title: Joint modeling of time to recurrence and cancer stage at recurrence in oncology trials.
abstract: This research was motivated by a clinical trial with bladder cancer patients who went through a surgery and were followed up for cancer recurrence. One of the main objectives of the trial was to evaluate the time to cancer recurrence in patients in control and experimental groups. At the time of recurrence, the disease stage was also evaluated. Because the stage of cancer at recurrence significantly impacts future treatment and patient prognosis of survival, analyzing the time to cancer recurrence and the stage at recurrence jointly provides more clinically relevant information than analyzing the time to recurrence alone. In this paper, we propose a stochastic model for the joint distribution of time to recurrence and cancer stage that (1) accounts for the recurrence caused by cancer cells surviving a treatment or a surgery and for the recurrence caused by spontaneous carcinogenesis, and (2) incorporates parameters that have biological meaning. To estimate the parameters, we use the maximum-likelihood method combined with the EM algorithm. To demonstrate the performance of our modeling, we evaluate the data from a clinical trial in patients with bladder cancer. We also use simulations to assess the sensitivity of the method.
authors.affiliation: a Advisory Analytics, QuintilesIMS , Durham , North Carolina , USA.
authors.forename: Olga
authors.initials: O
authors.lastname: Marchenko
authors.affiliation: b Department of Biostatistics , University of Michigan , Ann Arbor , Michigan , USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Tsodikov
authors.affiliation: c Department of Statistics , University of Michigan , Ann Arbor , Michigan , USA.
authors.forename: Robert
authors.initials: R
authors.lastname: Keener
authors.affiliation: d Department of Computer Science and Statistics , University of Rhode Island , Kingston , Rhode Island , USA.
authors.forename: Natallia
authors.initials: N
authors.lastname: Katenka
authors.affiliation: e Medical Affairs, Photocure ASA , Oslo , Norway.
authors.forename: Yngvil
authors.initials: Y
authors.lastname: Kloster Thomas
mesh_terms: D000465:Algorithms; D002986:Clinical Trials as Topic; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009364:Neoplasm Recurrence, Local; D009367:Neoplasm Staging
keywords: Cancer stage; EM algorithm; joint modeling; multinomial logit model; survival analysis; time to cancer recurrence