  Recently, the intervention calculus when the DAG is absent (IDA) method was
developed to estimate lower bounds of causal effects from observational
high-dimensional data. Originally it was introduced to assess the effect of
baseline biomarkers which do not vary over time. However, in many clinical
settings, measurements of biomarkers are repeated at fixed time points during
treatment exposure and, therefore, this method need to be extended. The purpose
of this paper is then to extend the first step of the IDA, the Peter Clarks
(PC)-algorithm, to a time-dependent exposure in the context of a binary
outcome. We generalised the PC-algorithm for taking into account the
chronological order of repeated measurements of the exposure and propose to
apply the IDA with our new version, the chronologically ordered PC-algorithm
(COPC-algorithm). A simulation study has been performed before applying the
method for estimating causal effects of time-dependent immunological biomarkers
on toxicity, death and progression in patients with metastatic melanoma. The
simulation study showed that the completed partially directed acyclic graphs
(CPDAGs) obtained using COPC-algorithm were structurally closer to the true
CPDAG than CPDAGs obtained using PC-algorithm. Also, causal effects were more
accurate when they were estimated based on CPDAGs obtained using
COPC-algorithm. Moreover, CPDAGs obtained by COPC-algorithm allowed removing
non-chronologic arrows with a variable measured at a time t pointing to a
variable measured at a time t' where t'< t. Bidirected edges were less present
in CPDAGs obtained with the COPC-algorithm, supporting the fact that there was
less variability in causal effects estimated from these CPDAGs. The
COPC-algorithm provided CPDAGs that keep the chronological structure present in
the data, thus allowed to estimate lower bounds of the causal effect of
time-dependent biomarkers.
