52 Application of gee procedures for sample size calculations in repeated measures experiments

This paper examined the robustness of the generalized linear mixed model (GLMM). The GLMM estimates fixed and random effects, and it is especially useful when the dependent variable is binary. It is also useful when the dependent variable involves repeated measures, since it can model correlation. The present study used Monte Carlo simulation to analyze the empirical Type I error rates of GLMMs in split-plot designs. The variables manipulated were sample size, group size, number of repeated measures, and correlation between repeated measures. Extreme conditions were also considered, including small samples, unbalanced groups, and different correlation in each group (pairing between group size and correlation between repeated measures). For balanced groups, the results showed that the group effect was robust under all conditions, while for unbalanced groups the effect tended to be conservative with positive pairing and liberal with negative pairing. Regarding time and interaction effects, the results showed, for both balanced and unbalanced groups, that: (a) The test was robust with low correlation (.2), but conservative for medium values of correlation (.4 and .6), and (b) the test tended to be conservative for positive and negative pairing, especially the latter.
 Este artículo examina la robustez del modelo lineal mixto generalizado (GLMM, por sus siglas en inglés). El GLMM estima efectos fijos y efectos aleatorios y es especialmente útil cuando la variable dependiente es binaria. También es útil cuando la variable dependiente es de medidas repetidas, ya que puede modelar la correlación. El presente estudio utilizó la simulación de Monte Carlo a fin de analizar las tasas de error de Tipo I empíricas de los GLMM en diseños split-plot. Las variables manipuladas fueron el tamaño de muestra, el tamaño de grupo, el número de medidas repetidas y la correlación entre las medidas repetidas. También se consideraron condiciones extremas, tales como muestras pequeñas, grupos no balanceados y diferente correlación en cada grupo (emparejamiento entre tamaño de grupo y correlación entre medidas repetidas). Para grupos balanceados, los resultados mostraron que el efecto grupo era robusto en todas las condiciones, mientras que para grupos no balanceados el efecto tendía a ser conservador con emparejamiento positivo y liberal con emparejamiento negativo. Con respecto a los efectos tiempo e interacción, los resultados mostraron, tanto para grupos balanceados como para no balanceados, que: (a) la prueba fue robusta con baja correlación (.2), ​​pero conservadora para valores medios de correlación (.4 y .6), y (b) la prueba tendía a ser conservadora para emparejamiento positivo y negativo, especialmente en este último.

/pdf/robustness-of-generalized-linear-mixed-models-for-split-plot-1x8ty8lo.pdf

Robustness of Generalized Linear Mixed Models for Split-Plot Designs with Binary Data

Zero-inflated count outcomes arise quite often in research and practice. Parametric models such as the zero-inflated Poisson and zero-inflated negative binomial are widely used to model such responses. However, interpretations of those models focus on the at-risk subpopulation of a two-component population mixture and fail to provide direct inference about marginal effects for the overall population. Recently, new approaches have been proposed to facilitate such marginal inferences for count responses with excess zeros. However, they are likelihood based and impose strong assumptions on data distributions. In this paper, we propose a new distribution-free, or semiparametric, alternative to provide robust inference for marginal effects when population mixtures are defined by zero-inflated count outcomes. The proposed method also applies to longitudinal studies with missing data following the general missing at random mechanism. The proposed approach is illustrated with both simulated and real study data.

A semiparametric marginalized zero-inflated model for analyzing healthcare utilization panel data with missingness.

Statistical hypotheses are translations of scientiﬁc hypotheses into statements about one or more distributions, often concerning their center. Tests that assess statistical hypotheses of center implicitly assume a speciﬁc center, e.g., the mean or median. Yet, scientiﬁc hypotheses do not always specify a particular center. This ambiguity leaves the possibility for a gap between scientiﬁc theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientiﬁc disciplines, “signiﬁcant results” of this kind are concerning. Rather than testing a single center, this paper proposes testing a family of plausible centers, such as that induced by the Huber loss function (the “Huber family”). Each center in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a pathwise optimization routine to ﬁt the Huber family. The favorable properties of the new test are veriﬁed through numerical simulation in one- and two-sample settings. Two experiments from psychology serve as real-world case studies.

Familial Inference

Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, significant results of this kind are concerning. Rather than testing a single centre, this paper proposes testing a family of plausible centres, such as that induced by the Huber loss function (the Huber family). Each centre in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a novel pathwise optimization routine to fit the Huber family. The favourable properties of the new test are demonstrated theoretically and experimentally. Two examples from psychology serve as real-world case studies.

Familial inference: Tests for hypotheses on a family of centres

Power analysis for cluster randomized control trials is difficult to perform when a binary response is modeled using the generalized linear mixed-effects model (GLMM). Although methods for clustered binary responses exist such as the generalized estimating equations, they do not apply to the context of GLMM. Also, because popular statistical packages such as R and SAS do not provide correct estimates of parameters for the GLMM for binary responses, Monte Carlo simulation, a popular ad-hoc method for estimating power when the power function is too complex to evaluate analytically or numerically, fails to provide correct power estimates within the current context as well. In this paper, a new approach is developed to estimate power for cluster randomized control trials when a binary response is modeled by the GLMM. The approach is easy to implement and seems to work quite well, as assessed by simulation studies. The approach is illustrated with a real intervention study to reduce suicide reattempt rates amo...

Power analysis for cluster randomized trials with binary outcomes modeled by generalized linear mixed-effects models

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Power analysis for cluster randomized trials with binary outcomes modeled by generalized linear mixed-effects models