Variability In Cluster Size Research Articles

Identifying Comorbidity Patterns in People with and without Alzheimer's Disease Using Latent Dirichlet Allocation.

Multimorbidity is common in older adults and complicates diagnosing and care for this population. We investigated co-occurrence patterns (clustering) of medical conditions in persons with Alzheimer's disease (AD) and their matched controls. The register-based Medication use and Alzheimer's disease study (MEDALZ) includes 70,718 community-dwelling persons with incident AD diagnosed during 2005-2011 in Finland and a matched comparison cohort. Latent Dirichlet Allocation was used to cluster the comorbidities (ICD-10 diagnosis codes). Modeling was performed separately for AD and control cohorts. We experimented with different numbers of clusters (also known as topics in the field of Natural Language Processing) ranging from five to 20. In both cohorts, 17 of the 20 most frequent diagnoses were the same. Based on a qualitative assessment by medical experts, the cluster patterns were not affected by the number of clusters, but the best interpretability was observed in the 10-cluster model. Quantitative assessment of the optimal number of clusters by log-likelihood estimate did not imply a specific optimal number of clusters. Multidimensional scaling visualized the variability in cluster size and (dis)similarity between the clusters with more overlapping of clusters and variation in group size seen in the AD cohort. Early signs and symptoms of AD were more commonly clustered together in the AD cohort than in the comparison cohort. This study experimented with using natural language processing techniques for clustering patterns from an epidemiological study. From the computed clusters, it was possible to qualitatively identify multimorbidity that differentiates AD cases and controls.

MULTILEVEL MODAL VALUE ANALYSIS FOR INTERPRETING CATEGORICAL K-MEDOIDS CLUSTERS DATA

Consumer segmentation plays a crucial role for business owners in developing their enterprises. K-Medoid is commonly used for segmentation functions due to its low computational complexity. However, K-Medoid has limitations, such as the variability in cluster sizes across different iterations and the challenge of determining the optimal number of clusters. The Davies-Bouldin Index (DBI) is a metric used to evaluate the number of clusters by calculating the ratio between the within-cluster distance and the between-cluster distance. Most segmentation studies typically stop at the formation of clusters without further interpretation, particularly when dealing with categorical data. This study aims to modify the use of K-Medoid and propose a method for interpreting clusters with categorical data. The research began with questionnaire design and the data collecting from 100 respondents, which was normalized in the second stage. Clustering used K-Medoid with variations K values from K=2 to K=10, with each K value tested 10 times. The clustering results were evaluated using the DBI to select the optimal clusters. Data interpretation conducted using modal values, calculated as the ratio of the number of times a specific attribute variable was selected by respondents to the total number of data points in the cluster. Utilization and hierarchical visualization of modal values proposed in this study offer insights into the dominant variables within an attribute and also depict the relationships between attributes based on the ranking of modal values. These advantages facilitate business analysts in labeling clusters for developing consumer-driven business strategies.

The least sample size essential for detecting changes in clustering solutions of streaming datasets.

The clustering analysis approach treats multivariate data tuples as objects and groups them into clusters based on their similarities or dissimilarities within the dataset. However, in modern world, a significant volume of data is continuously generated from diverse sources over time. In these dynamic scenarios, the data is not static but continually evolves. Consequently, the interesting patterns and inherent subgroups within the datasets also change and develop over time. The researchers have paid special attention to monitoring changes in cluster solutions of evolving streams. For this matter, several algorithms have been proposed in the literature. However, to date, no study has examined the effect of variability in cluster sizes on the evolution of cluster solutions. Moreover, no guidance is available on determining the impact of cluster sizes on the type of changes they experience in the streams. In the present simulation study using artificial datasets, the evolution of clusters is examined concerning the variability in cluster sizes. The findings are substantial because tracing and monitoring the changes in clustering solutions have a wide range of applications in every field of research. This study determines the minimum sample size required in the clustering of time-stamped datasets.

A Bayesian adaptive design approach for stepped-wedge cluster randomized trials.

The Bayesian group sequential design has been applied widely in clinical studies, especially in Phase II and III studies. It allows early termination based on accumulating interim data. However, to date, there lacks development in its application to stepped-wedge cluster randomized trials, which are gaining popularity in pragmatic trials conducted by clinical and health care delivery researchers. We propose a Bayesian adaptive design approach for stepped-wedge cluster randomized trials, which makes adaptive decisions based on the predictive probability of declaring the intervention effective at the end of study given interim data. The Bayesian models and the algorithms for posterior inference and trial conduct are presented. We present how to determine design parameters through extensive simulations to achieve desired operational characteristics. We further evaluate how various design factors, such as the number of steps, cluster size, random variability in cluster size, and correlation structures, impact trial properties, including power, type I error, and the probability of early stopping. An application example is presented. This study presents the incorporation of Bayesian adaptive strategies into stepped-wedge cluster randomized trials design. The proposed approach provides the flexibility to stop the trial early if substantial evidence of efficacy or futility is observed, improving the flexibility and efficiency of stepped-wedge cluster randomized trials.

Sample size calculation for cluster randomized trials with zero-inflated count outcomes.

Cluster randomized trials (CRT) have been widely employed in medical and public health research. Many clinical count outcomes, such as the number of falls in nursing homes, exhibit excessive zero values. In the presence of zero inflation, traditional power analysis methods for count data based on Poisson or negative binomial distribution may be inadequate. In this study, we present a sample size method for CRTs with zero-inflated count outcomes. It is developed based on GEE regression directly modeling the marginal mean of a zero-inflated Poisson outcome, which avoids the challenge of testing two intervention effects under traditional modeling approaches. A closed-form sample size formula is derived which properly accounts for zero inflation, ICCs due to clustering, unbalanced randomization, and variability in cluster size. Robust approaches, including t-distribution-based approximation and Jackknife re-sampling variance estimator, are employed to enhance trial properties under small sample sizes. Extensive simulations are conducted to evaluate the performance of the proposed method. An application example is presented in a real clinical trial setting.

Incorporating pragmatic features into power analysis for cluster randomized trials with a count outcome.

Cluster randomized designs are frequently employed in pragmatic clinical trials which test interventions in the full spectrum of everyday clinical settings in order to maximize applicability and generalizability. In this study, we propose to directly incorporate pragmatic features into power analysis for cluster randomized trials with count outcomes. The pragmatic features considered include arbitrary randomization ratio, overdispersion, random variability in cluster size, and unequal lengths of follow-up over which the count outcome is measured. The proposed method is developed based on generalized estimating equation (GEE) and it is advantageous in that the sample size formula retains a closed form, facilitating its implementation in pragmatic trials. We theoretically explore the impact of various pragmatic features on sample size requirements. An efficient Jackknife algorithm is presented to address the problem of underestimated variance by the GEE sandwich estimator when the number of clusters is small. We assess the performance of the proposed sample size method through extensive simulation and an application example to a real clinical trial is presented.

Overdispersion models for correlated multinomial data: Applications to blinding assessment.

Overdispersion models have been extensively studied for correlated normal and binomial data but much less so for correlated multinomial data. In this work, we describe a multinomial overdispersion model that leads to the specification of the first two moments of the outcome and allows the estimation of the global parameters using generalized estimating equations (GEE). We introduce a Global Blinding Index as a target parameter and illustrate the application of the GEE method to its estimation from (1) a clinical trial with clustering by practitioner and (2) a meta-analysis on psychiatric disorders. We examine the impact of a small number of clusters, high variability in cluster sizes, and the magnitude of the intraclass correlation on the performance of the GEE estimators of the Global Blinding Index using the data simulated from different models. We compare these estimators with the inverse-variance weighted estimators and a maximum-likelihood estimator, derived under the Dirichlet-multinomial model. Our results indicate that the performance of the GEE estimators was satisfactory even in situations with a small number of clusters, whereas the inverse-variance weighted estimators performed poorly, especially for larger values of the intraclass correlation coefficient. Our findings and illustrations may be instrumental for practitioners who analyze clustered multinomial data from clinical trials and/or meta-analysis.

The impact of varying cluster size in cross-sectional stepped-wedge cluster randomised trials

BackgroundCluster randomised trials with unequal sized clusters often have lower precision than with clusters of equal size. To allow for this, sample sizes are inflated by a modified version of the design effect for clustering. These inflation factors are valid under the assumption that randomisation is stratified by cluster size. We investigate the impact of unequal cluster size when that constraint is relaxed, with particular focus on the stepped-wedge cluster randomised trial, where this is more difficult to achieve.MethodsAssuming a multi-level mixed effect model with exchangeable correlation structure for a cross-sectional design, we use simulation methods to compare the precision for a trial with clusters of unequal size to a trial with clusters of equal size (relative efficiency). For a range of scenarios we illustrate the impact of various design features (the cluster-mean correlation – a function of the intracluster correlation and the cluster size, the number of clusters, number of randomisation sequences) on the average and distribution of the relative efficiency.ResultsSimulations confirm that the average reduction in precision, due to varying cluster sizes, is smaller in a stepped-wedge trial compared to the parallel trial. However, the variance of the distribution of the relative efficiency is large; and is larger under the stepped-wedge design compared to the parallel design. This can result in large variations in actual power, depending on the allocation of clusters to sequences. Designs with larger variations in cluster sizes, smaller number of clusters and studies with smaller cluster-mean correlations (smaller cluster sizes or smaller intra-cluster correlation) are particularly at risk.ConclusionThe actual realised power in a stepped-wedge trial might be substantially higher or lower than that estimated. This is particularly important when there are a small number of clusters or the variability in cluster sizes is large. Constraining the randomisation on cluster size, where feasible, might mitigate this effect.

Sample size considerations for stratified cluster randomization design with binary outcomes and varying cluster size.

Stratified cluster randomization trials (CRTs) have been frequently employed in clinical and healthcare research. Comparing with simple randomized CRTs, stratified CRTs reduce the imbalance of baseline prognostic factors among different intervention groups. Due to the popularity, there has been a growing interest in methodological development on sample size estimation and power analysis for stratified CRTs; however, existing work mostly assumes equal cluster size within each stratum and uses multilevel models. Clusters are often naturally formed with random sizes in CRTs. With varying cluster size, commonly used ad hoc approaches ignore the variability in cluster size, which may underestimate (overestimate) the required number of clusters for each group per stratum and lead to underpowered (overpowered) clinical trials. We propose closed-form sample size formulas for estimating the required total number of subjects and for estimating the number of clusters for each group per stratum, based on Cochran-Mantel-Haenszel statistic for stratified cluster randomization design with binary outcomes, accounting for both clustering and varying cluster size. We investigate the impact of various design parameters on the relative change in the required number of clusters for each group per stratum due to varying cluster size. Simulation studies are conducted to evaluate the finite-sample performance of the proposed sample size method. A real application example of a pragmatic stratified CRT of a triad of chronic kidney disease, diabetes, and hypertension is presented for illustration.

Sample size calculation for count outcomes in cluster randomization trials with varying cluster sizes

In many cluster randomization studies, cluster sizes are not fixed and may be highly variable. For those studies, sample size estimation assuming a constant cluster size may lead to under-powered studies. Sample size formulas have been developed to incorporate the variability in cluster size for clinical trials with continuous and binary outcomes. Count outcomes frequently occur in cluster randomized studies. In this paper, we derive a closed-form sample size formula for count outcomes accounting for the variability in cluster size. We compare the performance of the proposed method with the average cluster size method through simulation. The simulation study shows that the proposed method has a better performance with empirical powers and type I errors closer to the nominal levels.

Cluster randomized trials with a small number of clusters: which analyses should be used?

Background: Cluster randomized trials (CRTs) are increasingly used to assess the effectiveness of health interventions. Three main analysis approaches are: cluster-level analyses, mixed-models and generalized estimating equations (GEEs). Mixed models and GEEs can lead to inflated type I error rates with a small number of clusters, and numerous small-sample corrections have been proposed to circumvent this problem. However, the impact of these methods on power is still unclear. Methods: We performed a simulation study to assess the performance of 12 analysis approaches for CRTs with a continuous outcome and 40 or fewer clusters. These included weighted and unweighted cluster-level analyses, mixed-effects models with different degree-of-freedom corrections, and GEEs with and without a small-sample correction. We assessed these approaches across different values of the intraclass correlation coefficient (ICC), numbers of clusters and variability in cluster sizes. Results: Unweighted and variance-weighted cluster-level analysis, mixed models with degree-of-freedom corrections, and GEE with a small-sample correction all maintained the type I error rate at or below 5% across most scenarios, whereas uncorrected approaches lead to inflated type I error rates. However, these analyses had low power (below 50% in some scenarios) when fewer than 20 clusters were randomized, with none reaching the expected 80% power. Conclusions: Small-sample corrections or variance-weighted cluster-level analyses are recommended for the analysis of continuous outcomes in CRTs with a small number of clusters. The use of these corrections should be incorporated into the sample size calculation to prevent studies from being underpowered.

Unequal cluster sizes in stepped-wedge cluster randomised trials: a systematic review

ObjectivesTo investigate the extent to which cluster sizes vary in stepped-wedge cluster randomised trials (SW-CRT) and whether any variability is accounted for during the sample size calculation and analysis of...

Power analysis for stratified cluster randomisation trials with cluster size being the stratifying factor

ABSTRACTStratified cluster randomisation trial design is widely employed in biomedical research and cluster size has been frequently used as the stratifying factor. Conventional sample size calculation methods have assumed the cluster sizes to be constant within each stratum, which is rarely true in practice. Ignoring the random variability in cluster size leads to underestimated sample sizes and underpowered clinical trials. In this study, we proposed to directly incorporate the variability in cluster size (represented by coefficient of variability) into sample size calculation. This approach provides closed-form sample size formulas, and is flexible to accommodate arbitrary randomisation ratio and varying numbers of clusters across strata. Simulation study shows that the proposed approach achieves desired power and type I error over a wide spectrum of design configurations, including different distributions of cluster sizes. An application example is presented.

Methods for sample size determination in cluster randomized trials.

Background: The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required.Methods: We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method.Results: We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs.Conclusions: There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials.

Changing cluster composition in cluster randomised controlled trials: design and analysis considerations.

BackgroundThere are many methodological challenges in the conduct and analysis of cluster randomised controlled trials, but one that has received little attention is that of post-randomisation changes to cluster composition. To illustrate this, we focus on the issue of cluster merging, considering the impact on the design, analysis and interpretation of trial outcomes.MethodsWe explored the effects of merging clusters on study power using standard methods of power calculation. We assessed the potential impacts on study findings of both homogeneous cluster merges (involving clusters randomised to the same arm of a trial) and heterogeneous merges (involving clusters randomised to different arms of a trial) by simulation. To determine the impact on bias and precision of treatment effect estimates, we applied standard methods of analysis to different populations under analysis.ResultsCluster merging produced a systematic reduction in study power. This effect depended on the number of merges and was most pronounced when variability in cluster size was at its greatest. Simulations demonstrate that the impact on analysis was minimal when cluster merges were homogeneous, with impact on study power being balanced by a change in observed intracluster correlation coefficient (ICC). We found a decrease in study power when cluster merges were heterogeneous, and the estimate of treatment effect was attenuated.ConclusionsExamples of cluster merges found in previously published reports of cluster randomised trials were typically homogeneous rather than heterogeneous. Simulations demonstrated that trial findings in such cases would be unbiased. However, simulations also showed that any heterogeneous cluster merges would introduce bias that would be hard to quantify, as well as having negative impacts on the precision of estimates obtained. Further methodological development is warranted to better determine how to analyse such trials appropriately. Interim recommendations include avoidance of cluster merges where possible, discontinuation of clusters following heterogeneous merges, allowance for potential loss of clusters and additional variability in cluster size in the original sample size calculation, and use of appropriate ICC estimates that reflect cluster size.

Sample Size Calculation for Clustered Binary Data with Sign Tests Using Different Weighting Schemes

We propose a sample size calculation approach for testing a proportion using the weighted sign test when binary observations are dependent within a cluster. Sample size formulas are derived with nonparametric methods using three weighting schemes: equal weights to observations, equal weights to clusters, and optimal weights that minimize the variance of the estimator. Sample size formulas are derived incorporating intracluster correlation and the variability in cluster sizes. Simulation studies are conducted to evaluate a finite sample performance of the proposed sample size formulas. Empirical powers are generally close to nominal levels. The number of clusters required increases as the imbalance in cluster size increases and the intracluster correlation increases. The estimator using optimal weights yields the smallest sample size estimate among three estimators. For small values of intracluster correlation the sample size estimates derived from the optimal weight estimator are close to that derived from the estimator assigning equal weights to observations. For large values of intracluster correlation, the optimal weight sample size estimate is close to the sample size estimate assigning equal weights to clusters.

Methods for modelling change in cluster randomization trials.

Randomized trials are often designed to assess an intervention's ability to change patient knowledge, behaviour or health. The study outcome will then need to be measured at least twice for each subject--prior to random assignment and following implementation of the intervention. In this paper we consider methods for modelling change when data are obtained from cluster randomization trials where the unit of allocation is a family, school or community. Attention focuses on mixed effects linear regression extensions of (i) two-sample t-tests and (ii) analysis of covariance, in both cases accounting for dependencies among cluster members. Algebraic expressions for tests of the intervention effect are derived for the special case where there are a fixed number of subjects per cluster while simulation studies are used to compare the power of these procedures in the more realistic case where there is variability in cluster size. A key conclusion is that there can be considerable gains in power when allowing for different individual-level and cluster-level associations between the baseline and follow-up assessments. The discussion is illustrated using data from a school-based smoking prevention trial.

Sample size re-estimation in cluster randomization trials.

Cluster randomization trials in which families are the unit of allocation are commonly adopted for the evaluation of disease prevention interventions. Sample size estimation for cluster randomization trials depends on parameters that quantify the variability within and between clusters and the variability in cluster size. Accurate advance estimates of these nuisance parameters may be difficult to obtain and misspecification may lead to an underpowered study. Since families are typically recruited over time, we propose using a portion of the data to estimate the nuisance parameters and to re-estimate sample size based on the estimates. This extends the standard internal pilot study methods to the setting of cluster randomization trials. The effect of this design on the power, significance level and sample size is analysed via simulation and is shown to provide a flexible and practical approach to cluster randomization trials.