Simultaneous inference for multilevel linear mixed models - with an application to a large-scale school meal study

TY - JOUR

T1 - Simultaneous inference for multilevel linear mixed models - with an application to a large-scale school meal study

AU - Ritz, Christian

AU - Laursen, Rikke Pilmann

AU - Damsgaard, Camilla Trab

N1 - CURIS 2017 NEXS 174

PY - 2017

Y1 - 2017

N2 - In large multilevel studies effects of interest are often evaluated for a number of more or less related outcomes. For instance, the present work was motivated by the multiplicity issues that arose in the analysis of a cluster-randomized, crossover intervention study evaluating the health benefits of a school meal programme. We propose a novel and versatile framework for simultaneous inference on parameters estimated from linear mixed models that were fitted separately for several outcomes from the same study, but did not necessarily contain the same fixed or random effects. By combining asymptotic representations of parameter estimates from separate model fits we could derive the joint asymptotic normal distribution for all parameter estimates of interest for all outcomes considered. This result enabled the construction of simultaneous confidence intervals and calculation of adjusted p-values. For sample sizes of practical relevance we studied simultaneous coverage through simulation, which showed that the approach achieved acceptable coverage probabilities even for small sample sizes (10 clusters) and for 2–16 outcomes. The approach also compared favourably with a joint modelling approach. We also analysed data with 17 outcomes from the motivating study, resulting in adjusted p-values that were appreciably less conservative than Bonferroni adjustment.

AB - In large multilevel studies effects of interest are often evaluated for a number of more or less related outcomes. For instance, the present work was motivated by the multiplicity issues that arose in the analysis of a cluster-randomized, crossover intervention study evaluating the health benefits of a school meal programme. We propose a novel and versatile framework for simultaneous inference on parameters estimated from linear mixed models that were fitted separately for several outcomes from the same study, but did not necessarily contain the same fixed or random effects. By combining asymptotic representations of parameter estimates from separate model fits we could derive the joint asymptotic normal distribution for all parameter estimates of interest for all outcomes considered. This result enabled the construction of simultaneous confidence intervals and calculation of adjusted p-values. For sample sizes of practical relevance we studied simultaneous coverage through simulation, which showed that the approach achieved acceptable coverage probabilities even for small sample sizes (10 clusters) and for 2–16 outcomes. The approach also compared favourably with a joint modelling approach. We also analysed data with 17 outcomes from the motivating study, resulting in adjusted p-values that were appreciably less conservative than Bonferroni adjustment.

KW - Asymptotic normality

KW - Decorrelation

KW - Familywise error rate

KW - Generalized least squares

U2 - 10.1111/rssc.12161

DO - 10.1111/rssc.12161

M3 - Journal article

AN - SCOPUS:84976550552

SN - 0035-9254

VL - 66

SP - 295

EP - 311

JO - Journal of the Royal Statistical Society, Series C (Applied Statistics)

JF - Journal of the Royal Statistical Society, Series C (Applied Statistics)

IS - 2

ER -