Inference of nested variance components in a longitudinal myopia intervention trial

Abstract

This paper was motivated by a double-blind randomized clinical trial of myopia intervention. In addition to the primary goal of comparing treatment effects, we are concerned with the modelling of correlation that may come from two possible sources, one among the longitudinal observations and the other between measurements taken from both eyes per subject. The data are nested repeated measurements. We suggest three models for analysis. Each one expresses the correlation differently in various covariance structures. We articulate their differences and describe the implementations in estimation using commercial statistical software. The computer output can be further utilized to perform model selection with Schwarz criterion. Simulation studies are conducted to evaluate the performance under each model. Data of the myopia intervention trial are reanalysed with these models for illustration. The results indicate that atropine is more effective in reducing the progression rate, the rates are homogeneous across subjects, and, among the suggested models, the one with independent random effects of two eyes fits best. We conclude that model selection is a crucial step before making inference with estimates; otherwise the correlation may be attributed incorrectly to a different mechanism. The same conclusion applies to other variance components as well.

Efficacy and Adverse Effects of Atropine in Childhood Myopia

“…In addition, 268 Asian and 201 white participants underwent separate analysis in the 1.0% atropine group for ethnic comparison. The study characteristics are listed in the Table . Low-dose atropine was investigated in 2 studies, 27,37 moderatedose atropine in 7 studies, 24,28,29,34,[36][37][38] and high-dose atropine in 13 studies, 17,[23][24][25][26][27][28][29][30][31][32][33]35 together resulting in 22 experimental groups in 19 studies. Ten studies were conducted in Taiwan, 3 in the United States, 3 in Singapore, 2 in Mainland China, and 1 in Hong Kong.…”

“…Of the atropine vs control group comparison, 1 study 39 reported data on low-dose atropine; 5 studies, 24,34,[36][37][38] on moderate-dose atropine; and 11 studies, 17,[23][24][25][26][27][30][31][32][33]35 on high-dose atropine. Seven RCTs 17,[23][24][25][26][27][28] (n = 1349) and 9 cohort studies [31][32][33][34][35][36][37][38][39] (n = 1308) reported data on refraction.…”

Extended Bayesian model averaging for heritability in twin studies

“…It has been demonstrated in Hsiao et al [14] that the correlation may be explained in the wrong direction if the data were fitted with an incorrect model structure. Indeed, the estimates of variance components of errors and random effects can be biased, and therefore one may reach an incorrect conclusion about the existence of random effects.…”

“…In addition, environmental covariates such as sex, age, indicator of education more than 12 years of schooling (Education), sighted distances for reading (Distance), and hours of "close-up work" (watching TV, doing computer work, reading books, writing, sewing, drawing and so on) at childhood (KCHR), at elementary school age (PCHR) and at senior high school age (SCHR), respectively, were recorded in the questionnaire. Because the covariates, sex, anterior chamber depth, axial length and astigmatism were important risk factors associated with myopia [12,14], we forced each model to include these four variables. The EBMA approach begins with all combinations of the other eight variables.…”

“…Another approach to modeling the heterogeneity across subjects and correlation between two eyes is through a correlated eye-specific random effect e i for every individual [14],…”