Observation plans in longitudinal studies with time-varying treatments

In longitudinal studies individuals are followed over time and their time-varying information on treatment, outcomes, and covariates is collected at certain intervals. Ideally, one would want these intervals as short as possible to consider data collection continuous for all practical purposes. Unfortunately, continuous recording, though sometimes approximately possible for certain outcomes (e.g., death status), is infeasible for most study variables. Rather, the time-varying information is typically collected only during the times when subjects are observed. These times of observation are usually pre-specified in randomized experiments and in certain observational studies in which the subjects' data are recorded at regular intervals. For example, participants in the Multicenter AIDS Cohort Study (MACS) are scheduled to show up at the research center every 6 months,1 and participants in the Nurses' Health Study are asked to return a self-reported questionnaire every two years.2 On the other hand, in many observational studies the observation regime or plan varies across individuals. For example, some observational studies are based on information that is collected for clinical purposes (e.g., databases from health care organizations) and thus the recording of information occurs at irregular and possibly subject-specific intervals. Because the intervals may depend of an individual's clinical history (treatment, symptoms, etc.), we refer to these as dynamic observation plans. Some studies combine the features of dynamic and pre-specified (static) observation plans. For example, the French Hospital Database on HIV (FHDH) collects information whenever an individual comes to an outpatient or inpatient hospital visit for clinical reasons (dynamic observation plan) but also attempts to collect information at least every six months (static observation plan) by reviewing medical records.3 Even studies with a static observation plan like the MACS may have a dynamic component if individuals who do not show up for a scheduled visit do so because of reasons related to their clinical history. In epidemiology, cohort studies with a predominantly static observation plan are often referred to as interval cohorts because they have regular intervals between visits, whereas cohort studies with a dynamic observation plan are often referred to as clinical cohorts because the interval between visits depends on the clinical evolution of the patient. In this paper we discuss the biases that may arise in interval cohorts with static observation plans, and in clinical cohorts when the dynamic observation plans are not explicitly incorporated in the analysis. We also discuss some analytic approaches that, under certain conditions, allow to adjust for the bias caused by dynamic observation plans. We highlight issues that are implicit in previous work by Robins and colleagues on marginal structural models4,5 and missing data.6 This paper is structured as follows. Section 2 describes inverse probability weighting (IPW) techniques to estimate treatment effects in longitudinal studies with a single static plan (e.g., an interval cohort study). To fix ideas, we summarize the methods previously used to estimate the effect of anti-retroviral treatment on mean CD4 cell count in the MACS/Women's Interagency HIV Study (WIHS) cohorts.7,8 We describe the key assumption of coincidence between observation times and times of potential treatment change. Section 3 extends the discussion to studies in which subjects follow one of several static regimes. Section 4 considers studies with dynamic observation plans (e.g., clinical cohorts), describes two potential biases that may arise in these studies, and proposes IPW-based approaches to adjust for them. Section 5 presents an application of IPW to estimate the effect of antiretroviral treatment on the evolution of the mean CD4 cell count in the FHDH, and Section 6 presents some brief conclusions. Throughout the paper we use causal diagrams to describe the causal structure and some of the key assumptions underlying the IPW approach.