Pregnancies achieved through in-vitro fertilization (IVF) are associated with adverse first trimester outcomes in comparison to spontaneously achieved pregnancies. Human chorionic gonadotrophin 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 trimester of 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 abnormal pregnancies, and to assist and guide the clinician in better management and monitoring of post-IVF pregnancies. Therefore, being able to assess the association between longitudinally measured β-HCG and time to early miscarriage is of crucial interest to clinicians. A common joint modeling approach proposal to achieve this objective is to use subject-specific random effects in a mixed effects model for longitudinal β-HCG data as predictors in a model for the time-to-event (TTE) data. This work was motivated by an observational study with normal and abnormal pregnancies where serum concentrations of β-HCG were measured in 173 young 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 who experienced 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 observed β-HCG measurement and ten days after. For our dataset we consider a nonlinear mixed effects (NLME) model for both normal and abnormal pregnancies, but the joint model is considered only for the subgroup of miscarriage women. All the estimation procedures are based on the Stochastic Approximation of the EM (SAEM) algorithm implemented in the Monolix software.