Targeted Minimum Loss-Based Estimation of a Causal E ect Using Interval-Censored Time-to-Event Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 200

censoring and right-censoring, rendering the applicability of the current work
ubiquitous.
Because in practice the monitoring times and the covariate and outcome
processes may well be dependent on each other, we wish to avoid assuming in-
dependence between the monitoring times and other recorded measures. While
such an assumption is commonly made in classical survival analysis, it would
very often be dicult to justify in many applications. For example, in the
Tshepo study, although bimonthly scheduling was planned, actual monitoring
times varied widely and might have been aected by patients' covariate and
outcome processes. Similarly, unless it arises exclusively due to study termi-
nation, loss to follow-up will generally depend, to some extent, on a portion of
an individual's covariate and outcome processes; the methodology we develop
should therefore reflect this reality.
In this chapter, we first discuss how to frame a prototypical study where
measurements are periodically recorded in order to draw honest and transpar-
ent causal inference, with explicit assumptions that can be scrutinized in the
setting of each application considered. We then define precise causal param-
eters, construct estimators for these, and describe the asymptotic properties
of these estimators, allowing, notably, for the construction of approximate
confidence intervals and tests of hypothesis. In particular, we show that it is
possible to view the study structure considered here from the perspective of
the framework elaborated in van der Laan and Gruber (2011), and therefore,
to adapt the methodology therein developed. This approach consists of an
implementation of targeted minimum-loss-based estimation based on power-
ful causal identities originally derived in Bang and Robins (2005). In Sections
8.2 and 8.3, we describe in detail how the methodology of van der Laan and
Gruber (2011) may be used in the setting we consider, in a simplified scenario
whereby loss to follow-up does not occur during the study time frame. Such a
setting may sometimes be possible if sucient resources are invested in par-
ticipant follow-up. This slightly simplified scenario allows us to illustrate the