1. Epi-on-the-Island Time Series Regression (TSR) 6-10 July 2015 Tuesday 24: Multiple TSRs: (2-stage and all-in-one) Part 3: - summary Ben Armstrong London School of Hygiene and Tropical Medicine

2. Summary so far: multiple TSRs Epi TSR tradition almost always handles multiple site TSR data by a two-stage approach: –Site-specific TSR for each site –Meta-analyse coefficients of interest from sites All-in-one approaches also possible, though crude ones make strong assumptions of similarity between sites More sophisticated all-in-one models are possible, especially for Gaussian models …

3. 2 stage or all-in-one? 2-stage +s Most familiar in epi so far Get so see site-specific association estimates Makes least assumptions as to similarity of covariate-outcome associations across sites Most suitable if site-specific series are each quite informative (long)? All-in-one +s More power/precision Simpler, if covariate-outcome associations are similar across sites Extends to models drawing information from between-site exposure-outcome association (multi-level random intercept models) Most suitable if site-specific series are individually quite short?

4. All-in-one with fixed or random site effects? All-in-one with fixed site effects (or 2-stage) + Risk factors varying only between sites cannot confound - Lose power/precision Unusual, if random slopes wanted All-in-one with random site effects + More power/precision Fits naturally into mixed model/MLM framework and software - Can be subject to confounding by risk factors varying between sites if not controlled