JAMES M. ROBINS
ASSOCIATION, CAUSATION, AND MARGINAL STRUCTURAL
The subject-speciﬁc data from a longitudinal study consist of a string of
numbers. These numbers represent a series of empirical measurements.
Calculations are performed on these strings and causal inferences are
drawn. For example, an investigator might conclude that the analysis
provides strong evidence for “a direct effect of AZT on the survival of
AIDS patients controlling for the intermediate variable – therapy with
aerosolized pentamidine”. The nature of the relationship between the sen-
tence expressing these causal conclusions and the computer calculations
performed on the strings of numbers has been obscure. Since the computer
algorithms are well-deﬁned mathematical objects, it is useful to provide
formal mathematical deﬁnitions for the English sentences expressing the
investigator’s causal inferences, In Robins (1986, 1987), I proposed a
formal theory of counterfactual (Lewis 1973) causal inference that exten-
ded the Neyman–Rubin–Holland (Holland 1986) “point treatment” theory
to longitudinal studies with time-varying treatments, outcomes, and covari-
ates (concomitants). This theory translates any causal question concerning
the overall (net), direct, and/or indirect effects of a possibly time-varying
treatment on an outcome into a formal mathematical conjecture about
event trees, referred to as causally interpreted structured tree graphs.
Pearl (1995), and Spirtes, Glymour, and Schemes (hereafter SGS)
(1993) recently developed a formal theory of causal inference based on
causal directed acyclic graphs (DAGs). I showed that these causal DAGs
are mathematically equivalent to a particular special case of my more
general theory (Robins 1995).
In longitudinal studies, treatment often varies over time. The standard
approach to the estimation of the effect of a time-varying treatment on
an outcome of interest is to model the outcome at time t asafunction
of past treatment history. I have shown that this approach may be biased,
whether or not one further adjusts for the past history of time-dependent
Synthese 121: 151–179, 1999.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.