title: A sup-score test for the cure fraction in mixture models for long-term survivors.
abstract: The evaluation of cure fractions in oncology research under the well known cure rate model has attracted considerable attention in the literature, but most of the existing testing procedures have relied on restrictive assumptions. A common assumption has been to restrict the cure fraction to a constant under alternatives to homogeneity, thereby neglecting any information from covariates. This article extends the literature by developing a score-based statistic that incorporates covariate information to detect cure fractions, with the existing testing procedure serving as a special case. A complication of this extension, however, is that the implied hypotheses are not typical and standard regularity conditions to conduct the test may not even hold. Using empirical processes arguments, we construct a sup-score test statistic for cure fractions and establish its limiting null distribution as a functional of mixtures of chi-square processes. In practice, we suggest a simple resampling procedure to approximate this limiting distribution. Our simulation results show that the proposed test can greatly improve efficiency over tests that neglect the heterogeneity of the cure fraction under the alternative. The practical utility of the methodology is illustrated using ovarian cancer survival data with long-term follow-up from the surveillance, epidemiology, and end results registry.
authors.affiliation: Department of Statistics, Kansas State University 101 Dickens Hall, Manhattan, Kansas 66506, U.S.A.
authors.forename: Wei-Wen
authors.initials: WW
authors.lastname: Hsu
authors.affiliation: Department of Epidemiology and Biostatistics, Michigan State University B601 West Fee Hall, East Lansing, Michigan 48824, U.S.A.
authors.forename: David
authors.initials: D
authors.lastname: Todem
authors.affiliation: Departments of Biostatistics & Medical Informatics and Statistics, University of Wisconsin-Madison, 600 Highland Ave., Madison, Wisconsin 53792, U.S.A.
authors.forename: KyungMann
authors.initials: K
authors.lastname: Kim
mesh_terms: D003198:Computer Simulation; D005260:Female; D005500:Follow-Up Studies; D006801:Humans; D015233:Models, Statistical; D010051:Ovarian Neoplasms / Q000401:mortality; D012042:Registries; D012074:Remission Induction; D017741:Survivors / Q000706:statistics & numerical data*
keywords: Cure rate model; Goodness-of-fit; Likelihood ratio; Ovarian cancer; SEER registry; Score functions; Sensitivity analysis; Unidentified parameters