Alternative subgroup joint analysis proposal of nonlinear longitudinal and time-to-event data for modeling pregnancy miscarriage

Pregnancies achieved through in-vitro fertilization (IVF) are associated with adverse firsttrimester outcomes in comparison to spontaneously achieved pregnancies. Human chorionicgonadotrophin β subunit (β-HCG) is a well-known and accurate biomarker for the diagnosis and monitoring of pregnancy after IVF. Low levels of β-HCG during the first trimesterof pregnancy are related to miscarriage, ectopic pregnancy and failure of IVF procedure.Longitudinal profiles of β-HCG can be utilized to distinguish between normal and abnormalpregnancies, and to assist and guide the clinician in better management and monitoring ofpost-IVF pregnancies. Therefore, being able to assess the association between longitudinallymeasured β-HCG and time to early miscarriage is of crucial interest to clinicians. A commonjoint modeling approach proposal to achieve this objective is to use subject-specific randomeffects in a mixed effects model for longitudinal β-HCG data as predictors in a model for thetime-to-event (TTE) data. This work was motivated by an observational study with normaland abnormal pregnancies where serum concentrations of β-HCG were measured in 173young women during a gestational age of 9-86 days at a private clinic in Santiago, Chile.Some women experienced a miscarriage event but the rest did not. For those women whoexperienced miscarriage, their exact event times were unknown, in such case we have interval censored data, assuming that the event occurred between the last time of the observedβ-HCG measurement and ten days after. For our dataset we consider a nonlinear mixedeffects (NLME) model for both normal and abnormal pregnancies, but the joint model isconsidered only for the subgroup of miscarriage women. All the estimation procedures arebased on the Stochastic Approximation of the EM (SAEM) algorithm implemented in theMonolix software