Statistical Appendix to Modelling Dose-Response in Amblyopia: towards a child specific treatment plan

The Monitored Occlusion Treatment of Amblyopia Study (MOTAS) (Stewart et al. (2004)) was the first clinical study aimed at determining the dose-response relationship of occlusion therapy and exhibited several advantages over previous studies. Most importantly, the effects of refraction were differentiated from those of occlusion and concordance (compliance) with treatment was measured objectively. The study is described in more detail in section 2. The aim of this paper is to study more fully the dose-response relationship of occlusion, and to understand how this relationship is modified by patient characteristics. Previous analyses of these data (Stewart et al. (2004)) have been largely expository and exploratory. For example, in Stewart et al. (2004), the total dose vs. total improvement relationship was computed using semiparametric regression and bootstrap methods over the whole patient cohort. In this paper, we study the dose-response relationship longitudinally and on an interval-by-interval basis, modelling the effect of covariates using linear mixed regression models, in order to gain a quantitative understanding of the therapeutic benefits of occlusion therapy. In the next section, we give more details of the MOTAS study design and outline the strategy behind out analyses in section 2·3. In section 3 we describe a linear mixed model analysis accounting for the repeated measures nature of the data. An interval-by-interval analysis follows; the results are presented in section 4·1. Bayesian modelling and inference can be found in 5. A Bayesian analysis of dosing strategies is shown in section 5·3.