We present and compare multiple imputation methods for multilevel continuous and binary data where variables are systematically and sporadically missing.The methods are compared from a theoretical point of view and through an extensive simulation study motivated by a real dataset comprising multiple studies. Simulations are reproducible. The comparisons show why these multiple imputation methods are the most appropriate to handle missing values in a multilevel setting and why their relative performances can vary according to the missing data pattern, the multilevel structure and the type of missing variables.This study shows that valid inferences can only be obtained if the dataset gathers a large number of clusters. In addition, it highlights that heteroscedastic MI methods provide more accurate inferences than homoscedastic methods, which should be reserved for data with few individuals per cluster. Finally, the method of Quartagno and Carpenter (2016a) appears generally accurate for binary variables, the method of Resche-Rigon and White (2016) with large clusters, and the approach of Jolani et al. (2015) with small clusters.

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.

Prognostic models combine multiple prognostic factors to estimate the risk of future outcomes in individuals with a particular disease or health condition. A useful model provides accurate predictions to support decision making by individuals and caregivers. This chapter describes the three phases of prognostic model research development (including internal validation), external validation (including model updating), and impact on decision making and individual health outcomes. Methodology is detailed for each phase, including the need for large representative datasets, methods to avoid or reduce overfitting and optimism, and the use of both discrimination and calibration to assess a model’s predictive performance. TRIPOD reporting guidelines are introduced. Emphasis is also given to the application of models in practice, including linking the model to clinical decisions using risk thresholds, and evaluating this using measures of net benefit, decision curves, cost-effectiveness analyses, and impact studies (such as randomized trials) to evaluate the effectiveness of models in improving outcomes.

Most clinical specialties have a plethora of studies that develop or validate one or more prediction models, for example, to inform diagnosis or prognosis. Having many prediction model studies in a particular clinical field motivates the need for systematic reviews and meta-analyses, to evaluate and summarise the overall evidence available from prediction model studies, in particular about the predictive performance of existing models. Such reviews are fast emerging, and should be reported completely, transparently, and accurately. To help ensure this type of reporting, this article describes a new reporting guideline for systematic reviews and meta-analyses of prediction model research.