Closed-form REML estimators and sample size determination for mixed effects models for repeated measures under monotone missingness

Tang, Yongqiang

doi:10.1002/sim.7270

Cited by 6 publications

(31 citation statements)

References 33 publications

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“…The maximum likelihood (ML) estimator and restricted maximum likelihood (REML) estimator of

false({\underset{true_}{θ}}_{j}, σ_{j}^{2} false)

's are given, respectively, by (Tang, )

{\underset{true_}{\hat{θ}}}_{j, ML} = {\underset{true_}{\hat{θ}}}_{j}, {\hat{σ}}_{j, ML}^{2} = \frac{{\overset{S}{true}}_{j}}{n_{j}} and {\underset{true_}{\hat{θ}}}_{j, REML} = {\underset{true_}{\hat{θ}}}_{j}, {\hat{σ}}_{j, REML}^{2} = \frac{{\overset{S}{true}}_{j}}{n_{j} - q} .

…”

Section: Review Of Mmrm and Pmmsmentioning

confidence: 99%

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On the Multiple Imputation Variance Estimator for Control-Based and Delta-Adjusted Pattern Mixture Models

Tang

2017

Biometrics

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Control-based pattern mixture models (PMM) and delta-adjusted PMMs are commonly used as sensitivity analyses in clinical trials with non-ignorable dropout. These PMMs assume that the statistical behavior of outcomes varies by pattern in the experimental arm in the imputation procedure, but the imputed data are typically analyzed by a standard method such as the primary analysis model. In the multiple imputation (MI) inference, Rubin's variance estimator is generally biased when the imputation and analysis models are uncongenial. One objective of the article is to quantify the bias of Rubin's variance estimator in the control-based and delta-adjusted PMMs for longitudinal continuous outcomes. These PMMs assume the same observed data distribution as the mixed effects model for repeated measures (MMRM). We derive analytic expressions for the MI treatment effect estimator and the associated Rubin's variance in these PMMs and MMRM as functions of the maximum likelihood estimator from the MMRM analysis and the observed proportion of subjects in each dropout pattern when the number of imputations is infinite. The asymptotic bias is generally small or negligible in the delta-adjusted PMM, but can be sizable in the control-based PMM. This indicates that the inference based on Rubin's rule is approximately valid in the delta-adjusted PMM. A simple variance estimator is proposed to ensure asymptotically valid MI inferences in these PMMs, and compared with the bootstrap variance. The proposed method is illustrated by the analysis of an antidepressant trial, and its performance is further evaluated via a simulation study.

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“…The maximum likelihood (ML) estimator and restricted maximum likelihood (REML) estimator of

false({\underset{true_}{θ}}_{j}, σ_{j}^{2} false)

's are given, respectively, by (Tang, )

{\underset{true_}{\hat{θ}}}_{j, ML} = {\underset{true_}{\hat{θ}}}_{j}, {\hat{σ}}_{j, ML}^{2} = \frac{{\overset{S}{true}}_{j}}{n_{j}} and {\underset{true_}{\hat{θ}}}_{j, REML} = {\underset{true_}{\hat{θ}}}_{j}, {\hat{σ}}_{j, REML}^{2} = \frac{{\overset{S}{true}}_{j}}{n_{j} - q} .

…”

Section: Review Of Mmrm and Pmmsmentioning

confidence: 99%

“…Since

{\hat{σ}}_{j}^{2}

is unbiased for

σ_{j}^{2}

, but the REML estimator of

σ_{j}^{2}

is biased toward 0, the variance evaluated at

false({\underset{true_}{\hat{θ}}}_{j}, {\hat{σ}}_{j}^{2} false)

's tends to be slightly more conservative than the commonly used Kenward and Roger () variance, but they are asymptotically equivalent (Tang, ).…”

Section: Review Of Mmrm and Pmmsmentioning

confidence: 99%

On the Multiple Imputation Variance Estimator for Control-Based and Delta-Adjusted Pattern Mixture Models

Tang

2017

Biometrics

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“…We assume

\overset{Υ}{true} \sim F false(q, n - q - 1 false)

. The assumption holds exactly, and Equation yields the exact power if x g i is normally distributed . For nonnormal covariates, the power estimation based on the approximation

\overset{Υ}{true} \sim F false(q, n - q - 1 false)

generally leads to very accurate power estimate in randomized trials (ie, no systematic difference in the distribution of x g i between 2 groups), and this will be demonstrated in Section 4.…”

Section: A Generalized Sample Size Procedures For T Tests In Superiorimentioning

confidence: 98%

“…We will compare formulae and with the two‐step (TS) procedure described in Tang . Let

f false(\overset{n}{true} false)

be the d.f.…”

Section: A Generalized Sample Size Procedures For T Tests In Superiorimentioning

confidence: 99%

“…Sample size calculation for the t tests is usually based on the normal approximation and/or the asymptotic variance of the treatment effect. () These methods work well in large clinical trials but generally underestimate the size in small trials because the normal distribution cannot adequately approximate the t distribution, and the asymptotic variance underestimates the true variance of the estimated effect in ANCOVA and MMRM …”

Section: Introductionmentioning

confidence: 99%

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A noniterative sample size procedure for tests based on t distributions

Tang

2018

Statistics in Medicine

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A noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending Guenther's approach for the one sample and two sample t tests. The generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance (ANCOVA) and the mixed effects model for repeated measures in randomized clinical trials. The sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms, which are functions of the covariates in the model. But it does not require specifying the covariate distribution. The noniterative procedure is suitable for superiority tests, noninferiority tests, and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer. The method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials. We also derive accurate power formulae for ANCOVA and mixed effects model for repeated measures, and the formula for ANCOVA is exact for normally distributed covariates. Numerical examples demonstrate the accuracy of the proposed methods particularly in small samples.

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

Zhou

Zhang

2022

Statistics in Medicine

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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.

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Closed-form REML estimators and sample size determination for mixed effects models for repeated measures under monotone missingness

Cited by 6 publications

References 33 publications

On the Multiple Imputation Variance Estimator for Control-Based and Delta-Adjusted Pattern Mixture Models

On the Multiple Imputation Variance Estimator for Control-Based and Delta-Adjusted Pattern Mixture Models

A noniterative sample size procedure for tests based on t distributions

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

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