Statistics in review; Part 2: Generalised linear models time-to-event and time-series analysis evidence synthesis and clinical trials

Abstract

In Part I, we reviewed graphical display and data summary, followed by a consideration of linear regression models. Generalised linear models, structured in terms of an exponential response distribution and link function, are now introduced, subsuming logistic and Poisson regression. Time-to-event ("survival") analysis is developed from basic principles of hazard rate, and survival, cumulative distribution and density functions. Semi-parametric (Cox) and parametric (accelerated failure time) regression models are contrasted. Time-series analysis is explicated in terms of trend, seasonal, and other cyclical and irregular components, and further illustrated by development of a classical Box-Jenkins ARMA (autoregressive moving average) model for monthly ICU-patient hospital mortality rates recorded over 11 years. Multilevel (random-effects) models and principles of meta-analysis are outlined, and the review concludes with a brief consideration of important statistical aspects of clinical trials: sample size determination, interim analysis and "early stopping".