A Simulation Study on a Wald Statistic and Cochran's Q Statistic for Stratified Samples

Biometrics ◽  
1977 ◽  
Vol 33 (4) ◽  
pp. 643 ◽  
Author(s):  
Grant W. Somes ◽  
V. P. Bhapkar
Keyword(s):  
Simulation Study ◽  
Wald Statistic ◽  
Q Statistic

Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers

2017 ◽  
Vol 28 (4) ◽  
pp. 1019-1043 ◽  
Author(s):  
Shi-Fang Qiu ◽  
Xiao-Song Zeng ◽  
Man-Lai Tang ◽  
Wai-Yin Poon
Keyword(s):  
Sample Size ◽  
Null Hypothesis ◽  
Test Procedure ◽  
Sample Size Determination ◽  
Double Sampling ◽  
Score Statistic ◽  
Wald Statistic ◽  
Test Procedures ◽  
Practical Applications ◽  
Logit Transformation

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example.

scholarly journals A power approximation for the Kenward and Roger Wald test in the linear mixed model

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254811
Author(s):  
Sarah M. Kreidler ◽  
Brandy M. Ringham ◽  
Keith E. Muller ◽  
Deborah H. Glueck
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Wald Test ◽  
Small Sample ◽  
Power Calculation ◽  
Wald Statistic ◽  
Power Approximation ◽  
Group Randomized Trial ◽  
Approximate Moments ◽  
Image Position

We derive a noncentral F power approximation for the Kenward and Roger test. We use a method of moments approach to form an approximate distribution for the Kenward and Roger scaled Wald statistic, under the alternative. The result depends on the approximate moments of the unscaled Wald statistic. Via Monte Carlo simulation, we demonstrate that the new power approximation is accurate for cluster randomized trials and longitudinal study designs. The method retains accuracy for small sample sizes, even in the presence of missing data. We illustrate the method with a power calculation for an unbalanced group-randomized trial in oral cancer prevention.

A Reminder of the Fallibility of the Wald Statistic

1996 ◽  
Vol 50 (3) ◽  
pp. 226 ◽  
Author(s):  
Thomas R. Fears ◽  
Jacques Benichou ◽  
Mitchell H. Gail
Keyword(s):  
Wald Statistic
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