Fundamental statistical methods for prognosis research

This chapter introduces and describes the fundamental statistical measures, methods, and principles that form the bedrock of prognosis research. A major emphasis is given to linear regression for continuous outcomes, logistic regression for binary outcomes, and Cox regression and parametric survival models for time-to-event outcomes. It is shown how these models can be used to identify prognostic factors; obtain measures of prognostic value of such factors such as mean differences, odds ratios, and hazard ratios; and produce a model for predicting outcomes (and outcome risk) in new individuals. Details are provided on how the predictive performance of a prognostic model should be evaluated using a specific set of statistical techniques, including measuring and displaying overall fit, calibration, and discrimination. The importance of investigating non-linear prognostic associations (using methods such as fractional polynomials and cubic splines) are also covered. The chapter is designed to ensure that novice and experienced prognosis researchers have a firm grasp of the statistical principles underlying the four types of prognosis research discussed throughout the book.