Published

2018-07-01

Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences

Construcción de la matriz de diseño en modelos lineales de efectos mixtos generalizados en un contexto de ensayos clínicos de secuencias de tratamientos

DOI:

https://doi.org/10.15446/rce.v41n2.63332

Keywords:

Augmented regression, robust fixed-effects estimators, generalized least squares, maximum likelihood, quasi-likelihood, random effects linear models (en)
Cuasi-verosimilitud, diseño cruzado, efectos de arrastre, estimabilidad, estimadores robustos de efectos fijos, identificabilidad, inversas generalizadas, matriz de diseño, máxima verosimilitud, mínimos cuadrados generalizados, modelos lineales de efectos (es)

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The problem of constructing a design matrix of full rank for generalized linear mixed-effects models (GLMMs) has not been addressed in statistical literature in the context of clinical trials of treatment sequences. Solving this problem is important because the most popular estimation methods for GLMMs assume a design matrix of full rank, and GLMMs are useful tools in statistical practice. We propose new developments in GLMMs that address this problem. We present a new model for the design and analysis of clinical trials of treatment sequences, which utilizes some special sequences called skip sequences. We present a theorem showing that estimators computed through quasi-likelihood, maximum likelihood or generalized least squares, or through robust approaches, exist only if appropriate skip sequences are used. We prove theorems that establish methods for implementing skip sequences in practice. In particular, one of these theorems computes the necessary skip sequences explicitly. Our new approach allows building design matrices of full rank and facilitates the implementation of regression models in the experimental design and data analysis of clinical trials of treatment sequences. We also explain why the standard approach to constructing dummy variables is inappropriate in studies of treatment sequences. The methods are illustrated with a data analysis of the STAR*D study of sequences of treatments for depression.

La estimación de los efectos de arrastre es un problema difícil en el diseño y análisis de ensayos clínicos de secuencias de tratamientos, incluyendo ensayos cruzados. Excepto por diseños simples, estos efectos son usualmente no identificables y, por lo tanto, no estimables. La imposición de restricciones a los parámetros es a menudo no justificada y produce diferentes estimativos de los efectos de arrastre dependiendo de la restricción impuesta. Las inversas generalizadas o el balance de tratamientos a menudo permiten estimar los

efectos principales de tratamiento, pero no resuelven el problema de estimar la contribución de los efectos de arrastre de una secuencia de tratamiento. Además, los períodos de lavado no siempre son factibles o éticos. Los diseños con parámetros no identificables comúnmente tienen matrices de diseño que no son de rango completo. Por lo tanto, proponemos métodos para la construcción de matrices de rango completo, sin imponer restricciones artificiales en los efectos de arrastre. Nuestros métodos son aplicables en un contexto

de modelos lineales mixtos generalizados. Presentamos un nuevo modelo para el diseño y análisis de ensayos clínicos de secuencias de tratamientos, llamado Sistema Anticrónico, e introducimos secuencias de tratamiento especiales llamadas Secuencias de Salto. Demostramos que los efectos de arrastre son identificables sólo si se usan Secuencias de Salto apropiadas. Explicamos cómo implementar en la práctica estas secuencias, y presentamos un método para calcular las secuencias apropiadas. Presentamos aplicaciones al diseño de un estudio cruzado con 3 tratamientos y 3 períodos, y al análisis del estudio STAR*D de secuencias de tratamientos para la depresión.

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How to Cite

APA

Diaz, F. J. (2018). Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences. Revista Colombiana de Estadística, 41(2), 191–233. https://doi.org/10.15446/rce.v41n2.63332

ACM

[1]
Diaz, F.J. 2018. Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences. Revista Colombiana de Estadística. 41, 2 (Jul. 2018), 191–233. DOI:https://doi.org/10.15446/rce.v41n2.63332.

ACS

(1)
Diaz, F. J. Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences. Rev. colomb. estad. 2018, 41, 191-233.

ABNT

DIAZ, F. J. Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences. Revista Colombiana de Estadística, [S. l.], v. 41, n. 2, p. 191–233, 2018. DOI: 10.15446/rce.v41n2.63332. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/63332. Acesso em: 18 may. 2022.

Chicago

Diaz, Francisco J. 2018. “Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences”. Revista Colombiana De Estadística 41 (2):191-233. https://doi.org/10.15446/rce.v41n2.63332.

Harvard

Diaz, F. J. (2018) “Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences”, Revista Colombiana de Estadística, 41(2), pp. 191–233. doi: 10.15446/rce.v41n2.63332.

IEEE

[1]
F. J. Diaz, “Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences”, Rev. colomb. estad., vol. 41, no. 2, pp. 191–233, Jul. 2018.

MLA

Diaz, F. J. “Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences”. Revista Colombiana de Estadística, vol. 41, no. 2, July 2018, pp. 191-33, doi:10.15446/rce.v41n2.63332.

Turabian

Diaz, Francisco J. “Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences”. Revista Colombiana de Estadística 41, no. 2 (July 1, 2018): 191–233. Accessed May 18, 2022. https://revistas.unal.edu.co/index.php/estad/article/view/63332.

Vancouver

1.
Diaz FJ. Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences. Rev. colomb. estad. [Internet]. 2018Jul.1 [cited 2022May18];41(2):191-233. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/63332

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CrossRef citations3

1. Francisco J. Diaz. (2021). Using population crossover trials to improve the decision process regarding treatment individualization in N‐of‐1 trials. Statistics in Medicine, 40(20), p.4345. https://doi.org/10.1002/sim.9030.

2. Zhiwen Wang, Francisco J. Diaz. (2020). A graphical approach to assess the goodness-of-fit of random-effects linear models when the goal is to measure individual benefits of medical treatments in severely ill patients. BMC Medical Research Methodology, 20(1) https://doi.org/10.1186/s12874-020-01054-3.

3. Xuan Zhang, Jose de Leon, Benedicto Crespo-Facorro, Francisco J. Diaz. (2020). Measuring individual benefits of psychiatric treatment using longitudinal binary outcomes: Application to antipsychotic benefits in non-cannabis and cannabis users. Journal of Biopharmaceutical Statistics, 30(5), p.916. https://doi.org/10.1080/10543406.2020.1765371.


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