A joint analysis proposal of nonlinear longitudinal and time-to-event right-, interval-censored data for modeling pregnancy miscarriage

Pregnancy in-vitro fertilization (IVF) cases are associated with adverse first-trimester outcomes in comparison to spontaneously achieved pregnancies. Human chorionic gonadotrophin β subunit ( β -HCG) is a well-known biomarker for the diagnosis and monitoring of pregnancy after IVF. Low levels of β -HCG during this period are related to miscarriage, ectopic pregnancy, and IVF procedure failures. Longitudinal profiles of β -HCG can be used to distinguish between normal and abnormal pregnancies and to assist and guide the clinician in better management and monitoring of post-IVF pregnancies. Therefore, assessing the association between longitudinally measured β -HCG serum concentration and time to early miscarriage is of crucial interest to clinicians. A common joint modeling approach is to use the longitudinal β -HCG trajectory to determine the risk of miscarriage. This work was motivated by a follow-up study with normal and abnormal pregnancies where β -HCG serum concentrations were measured in 173 young women during a gestational age of 9–86 days in Santiago, Chile. Some women experienced a miscarriage event, and their exact event times were unknown, so we have interval-censored data, with the event occurring between the last time of the observed measurement and ten days later. However, for those women belonging to the normal pregnancy group; that is, carrying a pregnancy to a full-term event, right censoring data are observed. Estimation procedures are based on the Stochastic Approximation of the Expectation–Maximization (SAEM) algorithm.