trial. We evaluate whether partial clusters due to multiple visits delivered by different clinicians in the Whole Health Team arm and dynamic participant groups due to changing group leaders and/or participants across treatment sessions during treatment delivery in the Primary Care Group Education arm may impact the power of the trial. We also present a Bayesian approach to estimate the intraclass correlation coefficients. We present statistical models for each treatment arm of Whole Health Options and Pain Education trial in which power is estimated under different intraclass correlation coefficients and mapping matrices between participants and clinicians or treatment sessions. Power calculations are based on pairwise comparisons. In practice, sample size calculations depend on estimates of the intraclass correlation coefficients at the treatment sessions and clinician levels. To accommodate such complexities, we present a Bayesian framework for the estimation of intraclass correlation coefficients under different participant-to-session and participant-to-clinician mapping scenarios. We simulated continuous outcome data based on various clinical scenarios in Whole Health Options and Pain Education trial using a range of intraclass correlation coefficients and mapping matrices and used Gibbs samplers with conjugate priors to obtain posteriors of the intraclass correlation coefficients under those different scenarios. Posterior means and medians and their biases are calculated for the intraclass correlation coefficients to evaluate the operating characteristics of the Bayesian intraclass correlation coefficient estimators. Power for Whole Health Team versus Primary Care Group Education is sensitive to the intraclass correlation coefficient in the Whole Health Team arm. In these two arms, an increased number of clinicians, more evenly distributed workload of clinicians, or more homogeneous treatment group sizes leads to increased power. Our simulation study for the intraclass correlation coefficient estimation indicates that the posterior mean intraclass correlation coefficient estimator has less bias when the true intraclass correlation coefficients are large (i.e. 0.10), but when the intraclass correlation coefficient is small (i.e. 0.01), the posterior median intraclass correlation coefficient estimator is less biased. Knowledge of intraclass correlation coefficients and the structure of clustering are critical to the design of individually randomized group treatment trials with partially nested clusters. We demonstrate that the intraclass correlation coefficient of the Whole Health Team arm can affect power in the Whole Health Options and Pain Education trial. A Bayesian approach provides a flexible procedure for estimating the intraclass correlation coefficients under complex scenarios. More work is needed to educate the research community about the individually randomized group treatment design and encourage publication of intraclass correlation coefficients to help inform future trial designs.

SUMMARY The lymphocyte proliferative assay (LPA) of immune competence was conducted on 52 subjects, with up to 36 processing conditions per subject, to evaluate whether samples could be shipped or stored overnight, rather than being processed on fresh blood as currently required. The LPA study resulted in clustered binary data, with both cluster level and cluster-varying covariates. Two modelling strategies for the analysis of such clustered binary data are through the cluster-specific and population-averaged approaches. Whereas most research in this area has focused on the analysis of matched pairs data, in many situations, such as the LPA study, cluster sizes are naturally larger. Through considerations of interpretation and efficiency of these models when applied to large clusters, the mixed effect cluster-specific model was selected as most appropriate for the analysis of the LPA data. The model confirmed that the LPA response is significantly impaired in individuals infected with the human immunodeficiency virus (HIV). The LPA response was found to be significantly lower for shipped and overnight samples than for fresh samples, and this effect was significantly stronger among HIV-infected individuals. Surprisingly, an anticoagulant effect was not detected.

A simulation study of sample size demonstrated the importance of the number of events per variable to develop prediction models in clustered data