Joint modelling of competing risks and current status data: an application to a spontaneous labour study

The second stage of labour begins when the cervix is fully dilated and pushing begins until the fetus is delivered. A Caesarean delivery (CD) or operative vaginal delivery (OVD) is typically encouraged after the recommended time set by 'expert consensus'. This recommended time has been set out of concern for an increased chance of maternal and neonatal morbidities due to a prolonged second stage of labour, but without thorough consideration of heterogeneous risks for spontaneous vaginal delivery (SVD) and morbidities among women. To provide quantitative evidence for the recommendation, the first step is to compare the risks for SVD, CD or OVD, and the risks of maternal or neonatal morbidities simultaneously across the duration of the second stage of labour. To address such risk comparisons statistically, one needs to study the joint distribution for the time to delivery due to each mode and time to maternal or neonatal morbidity given information provided for each individual. We introduce a joint model which combines the competing risks data for delivery time and current status data for any type of maternal or neonatal morbidity given each woman's baseline characteristics. These two processes are assumed dependent through individual-specific frailty under the joint model. Our numerical studies include a simulation that reflects the structure of observed real data and a detailed real data analysis based on nearly 12000 spontaneous labours. Our finding indicates the necessity to incorporate maternal characteristic such as age or body mass index in assessing the probability for delivery due to SVD, CD or OVD and the onset of morbidities across the second stage of labour.