A new test for trait mean and variance detects unreported loci for blood-pressure variation.

Variability in quantitative traits has clinical, ecological, and evolutionary significance. Most genetic variants identified for complex quantitative traits have only a detectable effect on the mean of trait. We have developed the mean-variance test (MVtest) to simultaneously model the mean and log-variance of a quantitative trait as functions of genotypes and covariates by using estimating equations. The advantages of MVtest include the facts that it can detect effect modification, that multiple testing can follow conventional thresholds, that it is robust to non-normal outcomes, and that association statistics can be meta-analyzed. In simulations, we show control of type I error of MVtest over several alternatives. We identified 51 and 37 previously unreported associations for effects on blood-pressure variance and mean, respectively, in the UK Biobank. Transcriptome-wide association studies revealed 633 significant unique gene associations with blood-pressure mean variance. MVtest is broadly applicable to studies of complex quantitative traits and provides an important opportunity to detect novel loci.

Variable selection in high dimensions for discrete-outcome individualized treatment rules: Reducing severity of depression symptoms.

Despite growing interest in estimating individualized treatment rules, little attention has been given the binary outcome setting. Estimation is challenging with nonlinear link functions, especially when variable selection is needed. We use a new computational approach to solve a recently proposed doubly robust regularized estimating equation to accomplish this difficult task in a case study of depression treatment. We demonstrate an application of this new approach in combination with a weighted and penalized estimating equation to this challenging binary outcome setting. We demonstrate the double robustness of the method and its effectiveness for variable selection. The work is motivated by and applied to an analysis of treatment for unipolar depression using a population of patients treated at Kaiser Permanente Washington.

Detecting sparse microbial association signals adaptively from longitudinal microbiome data based on generalized estimating equations.

The association between the compositions of microbial communities and various host phenotypes is an important research topic. Microbiome association research addresses multiple domains, such as human disease and diet. Statistical methods for testing microbiome-phenotype associations have been studied recently to determine their ability to assess longitudinal microbiome data. However, existing methods fail to detect sparse association signals in longitudinal microbiome data. In this paper, we developed a novel method, namely aGEEMIHC, which is a data-driven adaptive microbiome higher criticism analysis based on generalized estimating equations to detect sparse microbial association signals from longitudinal microbiome data. aGEEMiHC adopts generalized estimating equations framework that fully considers the correlation among different observations from the same subject in longitudinal data. To be robust to diverse correlation structures for longitudinal data, aGEEMiHC integrates multiple microbiome higher criticism analyses based on generalized estimating equations with different working correlation structures. Extensive simulation experiments demonstrate that aGEEMiHC can control the type I error correctly and achieve superior performance according to a statistical power comparison. We also applied it to longitudinal microbiome data with various types of host phenotypes to demonstrate the stability of our method. aGEEMiHC is also utilized for real longitudinal microbiome data, and we found a significant association between the gut microbiome and Crohn's disease. In addition, our method ranks the significant factors associated with the host phenotype to provide potential biomarkers.

Glomerular Filtration Rate Estimation Using ß2-Microglobulin and ß-Trace Protein in Adults With Solid Tumors: A Prospective Cross-Sectional Study.

RATIONALE & OBJECTIVE: ß2-Microglobulin (B2M) and ß-trace protein (BTP) are novel endogenous filtration markers that may improve the accuracy of estimated glomerular filtration rate (eGFR) beyond creatinine and cystatin C (eGFRcr-cys), but they have not been assessed in patients with cancer. STUDY DESIGN: Cross-sectional analysis. SETTING & PARTICIPANTS: Prospective cohort of 1,200 patients with active solid tumors recruited between April 2015 and September 2017. EXPOSURE: CKD-EPI equations without race combining B2M and/or BTP with creatinine with or without cystatin C (2-, 3-, or 4-marker panel eGFR). OUTCOME: Performance of equations compared with eGFRcr-cys and non-GFR determinants of serum B2M and BTP (SB2M, and SBTP, respectively). Measured GFR (mGFR) was determined using the plasma clearance of chromium-51 labeled ethylenediamine tetraacetic acid (51Cr-EDTA). ANALYTICAL APPROACH: Bias was defined as the median of the differences between mGFR and eGFR, and 1-P30 was defined as the percentage of estimates that differed by more than 30% from the mGFR (1-P30). Linear regression was used to assess association of clinical and laboratory variables with SB2M, and SBTP after adjustment for mGFR. RESULTS: Mean age and mGFR were 58.8±13.2 SD years and 78.4±21.7 SD mL/min/1.73m2, respectively. Performance of the 3-marker and 4-marker panel equations was better than eGFRcr-cys (lesser bias and 1-P30). Performance of 2-marker panel equations was as good as eGFRcr-cys (lesser bias and similar 1-P30). SB2M and SBTP were not strongly influenced by cancer site. LIMITATIONS: Participants may have had better clinical performance status than the general population of patients with solid tumors. CONCLUSIONS: B2M and BTP can improve the accuracy of eGFR and may be useful as confirmatory tests in patients with solid tumors, either by inclusion in a multimarker panel equation with creatinine and cystatin C, or by substituting for cystatin C in combination with creatinine. PLAIN-LANGUAGE SUMMARY: The most accurate method to assess estimate kidney function is estimated glomerular filtration rate (eGFR) using creatinine and cystatin C (eGFRcr-cys). We studied whether using ß2-microglobulin (B2M) and/or ß-trace protein (BTP) with creatinine with or without cystatin C (2-, 3-, or 4-marker panel eGFR) might be useful in patients with active solid tumors. The performance of the 3-marker and 4-marker panel equations was better than eGFRcr-cys. Performance of 2-marker panel equations was as good as eGFRcr-cys. We conclude that B2M and BTP can improve the accuracy of eGFR and may be useful as a confirmatory test in patients with solid tumors either by inclusion in multimarker panel equation with creatinine and cystatin C or by substituting for cystatin C in combination with creatinine.

Homogeneity pursuit and variable selection in regression models for multivariate abundance data.

When building regression models for multivariate abundance data in ecology, it is important to allow for the fact that the species are correlated with each other. Moreover, there is often evidence species exhibit some degree of homogeneity in their responses to each environmental predictor, and that most species are informed by only a subset of predictors. We propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit (ie, grouping species with similar coefficient values while allowing differing groups for different covariates) and variable selection in regression models for multivariate abundance data. Using GEEs allows us to straightforwardly account for between-response correlations through a (reduced-rank) working correlation matrix. We augment the GEE with both adaptive fused lasso- and adaptive lasso-type penalties, which aim to cluster the species-specific coefficients within each covariate and encourage differing levels of sparsity across the covariates, respectively. Numerical studies demonstrate the strong finite sample performance of the proposed method relative to several existing approaches for modeling multivariate abundance data. Applying the proposed method to presence-absence records collected along the Great Barrier Reef in Australia reveals both a substantial degree of homogeneity and sparsity in species-environmental relationships. We show this leads to a more parsimonious model for understanding the environmental drivers of seabed biodiversity, and results in stronger out-of-sample predictive performance relative to methods that do not accommodate such features.

Longitudinal varying coefficient single-index model with censored covariates.

It is of interest to health policy research to estimate the population-averaged longitudinal medical cost trajectory from initial cancer diagnosis to death, and understand how the trajectory curve is affected by patient characteristics. This research question leads to a number of statistical challenges because the longitudinal cost data are often non-normally distributed with skewness, zero-inflation, and heteroscedasticity. The trajectory is nonlinear, and its length and shape depend on survival, which are subject to censoring. Modeling the association between multiple patient characteristics and nonlinear cost trajectory curves of varying lengths should take into consideration parsimony, flexibility, and interpretation. We propose a novel longitudinal varying coefficient single-index model. Multiple patient characteristics are summarized in a single-index, representing a patient's overall propensity for healthcare use. The effects of this index on various segments of the cost trajectory depend on both time and survival, which is flexibly modeled by a bivariate varying coefficient function. The model is estimated by generalized estimating equations with an extended marginal mean structure to accommodate censored survival time as a covariate. We established the pointwise confidence interval of the varying coefficient and a test for the covariate effect. The numerical performance was extensively studied in simulations. We applied the proposed methodology to medical cost data of prostate cancer patients from the Surveillance, Epidemiology, and End Results-Medicare-Linked Database.

Trajectories of fear of cancer recurrence and its influence factors: A longitudinal study on Chinese newly diagnosed cancer patients.

OBJECTIVE: The fear of cancer recurrence (FCR) is an ongoing and common psychological problem faced by cancer patients. The objective of this study was to explore the variation trend of FCR and its influencing factors in Chinese newly diagnosed cancer patients from admission to 2 months after discharge. Demographic and tumor characteristics, as well as experiential avoidance (EA), were used as predictors. METHOD: A longitudinal design and a consecutive sampling method were used to select 266 newly diagnosed cancer patients admitted to a tertiary cancer hospital in China from July to December 2022. Measurements of FCR and EA were obtained at admission (T1), 1 month after discharge (T2), and 2 months post-discharge (T3). Generalized estimating equations were used to identify factors associated with FCR for longitudinal data analysis. RESULTS: A total of 266 participants completed the follow-up. Both FCR and EA scores of patients with newly diagnosed cancer showed a significant trend of first increasing and then decreasing at baseline and follow-up (p < 0.001). The junior secondary and less education level, rural residence, advanced tumor and high EA level were risk factors for higher FCR. CONCLUSIONS: Our findings suggest that the FCR levels of most newly diagnosed cancer patients in China are different at the three time points and affected by different factors, with the highest level at 1 month after discharge. These results have significant implications for future identifying populations in need of targeted intervention based on their FCR trajectories.

How estimating nuisance parameters can reduce the variance (with consistent variance estimation).

We often estimate a parameter of interest ψ $$ \psi $$ when the identifying conditions involve a finite-dimensional nuisance parameter θ ∈ ℝ d $$ \theta \in {\mathbb{R}} $$ . Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators ψ ^ $$ \hat{\psi} $$ that solve unbiased estimating equations including θ $$ \theta $$ which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where θ ^ $$ \hat{\theta} $$ solves (partial) score equations and ψ $$ \psi $$ does not depend on θ $$ \theta $$ . This includes many causal inference settings where θ $$ \theta $$ describes the treatment probabilities, missing data settings where θ $$ \theta $$ describes the missingness probabilities, and measurement error settings where θ $$ \theta $$ describes the error distribution. These four additional results are: (1) Counter-intuitively, the asymptotic variance of ψ ^ $$ \hat{\psi} $$ is typically smaller when θ $$ \theta $$ is estimated. (2) If estimating θ $$ \theta $$ is ignored, the sandwich estimator for the variance of ψ ^ $$ \hat{\psi} $$ is conservative. (3) A consistent sandwich estimator for the variance of ψ ^ $$ \hat{\psi} $$ . (4) If ψ ^ $$ \hat{\psi} $$ with the true θ $$ \theta $$ plugged in is efficient, the asymptotic variance of ψ ^ $$ \hat{\psi} $$ does not depend on whether θ $$ \theta $$ is estimated. To illustrate we use observational data to calculate confidence intervals for (1) the effect of cazavi versus colistin on bacterial infections and (2) how the effect of antiretroviral treatment depends on its initiation time in HIV-infected patients.

Estimating average treatment effects for clustered RCTs with recruitment bias.

In clustered randomized controlled trials (RCTs), sample recruitment is often conducted after cluster randomization. This timing can lead to recruitment bias if access to the intervention affects the composition of study-eligible cluster entrants and study consenters. This article develops a potential outcomes framework in such settings that yields a causal estimand that pertains to the always-recruited in either research condition. A consistent inverse probability weighting (IPW) estimator is developed using data on recruits only, and a generalized estimating equations approach is used to obtain robust clustered SE estimators that adjust for estimation error in the IPW weights. A simple data collection strategy is discussed to improve the predictive accuracy of the logit propensity score models. Simulations show that the IPW estimator achieves nominal confidence interval coverage under the assumed identification conditions. An empirical application demonstrates the methods using data from an RCT testing the effects of a behavioral health intervention in schools. An R program for estimation is available for download.

Performance of mixed effects models and generalized estimating equations for continuous outcomes in partially clustered trials including both independent and paired data.

Many clinical trials involve partially clustered data, where some observations belong to a cluster and others can be considered independent. For example, neonatal trials may include infants from single or multiple births. Sample size and analysis methods for these trials have received limited attention. A simulation study was conducted to (1) assess whether existing power formulas based on generalized estimating equations (GEEs) provide an adequate approximation to the power achieved by mixed effects models, and (2) compare the performance of mixed models vs GEEs in estimating the effect of treatment on a continuous outcome. We considered clusters that exist prior to randomization with a maximum cluster size of 2, three methods of randomizing the clustered observations, and simulated datasets with uninformative cluster size and the sample size required to achieve 80% power according to GEE-based formulas with an independence or exchangeable working correlation structure. The empirical power of the mixed model approach was close to the nominal level when sample size was calculated using the exchangeable GEE formula, but was often too high when the sample size was based on the independence GEE formula. The independence GEE always converged and performed well in all scenarios. Performance of the exchangeable GEE and mixed model was also acceptable under cluster randomization, though under-coverage and inflated type I error rates could occur with other methods of randomization. Analysis of partially clustered trials using GEEs with an independence working correlation structure may be preferred to avoid the limitations of mixed models and exchangeable GEEs.

Covariate-adjusted generalized pairwise comparisons in small samples.

Semiparametric probabilistic index models allow for the comparison of two groups of observations, whilst adjusting for covariates, thereby fitting nicely within the framework of generalized pairwise comparisons (GPC). As with most regression approaches in this setting, the limited amount of data results in invalid inference as the asymptotic normality assumption is not met. In addition, separation issues might arise when considering small samples. In this article, we show that the parameters of the probabilistic index model can be estimated using generalized estimating equations, for which adjustments exist that lead to estimators of the sandwich variance-covariance matrix with improved finite sample properties and that can deal with bias due to separation. In this way, appropriate inference can be performed as is shown through extensive simulation studies. The known relationships between the probabilistic index and other GPC statistics allow to also provide valid inference for example, the net treatment benefit or the success odds.

Designing individually randomized group treatment trials with repeated outcome measurements using generalized estimating equations.

Individually randomized group treatment (IRGT) trials, in which the clustering of outcome is induced by group-based treatment delivery, are increasingly popular in public health research. IRGT trials frequently incorporate longitudinal measurements, of which the proper sample size calculations should account for correlation structures reflecting both the treatment-induced clustering and repeated outcome measurements. Given the relatively sparse literature on designing longitudinal IRGT trials, we propose sample size procedures for continuous and binary outcomes based on the generalized estimating equations approach, employing the block exchangeable correlation structures with different correlation parameters for the treatment arm and for the control arm, and surveying five marginal mean models with different assumptions of time effect: no-time constant treatment effect, linear-time constant treatment effect, categorical-time constant treatment effect, linear time by treatment interaction, and categorical time by treatment interaction. Closed-form sample size formulas are derived for continuous outcomes, which depends on the eigenvalues of the correlation matrices; detailed numerical sample size procedures are proposed for binary outcomes. Through simulations, we demonstrate that the empirical power agrees well with the predicted power, for as few as eight groups formed in the treatment arm, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator.

Longitudinal Modeling of Bacterial Sexually Transmitted Infections Among Sexual Minority Men Living with HIV.

Bacterial sexually transmitted infections (BSTIs) are largely preventable, yet their rates remain high across the U.S., particularly among sexual minority men (SMM) living with HIV (LWH). We explored longitudinal factors associated with BSTI acquisition in a national online sample of SMM LWH with recent suboptimal adherence to antiretroviral therapy (ART) or virologic non-suppression, such as spread within sexual networks, drug use in a sexual context (chemsex), and mental health issues. Participants completed online surveys over 12 months as part of an eHealth intervention. Over 12 months, 30% of participants self-reported at least one BSTI, with 28-45% reporting recurrent infections in consecutive surveys. Using generalized estimating equations with a binomial distribution and an exchangeable correlation structure, we found that BSTI accumulation was associated with chemsex, a higher number of anal sex partners, participation in exchange sex, and depressive symptoms. To reduce the burden of BSTIs among SMM LWH, public health initiatives and clinical settings should adopt a comprehensive sexual health approach, addressing chemsex, exchange sex, and associated mental health conditions. Addressing these factors can mitigate BSTI recurrence and improve overall sexual health among SMM LWH.

Assessment of the 2023 European Kidney Function Consortium (EKFC) equations in a Chinese adult population.

OBJECTIVES: The European Kidney Function Consortium (EKFC) developed two novel equations in 2023 for estimating glomerular filtration rate (GFR): one sex-free cystatin C-based equation (EKFCCys) and one creatinine-cystatin C combined equation (EKFCCr-Cys). This study compared their performance with the previous creatinine-based EKFC equation (EKFCCr) and commonly used Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Berlin Initiative Study (BIS) equations in Chinese adults. METHODS: A total of 2,438 Chinese adults (mean age=53.04 years) who underwent the 99mTc-DTPA renal dynamic imaging for reference GFR (rGFR) were included. Diagnostic value was evaluated using correlation coefficients, sensitivity, specificity, and area under the receiver operating characteristic curve (ROCAUC). Performance was assessed in terms of bias, precision (interquartile range of the median difference [IQR]), accuracy (percentage of estimates ±30 % of rGFR [P30], and root-mean-square error [RMSE]) across age, sex, and rGFR subgroups. Gender differences in bias and P30 were also analyzed. RESULTS: Average rGFR was 73.37 mL/min/1.73 m2. EKFC equations showed stronger correlations and larger AUCs compared to the parallel CKD-EPI equations, with EKFCCr-Cys demonstrating the greatest improvement (R=0.771, ROCAUC=0.913). Concerning bias, precision, and accuracy, EKFC equations consistently outperformed CKD-EPI equations. EKFCCr-Cys and EKFCCr performed acceptably well in the entire population and were equivalent to BIS equations in the elderly. All equations, including EKFCCys, showed similar P30 accuracy across sexes. CONCLUSIONS: EKFC equations provided a reasonable alternative for estimating GFR in the Chinese adult population. While EKFCCys did not outperform EKFCCr, EKFCCr-Cys improved the accuracy of single-marker equations.

Comparison of estimated GFR using cystatin C versus creatinine in pediatric kidney transplant recipients.

BACKGROUND: An accurate, rapid estimate of glomerular filtration rate (GFR) in kidney transplant patients affords early detection of transplant deterioration and timely intervention. This study compared the performance of serum creatinine (Cr) and cystatin C (CysC)-based GFR equations to measured GFR (mGFR) using iohexol among pediatric kidney transplant recipients. METHODS: CysC, Cr, and mGFR were obtained from 45 kidney transplant patients, 1-18 years old. Cr- and CysC-estimated GFR (eGFR) was compared against mGFR using the Cr-based (Bedside Schwartz, U25-Cr), CysC-based (Gentian CysC, CAPA, U25-CysC), and Cr-CysC combination (CKiD Cr-CysC, U25 Cr-CysC) equations in terms of bias, precision, and accuracy. Bland-Altman plots assessed the agreement between eGFR and mGFR. Secondary analyses evaluated the formulas in patients with biopsy-proven histological changes, and K/DOQI CKD staging. RESULTS: Bias was small with Gentian CysC (0.1 ml/min/1.73 m2); 88.9% and 37.8% of U25-CysC estimations were within 30% and 10% of mGFR, respectively. In subjects with histological changes on biopsy, Gentian CysC had a small bias and U25-CysC were more accurate-both with 83.3% of and 41.7% of estimates within 30% and 10% mGFR, respectively. Precision was better with U25-CysC, CKiD Cr-CysC, and U25 Cr-CysC. Bland-Altman plots showed the Bedside Schwartz, Gentian CysC, CAPA, and U25-CysC tend to overestimate GFR when > 100 ml/min/1.72 m2. CAPA misclassified CKD stage the least (whole cohort 24.4%, histological changes on biopsy 33.3%). CONCLUSIONS: In this small cohort, CysC-based equations with or without Cr may have better bias, precision, and accuracy in predicting GFR.

Corneal densitometry in Chinese adults with healthy corneas: associations with sex, age, ocular metrics, and optical characteristics.

BACKGROUND: Standardized corneal densitometry (CD) values in large samples of healthy Chinese individuals are scarce. Therefore, we aimed to determine the standard CD values using a Scheimpflug camera in healthy corneas, investigate the correlations of sex, age, and ocular parameters with corneal density, and explore the impact of corneal density on the forward scattering and optical quality of the eye. METHODS: This retrospective observational study involved 990 healthy Chinese individuals, including 494 males and 496 females (mean age: 23.88 ± 6.90 years). The CD values at various depths and radial areas of 0-12 mm were measured using a Scheimpflug camera. Densitometric measurements were expressed in standardized grayscale units (GSU). The optical scatter index (OSI), modulation transfer function cutoff values (MTFcutoff), and Strehl's ratio (SR) were also determined using an optical quality analysis system. RESULTS: The average CD within a 12 mm diameter area was 16.26 ± 1.35 GSU. The highest and lowest optical densities at different depths were observed in the anterior (21.41 ± 2.16 GSU) and posterior (12.00 ± 1.01 GSU) layers, respectively (P < 0.001). Similarly, the maximum and minimum optical densities at different radial areas were observed in the 10-12 mm (14.09 ± 0.93 GSU) and 2-6 mm (25.93 ± 4.77 GSU) circles, respectively (P < 0.001). There was no significant difference in the average CD within a 12 mm diameter area between males and females (P > 0.05). However, upon adjusting for age, central corneal thickness (CCT), corneal curvature, white-to-white (WTW) corneal diameter, and axial length, females exhibited a greater average CD within the 12 mm diameter and in the 6-10 mm and 10-12 mm circles than males. Age-related changes in CD were evident, except in the 2-6 mm circle. CCT, corneal curvature, WTW corneal diameter, and partial depth correlated with CD in the radial area, and CD in different areas correlated with the OSI, MTFcutoff, and SR (P < 0.05). CONCLUSIONS: This study provides the normative CD measurement data of Chinese adults with healthy corneas, emphasizing the significance of sex, age, CCT, corneal curvature, and WTW corneal diameter in CD evaluation. Notably, elevated CD can lead to increased forward scattering within the eye, thereby affecting the optical quality.

Sleeping more than 8 h: a silent factor contributing to decreased muscle mass in Chinese community-dwelling older adults.

BACKGROUND: Muscle mass loss is an age-related process that can be exacerbated by lifestyle, environmental and other factors, but can be mitigated by good sleep. The objective of this study was to investigate the correlation between varying time lags of sleep duration and the decline in muscle mass among individuals aged 60 years or older by using real-world health monitoring data obtained from wearable devices and smart home health monitoring devices. METHODS: This study included 86,037 observations from 2,869 participants in the Mobile Support System database. Missing data were supplemented by multiple imputation. The investigation utilized generalized estimating equations and restricted cubic spline curve to examine the relationship between sleep duration and low muscle mass. Various lag structures, including 0, 1, 2, 0-1, 0-2, and 1-2 months, were fitted, and the interaction effect of observation time with sleep duration was estimated for each lag structure. Additionally, subgroup analyses were conducted. The models were adjusted for various covariates, including gender, age, body mass index, footsteps, smoking status, drinking status, marital status, number of chronic diseases, number of medications, diabetes mellitus, hyperlipidemia, coronary artery disease, respiratory disease, and musculoskeletal disease and an interaction term between time and sleep duration. RESULTS: The results of the generalized estimating equation showed a significant correlation (p < 0.001) between sleep duration of 8 h or more and low muscle mass in older adults, using 6-7 h of sleep as a reference. This effect was seen over time and prolonged sleep accumulated over multiple months had a greater effect on muscle mass loss than a single month. The effect of long sleep duration on muscle mass loss was significantly greater in females than in males and greater in the over-75 than in the under-75 age group. Restricted cubic spline plots showed a non-linear relationship between sleep duration and low muscle mass (p < 0.001). CONCLUSIONS: This study found an association between sustained nighttime sleep of more than eight hours and decreased muscle mass in older adults, especially older women.

Leveraging baseline covariates to analyze small cluster-randomized trials with a rare binary outcome.

Cluster-randomized trials (CRTs) involve randomizing entire groups of participants-called clusters-to treatment arms but are often comprised of a limited or fixed number of available clusters. While covariate adjustment can account for chance imbalances between treatment arms and increase statistical efficiency in individually randomized trials, analytical methods for individual-level covariate adjustment in small CRTs have received little attention to date. In this paper, we systematically investigate, through extensive simulations, the operating characteristics of propensity score weighting and multivariable regression as two individual-level covariate adjustment strategies for estimating the participant-average causal effect in small CRTs with a rare binary outcome and identify scenarios where each adjustment strategy has a relative efficiency advantage over the other to make practical recommendations. We also examine the finite-sample performance of the bias-corrected sandwich variance estimators associated with propensity score weighting and multivariable regression for quantifying the uncertainty in estimating the participant-average treatment effect. To illustrate the methods for individual-level covariate adjustment, we reanalyze a recent CRT testing a sedation protocol in 31 pediatric intensive care units.

Information content of stepped wedge designs under the working independence assumption.

The stepped wedge design is increasingly popular in pragmatic trials and implementation science research studies for evaluating system-level interventions that are perceived to be beneficial to patient populations. An important step in planning a stepped wedge design is to understand the efficiency of the treatment effect estimator and hence the power of the study. We develop several novel analytical results for designing stepped wedge cluster randomized trials analyzed through generalized estimating equations under a misspecified working independence correlation structure. We first contribute a general variance expression of the treatment effect estimator when data collection is scheduled for each cluster-period. Because resource and patient-centered considerations may intentionally call for an incomplete design with outcome data being omitted for certain cluster-periods, we further derive the information content based on the robust sandwich variance to identify data elements that may be preferentially omitted with minimum loss of precision in estimating the treatment effect. We prove that centrosymmetric pairs of cluster-periods, treatment sequences and periods have identical information content and thus contribute equally to the treatment effect estimation, as long as the true covariance structure for the cluster-period means remains centrosymmetric. Finally, we provide an example of how to obtain an incomplete stepped wedge design that admits a more efficient independence GEE estimator but requires less data collection effort. Our results elegantly extend existing ones from linear mixed models coupled with model-based variances to accommodate a misspecified independence working correlation structure through the robust sandwich variances.

Marginal modeling of cluster-period means and intraclass correlations in stepped wedge designs with binary outcomes.

Stepped wedge cluster randomized trials (SW-CRTs) with binary outcomes are increasingly used in prevention and implementation studies. Marginal models represent a flexible tool for analyzing SW-CRTs with population-averaged interpretations, but the joint estimation of the mean and intraclass correlation coefficients (ICCs) can be computationally intensive due to large cluster-period sizes. Motivated by the need for marginal inference in SW-CRTs, we propose a simple and efficient estimating equations approach to analyze cluster-period means. We show that the quasi-score for the marginal mean defined from individual-level observations can be reformulated as the quasi-score for the same marginal mean defined from the cluster-period means. An additional mapping of the individual-level ICCs into correlations for the cluster-period means further provides a rigorous justification for the cluster-period approach. The proposed approach addresses a long-recognized computational burden associated with estimating equations defined based on individual-level observations, and enables fast point and interval estimation of the intervention effect and correlations. We further propose matrix-adjusted estimating equations to improve the finite-sample inference for ICCs. By providing a valid approach to estimate ICCs within the class of generalized linear models for correlated binary outcomes, this article operationalizes key recommendations from the CONSORT extension to SW-CRTs, including the reporting of ICCs.