title: Risk-adjusted monitoring of time to event in the presence of long-term survivors.
abstract: The use of control charts for monitoring schemes in medical context should consider adjustments to incorporate the specific risk for each individual. Some authors propose the use of a risk-adjusted survival time cumulative sum (RAST CUSUM) control chart to monitor a time-to-event outcome, possibly right censored, using conventional survival models, which do not contemplate the possibility of cure of a patient. We propose to extend this approach considering a risk-adjusted CUSUM chart, based on a cure rate model. We consider a regression model in which the covariates affect the cure fraction. The CUSUM scores are obtained for Weibull and log-logistic promotion time model to monitor a scale parameter for nonimmune individuals. A simulation study was conducted to evaluate and compare the performance of the proposed chart (RACUF CUSUM) with RAST CUSUM, based on optimal control limits and average run length in different situations. As a result, we note that the RAST CUSUM chart is inappropriate when applied to data with a cure rate, while the proposed RACUF CUSUM chart seems to have similar performance if applied to data without a cure rate. The proposed chart is illustrated with simulated data and with a real data set of patients with heart failure treated at the Heart Institute (InCor), at the University of São Paulo, Brazil.
authors.affiliation: Instituto de Matemática e Estatística, USP, 05508-090, São Paulo, Brazil. jwesley@ime.usp.br.
authors.forename: Jocelânio W
authors.initials: JW
authors.lastname: Oliveira
authors.affiliation: Departamento de Estatística, CCET, UFRN, 59078-970, Natal, Brazil.
authors.forename: Dione M
authors.initials: DM
authors.lastname: Valença
authors.affiliation: Departamento de Estatística, CCET, UFRN, 59078-970, Natal, Brazil.
authors.forename: Pledson G
authors.initials: PG
authors.lastname: Medeiros
authors.affiliation: Instituto do Coração, FMUSP, 05403-900, São Paulo, Brazil.
authors.forename: Magaly
authors.initials: M
authors.lastname: Marçula
mesh_terms: D001938:Brazil; D003198:Computer Simulation; D006333:Heart Failure / Q000401:mortality / Q000628:therapy; D006801:Humans; D016015:Logistic Models; D015233:Models, Statistical; D020379:Risk Adjustment; D017741:Survivors / Q000706:statistics & numerical data*; D013997:Time Factors
keywords: Cure rate; Risk-adjusted CUSUM; Statistical process control; Survival analysis