title: Penalised logistic regression and dynamic prediction for discrete-time recurrent event data.
abstract: We consider methods for the analysis of discrete-time recurrent event data, when interest is mainly in prediction. The Aalen additive model provides an extremely simple and effective method for the determination of covariate effects for this type of data, especially in the presence of time-varying effects and time varying covariates, including dynamic summaries of prior event history. The method is weakened for predictive purposes by the presence of negative estimates. The obvious alternative of a standard logistic regression analysis at each time point can have problems of stability when event frequency is low and maximum likelihood estimation is used. The Firth penalised likelihood approach is stable but in removing bias in regression coefficients it introduces bias into predicted event probabilities. We propose an alterative modified penalised likelihood, intermediate between Firth and no penalty, as a pragmatic compromise between stability and bias. Illustration on two data sets is provided.
authors.affiliation: Department of Statistics, Tripoli University, Tripoli, Libya. eelgmati@hotmail.com.
authors.forename: Entisar
authors.initials: E
authors.lastname: Elgmati
authors.affiliation: Department of Statistics, Universidade Federal da Bahia, Salvador, Brazil. fiaccone@ufba.br.
authors.forename: Rosemeire L
authors.initials: RL
authors.lastname: Fiaccone
authors.affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle, UK. robin.henderson@ncl.ac.uk.
authors.forename: R
authors.initials: R
authors.lastname: Henderson
authors.affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle, UK. john.matthews@ncl.ac.uk.
authors.forename: John N S
authors.initials: JN
authors.lastname: Matthews
mesh_terms: D016058:Analgesia, Patient-Controlled / Q000706:statistics & numerical data; D015982:Bias; D056808:Biostatistics; D003968:Diarrhea, Infantile / Q000453:epidemiology; D006801:Humans; D007223:Infant; D016013:Likelihood Functions; D016015:Logistic Models; D011336:Probability; D016019:Survival Analysis
keywords: Additive model; Event history; Logistic regression; Penalised likelihood