Fundamental statistical methods for prognosis research

Abstract

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.

The use of electronic healthcare records for colorectal cancer screening referral decisions and risk prediction model development

“…I.e. 85% out of all possible pairs of participants, the individual with higher predicted CRC free survival had a longer CRC free survival than the other participant in the selected pair (and vice versa for event probability) [30]. Van Houwelingen's heuristic shrinkage was 0.998.…”

“…reach the study end before the outcome occurs, move GP practices, death etc). Patients who are rightcensored in this way provide valuable information up to their final point of follow up [30]. Employing survival models is a more efficient use of the data by maximising events at the tail end.…”

“…Employing survival models is a more efficient use of the data by maximising events at the tail end. Furthermore, the predictions for these models are over a period of two years and it is argued that predictions for time periods over 6 months should consider time-to-event regression modelling [30]. Similar studies using electronic health records for model development and validation in a primary care setting have also used survival analysis aiding comparability of the model in a screening context [15,16].…”

Diabetic retinopathy progression in patients under monitoring for treatment or vision loss: external validation and update of a multivariable prediction model

“…21 To update the model with additional predictors, flexible parametric models (Royston-Parmar models) will be fitted using a multivariable fractional polynomial approach to consider non-linear functions for continuous variables while using backward elimination for the additional predictors considered. 28 We will use a p>0.157 as a proxy for selection based on Akaike information criterion. 29 All predictors from the original model will be forced to remain in the model regardless of statistical significance, therefore, only the four additional variables Patient notes *Among the predictors, ocular features (DR stage in each eye) and visual acuity will be recorded for both eyes at every visit along with the date of measurement.…”

Risk prediction models for discrete ordinal outcomes: Calibration and the impact of the proportional odds assumption

“…For dichotomous outcomes, there is a large body of methodological literature and guidance on how prediction models should be constructed and how their performance should be evaluated in terms of discrimination and calibration. 11 , 12 , 13 , 14 , 15 , 16 , 17 Methods to assess discrimination and calibration have been extended to models for nominal outcomes. 18 , 19 , 20 For ordinal outcomes, discrimination measures have been proposed but calibration has been barely addressed.…”