Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

Liu, Jingxia; Colditz, Graham A.

doi:10.1002/bimj.201600262

Cited by 18 publications

(35 citation statements)

References 36 publications

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“…Second, we use generalized estimating equations (GEE) instead of a linear extrapolation to model amplitude progressions [29]. GEE are commonly used in longitudinal biomedical and environmental studies to assess the effect of an intervention [45]. This is because GEE can account for the correlation structure that results from repeated measurements of the same individual, leading to more consistent estimation of differences when compared to parametric tests that neglect correlation [46].…”

Section: Discussionmentioning

confidence: 99%

SIRT3 promotes auditory function in young adult FVB/nJ mice but is dispensable for hearing recovery after noise exposure

et al. 2020

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Noise-induced hearing loss (NIHL) affects millions of people worldwide and presents a large social and personal burden. Pharmacological activation of SIRT3, a regulator of the mitochondrial oxidative stress response, has a protective effect on hearing thresholds after traumatic noise damage in mice. In contrast, the role of endogenously activated SIRT3 in hearing recovery has not been established. Here we tested the hypothesis that SIRT3 is required in mice for recovery of auditory thresholds after a noise exposure that confers a temporary threshold shift (TTS). SIRT3-specific immunoreactivity is present in outer hair cells, around the post-synaptic regions of inner hair cells, and faintly within inner hair cells. Prior to noise exposure, homozygous Sirt3-KO mice have slightly but significantly higher thresholds than their wild-type littermates measured by the auditory brainstem response (ABR), but not by distortion product otoacoustic emissions (DPOAE). Moreover, homozygous Sirt3-KO mice display a significant reduction in the progression of their peak 1 amplitude at higher frequencies prior to noise exposure. After exposure to a single sub-traumatic noise dose that does not permanently reduce cochlear function, compromise cell survival, or damage synaptic structures in wild-type mice, there was no difference in hearing function between the two genotypes, measured by ABR and DPOAE. The numbers of hair cells and auditory synapses were similar in both genotypes before and after noise exposure. These loss-of-function studies complement previously published gain-of-function studies and help refine our understanding of SIRT3's role in cochlear homeostasis under different damage paradigms. They suggest that SIRT3 may promote spiral ganglion neuron function. They imply that cellular mechanisms of homeostasis, in addition to the mitochondrial oxidative stress response, act to restore hearing after TTS. Finally, we present a novel application of a biomedical statistical analysis for identifying changes between peak 1 amplitude progressions in ABR waveforms after damage.

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Section: Discussionmentioning

confidence: 99%

SIRT3 promotes auditory function in young adult FVB/nJ mice but is dispensable for hearing recovery after noise exposure

et al. 2020

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“…The ratio of the required sample size for a stratified trial vs that for a comparably powered unstratified trial is useful in determining whether the benefits of stratification outweigh the potential costs. Similar metrics have been discussed in the context of IRTs, 1,3 for unequal vs equal cluster sizes in CRTs, 33,34 and in simulation studies of CRT analysis methods. 35 Here, we present analytic formulas for the sample size required for a stratified trial and the ratio of the sample sizes required for stratified vs unstratified IRTs and CRTs with binary outcomes in the context of stratification by a cluster-level covariate.…”

mentioning

confidence: 83%

“…These formulas require the full specification of the distribution of cluster sizes. Alternative estimates of the design effects for CRTs with unequal cluster size can also be used, for example, using the harmonic mean of the cluster sizes, or finding the design effect for the corresponding trial with equal cluster sizes and multiplying by the relative efficiency of the trial with equal cluster sizes compared with that with unequal cluster sizes . An upper bound for the sample size required can be obtained by using

F = 1 + [(C V_{m}^{2} + 1) \overline{m} - 1] ρ

, which we denote by F B , where

C V_{m} = \frac{σ_{m}}{\overline{m}}

and σ m is the standard deviation of the cluster sizes .…”

Section: Stratified Cluster Randomized Trialsmentioning

confidence: 99%

Sample size estimation for stratified individual and cluster randomized trials with binary outcomes

Kennedy‐Shaffer

Hughes

2020

Statistics in Medicine

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Individual randomized trials (IRTs) and cluster randomized trials (CRTs) with binary outcomes arise in a variety of settings and are often analyzed by logistic regression (fitted using generalized estimating equations for CRTs). The effect of stratification on the required sample size is less well understood for trials with binary outcomes than for continuous outcomes. We propose easy‐to‐use methods for sample size estimation for stratified IRTs and CRTs and demonstrate the use of these methods for a tuberculosis prevention CRT currently being planned. For both IRTs and CRTs, we also identify the ratio of the sample size for a stratified trial vs a comparably powered unstratified trial, allowing investigators to evaluate how stratification will affect the required sample size when planning a trial. For CRTs, these can be used when the investigator has estimates of the within‐stratum intracluster correlation coefficients (ICCs) or by assuming a common within‐stratum ICC. Using these methods, we describe scenarios where stratification may have a practically important impact on the required sample size. We find that in the two‐stratum case, for both IRTs and for CRTs with very small cluster sizes, there are unlikely to be plausible scenarios in which an important sample size reduction is achieved when the overall probability of a subject experiencing the event of interest is low. When the probability of events is not small, or when cluster sizes are large, however, there are scenarios where practically important reductions in sample size result from stratification.

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“…The relative efficiency of unequal vs equal cluster sizes when testing the treatment effect in two‐arm CRTs was investigated continuous, binary and count outcomes. It is noteworthy that the aforementioned works on count outcomes 8,12,14 all employed the Poisson model, which by definition imposes the restriction that the mean and variance of the count outcome are equal 15 . In practice, however, the phenomenon of a count variable having a variance larger than its mean (referred to as overdispersion) has been widely reported in biomedical research 16,17 .…”

Section: Introductionmentioning

confidence: 99%

“…Finally, most of existing methods 8,12,14 assume patients to contribute an equal length of follow‐up, during which the counts of certain events are measured. In pragmatic CRT trials, patients may experience early treatment discontinuation or early dropouts, hence lead to varying lengths of follow‐up to measure the count outcome.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

2020

Statistics in Medicine

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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.

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Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

Cited by 18 publications

References 36 publications

SIRT3 promotes auditory function in young adult FVB/nJ mice but is dispensable for hearing recovery after noise exposure

SIRT3 promotes auditory function in young adult FVB/nJ mice but is dispensable for hearing recovery after noise exposure

Sample size estimation for stratified individual and cluster randomized trials with binary outcomes

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

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