Sample size issues in time series regression studies

Abstract

Introduction. Regression analyses of time series of disease counts on environmental determinants, especially air pollution and weather, have been a prominent component of environmental epidemiology in recent decades, with no sign of diminishing. For planning such studies, it would be useful to predict the precision of estimated coefficients and hence power to identify non-null associations given the number of observations (eg days), the total number of disease events or mean events/day, number of series (if multiple) and any other relevant features. Methods. We derived approximate expressions for precision from basic statistical theory. For simplicity, this presentation assumes that the exposure variable is scaled in units of standard deviation of usable exposure variation (that conditional on covariates). Results. We confirmed the adequacy of the approximate expressions for precision by comparison with those realised in full analysis of actual data. In single series studies with Poisson outcome distribution, precision depends only on total number of disease events regardless of how many days those are spread over: standard error = 1/√(total deaths). With large overdispersion number of days can be independently important, with number of days dominating in some realistic situations. In multiple time series studies focusing on the meta-analytic mean coefficient, with no between-series heterogeneity or within-series overdispersion the total number of events (in all series) is again the sole determinant, but with such heterogeneity number of series becomes important. For any of the above scenarios, power can be calculated from the predicted precision. Conclusions. Predicting precision in from a planned time series study is possible given limited assumptions. The total number of disease events is the dominant factor when overdispersion and between-series heterogeneity is low.