DEVELOPMENT OF A CLINICAL-PREDICTION MODEL FOR AN ORDINAL OUTCOME - THE WORLD-HEALTH-ORGANIZATION MULTICENTER STUDY OF CLINICAL SIGNS AND ETIOLOGIC AGENTS OF PNEUMONIA, SEPSIS AND MENINGITIS IN YOUNG INFANTS

This paper describes the methodologies used to develop a prediction mo del to assist health workers in developing countries in facing one of the most difficult health problems in all parts of the world: the pres entation of an acutely ill young infant. Statistical approaches for de veloping the clinical prediction model faced at least two major diffic ulties. First, the number of predictor variables, especially clinical signs and symptoms, is very large, necessitating the use of data reduc tion techniques that are blinded to the outcome. Second, there is no u niquely accepted continuous outcome measure or final binary diagnostic criterion. For example, the diagnosis of neonatal sepsis is ill-defin ed. Clinical decision makers must identify infants likely to have posi tive cultures as well as to grade the severity of illness. In the WHO/ ARI Young Infant Multicentre Study we have found an ordinal outcome sc ale made up of a mixture of laboratory and diagnostic markers to have several clinical advantages as well as to increase the power of tests for risk factors. Such a mixed ordinal scale does present statistical challenges because it may violate constant slope assumptions of ordina l regression models. In this paper we develop and validate an ordinal predictive model after choosing a data reduction technique. We show ho w ordinality of the outcome is checked against each predictor. We desc ribe new but simple techniques for graphically examining residuals fro m ordinal logistic models to detect problems with variable transformat ions as well as to detect non-proportional odds and other lack of fit. We examine an alternative type of ordinal logistic model, the continu ation ratio model, to determine if it provides a better fit. We find t hat it does not but that this model is easily modified to allow the re gression coefficients to vary with cut-offs of the response variable. Complex terms in this extended model are penalized to allow only as mu ch complexity as the data will support. We approximate the extended co ntinuation ratio model with a model with fewer terms to allow us to dr aw a nomogram for obtaining various predictions. The model is validate d for calibration and discrimination using the bootstrap. We apply muc h of the modelling strategy described in Harrell, Lee and Mark (Statis t. Med. 15, 361-387 (1998)) for survival analysis, adapting it to ordi nal logistic regression and further emphasizing penalized maximum like lihood estimation and data reduction. (C) 1998 John Wiley & Sons, Ltd.