Small Number Of Clusters Research Articles

Estimating an adjusted risk difference in a cluster randomized trial with individual-level analyses.

In cluster randomized trials (CRTs) with a binary outcome, intervention effects are usually reported as odds ratios, but the CONSORT statement advocates reporting both a relative and an absolute intervention effect. With a simulation study, we assessed several methods to estimate a risk difference (RD) in the framework of a CRT with adjustment on both individual- and cluster-level covariates. We considered both a conditional approach (with the generalized linear mixed model [GLMM]) and a marginal approach (with the generalized estimating equation [GEE]). For both approaches, we considered the Gaussian, binomial, and Poisson distributions. When considering the binomial or Poisson distribution, we used the g-computation method to estimate the RD. Convergence problems were observed with the GEE approach, especially with low intra-cluster coefficient correlation values, small number of clusters, small mean cluster size, high number of covariates, and prevalences close to 0. All methods reported no bias. The Gaussian distribution with both approaches and binomial and Poisson distributions with the GEE approach had satisfactory results in estimating the standard error. Results for type I error and coverage rates were better with the GEE than GLMM approach. We recommend using the Gaussian distribution because of its ease of use (the RD is estimated in one step only). The GEE approach should be preferred and replaced with the GLMM approach in cases of convergence problems.

The fixed-effects model for robust analysis of stepped-wedge cluster trials with a small number of clusters and continuous outcomes: a simulation study

BackgroundStepped-wedge cluster trials (SW-CTs) describe a cluster trial design where treatment rollout is staggered over the course of the trial. Clusters are commonly randomized to receive treatment beginning at different time points in this study design (commonly referred to as a Stepped-wedge cluster randomized trial; SW-CRT), but they can also be non-randomized. Trials with this design regularly have a low number of clusters and can be vulnerable to covariate imbalance. To address such covariate imbalance, previous work has examined covariate-constrained randomization and analysis adjustment for imbalanced covariates in mixed-effects models. These methods require the imbalanced covariate to always be known and measured. In contrast, the fixed-effects model automatically adjusts for all imbalanced time-invariant covariates, both measured and unmeasured, and has been implicated to have proper type I error control in SW-CTs with a small number of clusters and binary outcomes.MethodsWe present a simulation study comparing the performance of the fixed-effects model against the mixed-effects model in randomized and non-randomized SW-CTs with small numbers of clusters and continuous outcomes. Additionally, we compare these models in scenarios with cluster-level covariate imbalances or confounding.ResultsWe found that the mixed-effects model can have low coverage probabilities and inflated type I error rates in SW-CTs with continuous outcomes, especially with a small number of clusters or when the ICC is low. Furthermore, mixed-effects models with a Satterthwaite or Kenward-Roger small sample correction can still result in inflated or overly conservative type I error rates, respectively. In contrast, the fixed-effects model consistently produced the target level of coverage probability and type I error rates without dramatically compromising power. Furthermore, the fixed-effects model was able to automatically account for all time-invariant cluster-level covariate imbalances and confounding to robustly yield unbiased estimates.ConclusionsWe recommend the fixed-effects model for robust analysis of SW-CTs with a small number of clusters and continuous outcomes, due to its proper type I error control and ability to automatically adjust for all potential imbalanced time-invariant cluster-level covariates and confounders.

Agro-morphological genetic diversity assessment of Amaranthus genotypes from Ethiopia based on qualitative traits

Amaranths are a promising plant in the family of Amaranthaceae because of their nutritional and functional properties, such as their high antioxidant content and dietary fiber content. However, it's being disregarded for several reasons, such as ignorance, a lack of in-depth research, and the plant's long-term genetic growth in Ethiopia, among other factors. In the current work, we described the genetic diversity of 120 amaranth genotypes using qualitative criteria. The experiment, which was configured with an alpha lattice design and duplicated twice, was run for two seasons in 2020 and 2021. Twenty qualitative descriptors were looked for in the gathered data. Among the 20 qualitative variables that were assessed, the chi-square test result indicated the presence of prevailing phenotypic variation. The results of the agro-morphological characterization also revealed a significant amount of variance. The overall mean of the Shannon diversity indices (H') was 0.61. The indices for germination rate, leaf margin, prominence of leaf veins, and the existence of auxiliary inflorescence varied from 0.12 to 0.99. The estimated diversity indices showed more intra-regional diversity (0.66) than inter-regional diversity (0.34), demonstrating the existence of gene flow between growing regions. Shannon–Weaver Diversity Index, ranged from 0.00 for auxiliary inflorescence to 1.94 for leaf coloration, with an overall mean of 19 characters (95%) that were found to have high diversity (> 0.76) while auxiliary inflorescence was invariant. Except for auxiliary inflorescence, all qualitative features showed a lot of variation. Additionally, Amaranthus hybridus L. subsp. cruentus (L.) Theil recorded the greatest Shannon diversity index (0.47) while Amaranthus spinosus L. recorded the lowest (0.00). The hierarchical clustering grouped all the genotypes into three clusters. The first cluster included the most genotypes (58), followed by the second (47), and the third cluster contained the fewest (15). Principal component analysis showed that the first six principal components with eigenvalues greater than one contributed 72% of the variability among genotypes. The study unequivocally demonstrated that, even when the genotypes were grouped into a small number of clusters, there was still enough divergence within the clusters to demonstrate the genotypes of amaranth to have a high genetic diversity. These results indicate that there is substantial genetic diversity among Ethiopian amaranth genotypes, which should be safeguarded and may be utilized in breeding in the future.

Selection of number of clusters and warping penalty in clustering functional electrocardiogram.

Clustering functional data aims to identify unique functional patterns in the entire domain, but this can be challenging due to phase variability that distorts the observed patterns. Curve registration can be used to remove this variability, but determining the appropriate level of warping flexibility can be complicated. Curve registration also requires a target to which a functional object is aligned, typically the cross-sectional mean of functional objects within the same cluster. However, this mean is unknown prior to clustering. Furthermore, there is a trade-off between flexible warping and the number of resulting clusters. Removing more phase variability through curve registration can lead to fewer remaining variations in the functional data, resulting in a smaller number of clusters. Thus, the optimal number of clusters and warping flexibility cannot be uniquely identified. We propose to use external information to solve the identification issue. We define a cross validated Kullback-Leibler information criterion to select the number of clusters and the warping penalty. The criterion is derived from the predictive classification likelihood considering the joint distribution of both the functional data and external variable and penalizes the uncertainty in the cluster membership. We evaluate our method through simulation and apply it to electrocardiographic data collected in the Chronic Renal Insufficiency Cohort study. We identify two distinct clusters of electrocardiogram (ECG) profiles, with the second cluster exhibiting ST segment depression, an indication of cardiac ischemia, compared to the normal ECG profiles in the first cluster.

Covariate-constrained randomization in cluster randomized 2 × 2 factorial trials: application to a diabetes prevention study

BackgroundCluster randomized trials (CRTs) are randomized trials where randomization takes place at an administrative level (e.g., hospitals, clinics, or schools) rather than at the individual level. When the number of available clusters is small, researchers may not be able to rely on simple randomization to achieve balance on cluster-level covariates across treatment conditions. If these cluster-level covariates are predictive of the outcome, covariate imbalance may distort treatment effects, threaten internal validity, lead to a loss of power, and increase the variability of treatment effects. Covariate-constrained randomization (CR) is a randomization strategy designed to reduce the risk of imbalance in cluster-level covariates when performing a CRT. Existing methods for CR have been developed and evaluated for two- and multi-arm CRTs but not for factorial CRTs.MethodsMotivated by the BEGIN study—a CRT for weight loss among patients with pre-diabetes—we develop methods for performing CR in 2 × 2 factorial cluster randomized trials with a continuous outcome and continuous cluster-level covariates. We apply our methods to the BEGIN study and use simulation to assess the performance of CR versus simple randomization for estimating treatment effects by varying the number of clusters, the degree to which clusters are associated with the outcome, the distribution of cluster level covariates, the size of the constrained randomization space, and analysis strategies.ResultsCompared to simple randomization of clusters, CR in the factorial setting is effective at achieving balance across cluster-level covariates between treatment conditions and provides more precise inferences. When cluster-level covariates are included in the analyses model, CR also results in greater power to detect treatment effects, but power is low compared to unadjusted analyses when the number of clusters is small.ConclusionsCR should be used instead of simple randomization when performing factorial CRTs to avoid highly imbalanced designs and to obtain more precise inferences. Except when there are a small number of clusters, cluster-level covariates should be included in the analysis model to increase power and maintain coverage and type 1 error rates at their nominal levels.

Multicomponent family support intervention in intensive care units: statistical analysis plan for the cluster-randomized controlled FICUS trial

The FICUS trial is a cluster-randomized superiority trial to determine the effectiveness of a nurse-led, interprofessional family support intervention (FSI) on the quality of care, family management and individual mental health of family members of critically ill patients, compared to usual care. This paper describes the statistical analysis plan of the FICUS trial. The primary outcome is quality of family care, assessed by the Family Satisfaction in ICU Questionnaire (FS-ICU-24R) at patient discharge from the ICU. Several secondary outcomes are additionally assessed 3, 6, and 12 months thereafter. Sixteen clusters (ICUs) were randomly assigned 1:1 to FSI or usual care using minimization (8 per treatment). The target sample size is 56 patients per cluster (896 in total). Recruitment has been completed in January 2024. The follow-up of the last participant will be completed in early 2025. The primary and secondary outcomes will be analyzed by linear mixed-effects models (LMM). The main model for the primary outcome will include a random intercept per cluster with treatment (FSI vs. usual care) as the only explanatory variable due to the relatively small number of clusters. In addition, covariate-adjusted analyses will be conducted, including two cluster-level characteristics used in the minimization as well as participant-level characteristics. Moreover, a number of subgroup analyses by cluster- and participant-level characteristics are pre-specified.Trial registration ClinicalTrials.gov NCT05280691. Registered on February 20, 2022.

Exploiting Signal Coherence to Simultaneously Detect and Locate Earthquakes

Abstract This study introduces an earthquake detection and location technique that exploits the spatial coherence of the seismic wavefield. The method leverages the signal coherence across clusters of seismic stations to generate characteristic functions that are backprojected (migrated) to detect and locate seismic events. The effectiveness of the technique is assessed using a limited set of stations from the Oklahoma wavefield experiment, with minimal tuning of processing parameters. The technique is then applied to one day of continuous data, leading to the detection of new seismic events compared with an analyst-based catalog. Noteworthy advantages of this method include its independence from prior information or assumptions (such as template waveform) and its ability to operate effectively with a network design for which seismometers are deployed in a relatively small number of clusters rather than distributed throughout a region.

Specialization, market access and real income

This paper estimates the impact of external demand shocks on real income. We utilize a first order approximation to a wide class of small open economy models that feature sector-level gravity in trade flows, which allows us to measure foreign shocks and characterize their welfare impact in terms of reduced-form elasticities. We use machine learning techniques to group 4-digit manufacturing sectors into a smaller number of clusters, and show that the cluster-level elasticities of income with respect to foreign shocks can be estimated using high-dimensional statistical techniques. Foreign demand shocks in complex intermediate and capital goods have large positive impacts on real income, whereas impacts in other sectors are negligible. We show that the estimates imply that countries that specialize in these sectors enjoy greater gains from increased openness, and that (small) export subsidies to these sectors are welfare-improving. Finally, a calibrated multi-sector production and trade model with input–output linkages and external economies of scale can match the empirical estimates.

Identifying bias in network clustering quality metrics.

We study potential biases of popular network clustering quality metrics, such as those based on the dichotomy between internal and external connectivity. We propose a method that uses both stochastic and preferential attachment block models construction to generate networks with preset community structures, and Poisson or scale-free degree distribution, to which quality metrics will be applied. These models also allow us to generate multi-level structures of varying strength, which will show if metrics favour partitions into a larger or smaller number of clusters. Additionally, we propose another quality metric, the density ratio. We observed that most of the studied metrics tend to favour partitions into a smaller number of big clusters, even when their relative internal and external connectivity are the same. The metrics found to be less biased are modularity and density ratio.

Bias-corrected and doubly robust inference for the three-level longitudinal cluster-randomized trials with missing continuous outcomes and small number of clusters: Simulation study and application to a study for adults with serious mental illnesses

Longitudinal cluster-randomized designs have been popular tools for comparative effective research in clinical trials. The methodologies for the three-level hierarchical design with longitudinal outcomes need to be better understood under more pragmatic settings; that is, with a small number of clusters, heterogeneous cluster sizes, and missing outcomes. Generalized estimating equations (GEEs) have been frequently used when the distribution of data and the correlation model are unknown. Standard GEEs lead to bias and an inflated type I error rate due to the small number of available clinics and non-completely random missing data in longitudinal outcomes. We evaluate the performance of inverse probability weighted (IPW) estimating equations, with and without augmentation, for two types of missing data in continuous outcomes and individual-level treatment allocation mechanisms combined with two bias-corrected variance estimators. Our intensive simulation results suggest that the proposed augmented IPW method with bias-corrected variance estimation successfully prevents the inflation of false positive findings and improves efficiency when the number of clinics is small, with moderate to severe missing outcomes. Our findings are expected to aid researchers in choosing appropriate analysis methods for three-level longitudinal cluster-randomized designs. The proposed approaches were applied to analyze data from a longitudinal cluster-randomized clinical trial involving adults with serious mental illnesses.

Tuberculosis in Prisons: Importance of Considering the Clustering in the Analysis of Cross-Sectional Studies

The level of clustering and the adjustment by cluster-robust standard errors have yet to be widely considered and reported in cross-sectional studies of tuberculosis (TB) in prisons. In two cross-sectional studies of people deprived of liberty (PDL) in Medellin, we evaluated the impact of adjustment versus failure to adjust by clustering on prevalence ratio (PR) and 95% confidence interval (CI). We used log-binomial regression, Poisson regression, generalized estimating equations (GEE), and mixed-effects regression models. We used cluster-robust standard errors and bias-corrected standard errors. The odds ratio (OR) was 20% higher than the PR when the TB prevalence was >10% in at least one of the exposure factors. When there are three levels of clusters (city, prison, and courtyard), the cluster that had the strongest effect was the courtyard, and the 95% CI estimated with GEE and mixed-effect models were narrower than those estimated with Poisson and binomial models. Exposure factors lost their significance when we used bias-corrected standard errors due to the smaller number of clusters. Tuberculosis transmission dynamics in prisons dictate a strong cluster effect that needs to be considered and adjusted for. The omission of cluster structure and bias-corrected by the small number of clusters can lead to wrong inferences.

Association of traits promoting resistance to the adzuki bean beetle, Callosobruchus chinensis (L.) (Coleoptera: Bruchidae) in pea genotypes grown at various soil fertility levels

Adzuki bean beetle, Callosobruchus chinensis (L.) (Coleoptera: Bruchidae), is one of the most important pests of pea (Pisum sativum L.) crops in Ethiopia. The study focused on the association of resistance potential in the no-choice test of pea genotypes managed at different fertility levels and trait contributions. Based on the significance of fertility levels, genotypes were grouped into four, six, and five clusters, viz. Under neither rhizobium and phosphorus, rhizobium alone and rhizobium and phosphorus, respectively. Regardless of fertility levels, the inter-cluster distance (D2) values of the two potential clusters were highly significant (P < 0.01). At all fertility levels, the average performance of genotypes in each cluster for individual traits to infestation varied significantly. Genotype distribution patterns tended to group together into a small number of clusters. Eighty genotypes of the pea (Pisum sativum L. subsp. sativum and Pisum sativum L. subsp. abyssinicum A. Braun) were systematically managed under three fertility levels, and the first four principal components accounted for 94%, 92.3%, and 94.2% of the total variation. The primary trait that determines the resistance potential of pea genotypes is the trait susceptibility index (SI), which exhibits highly significant and adverse associations with critical traits such as the date of adult emergency and the percentage of seed coat, while exhibiting highly significant and favorable associations with the remaining traits at all fertility levels. The remaining characteristics showed highly significant positive or negative correlations within and particularly with the characteristics that determine resistance. Therefore, the cultivar "Adi" from "Pisum sativum L. subsp. sativum" had higher susceptibility compared to other genotypes, while the small-seeded pea genotypes "Pisum sativum L. subsp. abyssinicum A. Braun"; fpcoll-1/07, fpcoll-2/07, fpcoll-21/07, and fpcoll-43/07 were moderately resistant.

Structural and mechanical properties of folded protein hydrogels with embedded microbubbles.

Globular folded proteins are powerful building blocks to create biomaterials with mechanical robustness and inherent biological functionality. Here we explore their potential as advanced drug delivery scaffolds, by embedding microbubbles (MBs) within a photo-activated, chemically cross-linked bovine serum albumin (BSA) protein network. Using a combination of circular dichroism (CD), rheology, small angle neutron scattering (SANS) and microscopy we determine the nanoscale and mesoscale structure and mechanics of this novel multi-composite system. Optical and confocal microscopy confirms the presence of MBs within the protein hydrogel, their reduced diffusion and their effective rupture using ultrasound, a requirement for burst drug release. CD confirms that the inclusion of MBs does not impact the proportion of folded proteins within the cross-linked protein network. Rheological characterisation demonstrates that the mechanics of the BSA hydrogels is reduced in the presence of MBs. Furthermore, SANS reveals that embedding MBs in the protein hydrogel network results in a smaller number of clusters that are larger in size (∼16.6% reduction in number of clusters, 17.4% increase in cluster size). Taken together, we show that MBs can be successfully embedded within a folded protein network and ruptured upon application of ultrasound. The fundamental insight into the impact of embedded MBs in protein scaffolds at the nanoscale and mesoscale is important in the development of future platforms for targeted and controlled drug delivery applications.

Unsupervised recognition and prediction of daily patterns in heating loads in buildings

This paper presents a multistep methodology combining unsupervised and supervised learning techniques for the identification of the daily heating energy consumption patterns in buildings. The relevant number of typical profiles is obtained through unsupervised clustering processes. Then Classification and Regression Trees are used to predict the profile type corresponding to external variables, including calendar and climatic variables, from any given day. The methodology is tested with a variety of datasets for three different buildings with different uses connected to the district heating network in Tartu (Estonia). The three buildings under analysis present different energy behaviors (residential, kindergarten and commercial buildings). The paper shows that unsupervised clustering is effective for pattern recognition since the results from the classification and regression trees match the results from the unsupervised clustering. Three main patterns have been identified in each building, seasonality and daily mean temperature being the variables that have the greatest effect. The results concluded that the best classification accuracy is obtained with a small number of clusters with a classification accuracy from 0.7 to 0.85, approximately.

Cluster randomised trials with a binary outcome and a small number of clusters: comparison of individual and cluster level analysis method

BackgroundCluster randomised trials (CRTs) are often designed with a small number of clusters, but it is not clear which analysis methods are optimal when the outcome is binary. This simulation study aimed to determine (i) whether cluster-level analysis (CL), generalised linear mixed models (GLMM), and generalised estimating equations with sandwich variance (GEE) approaches maintain acceptable type-one error including the impact of non-normality of cluster effects and low prevalence, and if so (ii) which methods have the greatest power. We simulated CRTs with 8–30 clusters, altering the cluster-size, outcome prevalence, intracluster correlation coefficient, and cluster effect distribution. We analysed each dataset with weighted and unweighted CL; GLMM with adaptive quadrature and restricted pseudolikelihood; GEE with Kauermann-and-Carroll and Fay-and-Graubard sandwich variance using independent and exchangeable working correlation matrices. P-values were from a t-distribution with degrees of freedom (DoF) as clusters minus cluster-level parameters; GLMM pseudolikelihood also used Satterthwaite and Kenward-Roger DoF.ResultsUnweighted CL, GLMM pseudolikelihood, and Fay-and-Graubard GEE with independent or exchangeable working correlation matrix controlled type-one error in > 97% scenarios with clusters minus parameters DoF. Cluster-effect distribution and prevalence of outcome did not usually affect analysis method performance. GEE had the least power. With 20–30 clusters, GLMM had greater power than CL with varying cluster-size but similar power otherwise; with fewer clusters, GLMM had lower power with common cluster-size, similar power with medium variation, and greater power with large variation in cluster-size.ConclusionWe recommend that CRTs with ≤ 30 clusters and a binary outcome use an unweighted CL or restricted pseudolikelihood GLMM both with DoF clusters minus cluster-level parameters.

Using Robust Standard Errors for the Analysis of Binary Outcomes with a Small Number of Clusters

Binary outcomes are often analyzed in cluster randomized trials (CRTs) using logistic regression and cluster robust standard errors (CRSEs) are routinely used to account for the dependent nature of nested data in such models. However, CRSEs can be problematic when the number of clusters is low (e.g., < 50) and, with CRTs, a low number of clusters is quite common. We investigate the use of the CR2 CRSE and an empirical degrees of freedom adjustment (dofBM) proposed by Bell and McCaffrey with a simulation using binary outcomes and illustrate its use with an applied example. Findings show that the CR2 (w/dofBM) standard errors are relatively unbiased with coverage and power rates for group-level predictors that are comparable to that of a multilevel logistic regression model and can be used even with as few as 10 clusters. To promote its use, a free graphical SPSS extension is provided that can fit logistic (and linear) regression models with a variety of CRSEs and dof adjustments.

KLASIFIKASI DATA NASABAH KREDIT PINJAMAN MENGGUNAKAN DATA MINING DENGAN METODE K-MEANS PADA MEGA CENTRAL FINANCE

Mega Central Finance (MCF) Group is a company under CT.Corpora. The Mega Central Finance (MCF) Group company functions as a company engaged in financing and credit, located in Muara Bulian. The purpose of this study using the "K-means" data mining method is to obtain data reports on customers who are entitled to receive loans from the Mega Central Finance (MCF) Group. Clustering includes inputting data from customers who apply for loans, then entering the registration process to enter the customer's name, the calculation process using RapidMiner. It takes several variables used in clustering, namely the variable "Amount of Loans, Term, Income, Number of Pickup Vehicles". The results of clustering obtained three clusters, namely cluster 1 there are 7 active customer data which has a very small number of clusters. Cluster 2 contains 93 passive customer data which has a cluster number with the highest number of customer data from cluster 1 and cluster 3. Cluster 3 contains 50 repeat order customer data which has a moderate number of clusters. Finally, the results from the three clusters above are obtained.

On the Implementation of Approximate Randomization Tests in Linear Models with a Small Number of Clusters

Abstract This paper provides a user’s guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017a. “Randomization Tests under an Approximate Symmetry Assumption.” Econometrica 85 (3): 1013–30) when specialized to linear regressions with clustered data. An important feature of the methodology is that it applies to settings in which the number of clusters is small – even as small as five. We provide a step-by-step algorithmic description of how to implement the test and construct confidence intervals for the parameter of interest. In doing so, we additionally present three novel results concerning the methodology: we show that the method admits an equivalent implementation based on weighted scores; we show the test and confidence intervals are invariant to whether the test statistic is studentized or not; and we prove convexity of the confidence intervals for scalar parameters. We also articulate the main requirements underlying the test, emphasizing in particular common pitfalls that researchers may encounter. Finally, we illustrate the use of the methodology with two applications that further illuminate these points: one to a linear regression with clustered data based on Meng, Qian, and Yared (2015. “The Institutional Causes of china’s Great Famine, 1959–1961.” The Review of Economic Studies 82 (4): 1568–611) and a second to a linear regression with temporally dependent data based on Munyo and Rossi (2015. “First-day Criminal Recidivism.” Journal of Public Economics 124: 81–90). The companion R and Stata packages facilitate the implementation of the methodology and the replication of the empirical exercises.

Evaluating the performance of Bayesian and restricted maximum likelihood estimation for stepped wedge cluster randomized trials with a small number of clusters

BackgroundStepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials.MethodsWe conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect.ResultsBoth REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias.ConclusionsThe use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

Finite‐sample adjustments in variance estimators for clustered competing risks regression

The marginal Fine-Gray proportional subdistribution hazards model is a popular approach to directly study the association between covariates and the cumulative incidence function with clustered competing risks data, which often arise in multicenter randomized trials or multilevel observational studies. To account for the within-cluster correlations between failure times, the uncertainty of the regression parameters estimators is quantified by the robust sandwich variance estimator, which may have unsatisfactory performance with a limited number of clusters. To overcome this limitation, we propose four bias-corrected variance estimators to reduce the negative bias of the usual sandwich variance estimator, extending the bias-correction techniques from generalized estimating equations with noncensored exponential family outcomes to clustered competing risks outcomes. We further compare their finite-sample operating characteristics through simulations and two real data examples. In particular, we found the Mancl and DeRouen (MD) type sandwich variance estimator generally has the smallest bias. Furthermore, with a small number of clusters, the Wald -confidence interval with the MD sandwich variance estimator carries close to nominal coverage for the cluster-level effect parameter. The -confidence intervals based on the sandwich variance estimator with any one of the three types of multiplicative bias correction or the -confidence interval with the Morel, Bokossa and Neerchal (MBN) type sandwich variance estimator have close to nominal coverage for the individual-level effect parameter. Finally, we develop a user-friendly R package crrcbcv implementing the proposed sandwich variance estimators to assist practical applications.