Analysis of gap times based on panel count data with informative observation times and unknown start time

In biomedical studies, one is often interested in repeat events with longitudinal observations occurring only intermittently, resulting in panel count data. The first stage of labor, measured through unit-increments of cervical dilation in pregnant women, provides such an example. Obstetricians are interested in assessing the gap time distribution of per-unit increments of cervical dilation for better management of labor process. Typically, only intermittent medical examinations for cervical dilation occur after (already dilated) women get admitted to hospital. The observation frequency is very likely correlated to how fast/slow she dilates. Thus one could view such data as panel count data with informative observation times and unknown start time. Here, we propose semiparametric proportional rate models for the event process and the observation process, with a multiplicative subject-specific frailty variable capturing the correlation between the two processes. Inference procedures for the gap times between consecutive events are proposed when the start times are known as well when unknown, using likelihood based approach and estimating equations. The methodology is assessed through simulation study and through large sample property. A detailed analysis using the proposed methods is applied to data from two studies: the Collaborative Perinatal Project and the Consortium on Safe Labor.

生物医学研究中，研究者常关注仅间歇开展纵向观测的重复事件，此类数据即为面板计数数据（panel count data）。以孕妇宫颈扩张的单位增量作为观测指标的第一产程，便是这类数据的典型实例。产科医生亟需评估宫颈扩张每单位增量的间隔时间分布，以优化产程管理。通常而言，宫颈已出现扩张的孕妇入院待产之后，仅会接受间歇式的宫颈扩张医学检查，且检查频率往往与孕妇宫颈扩张的快慢存在关联。因此，此类数据可被视为带有信息观测时间与未知起始时间的面板计数数据。本文针对事件过程与观测过程构建半参数比例速率模型（semiparametric proportional rate models），并引入受试者特异性乘性脆弱变量（frailty variable）以刻画两类过程间的相关性。本文基于似然方法与估计方程，分别针对起始时间已知与未知两种场景，提出了连续事件间隔时间的推断流程。本文通过模拟实验与大样本性质分析对所提方法进行了验证。最后，我们将所提方法应用于两项研究的真实数据：围产期合作研究（Collaborative Perinatal Project）与安全分娩联盟研究（Consortium on Safe Labor），并展开了详细的数据分析。