Causal Inference in a Placebo-Controlled Clinical Trial with Binary Outcome and Ordered Compliance
Goetghebeur, Els, Molenberghs, Geert, Journal of the American Statistical Association
We propose a likelihood-based method to analyze the causal effect of partial compliance (i.e., unplanned partial exposure to treatment or placebo) in the LRC-CPPT data, a prevention trial with long term follow-up previously analyzed by Efron and Feldman. Initially, we construct ordered compliance categories and dichotomize response. Assuming increased exposure to cholestyramine does not increase cholesterol, we estimate exposure-response curves in different compliance subsets. Subjects in different arms with similar levels of compliance to the assignment may have a different placebo prognosis (i.e., success probability under a possible zero exposure level). The sole assumption that the placebo group reflects response to zero exposure for the treatment group as a whole allows estimation of a causal parameter in a special case only. When a single parameter represents the association between responses to possible treatment exposures and treatment compliance, simple estimates are derived for a set of causal parameters. The example is analyzed in detail, and more general applicability and extensions of the method are discussed.
KEY WORDS: Coarsening; Counterfactual framework; Efficacy; Intention to treat; Interval censoring; Ordinal data.
1.1 The LRC-CPPT Trial
In this article we revisit the 337 patients of the Lipid Research Clinics Coronary Primary Prevention Trial (LRC-CPPT) analyzed by Efron and Feldman (EF) (1991). Those authors studied the effect on cholesterol reduction of six daily packets of cholestyramine or placebo over a period of years. The physicians estimated the percentage of prescribed dose taken, based on packet count or expert opinion. A scatterplot of this summary of compliance versus the achieved cholesterol reduction by group, with added lowess curves, is given in Figure 1.
The following questions are addressed: (1) Do patients who are more compliant with active therapy also benefit more and by how much?; (2) How do baseline risks vary over the observed compliance levels with treatment and with placebo?; (3) What could the population as a whole have gained in addition to the placebo response if they were all exposed to the full intended dose? (For a discussion of the relevance to decisions on drug development and treatment policies, see Goetghebeur and Shapiro 1995.)
To estimate their causal parameters, EF assumed that compliance with assignment is an attribute of the patient and hence is independent of the assigned drug. We will categorize compliance, which was measured imprecisely (e.g. [less than or equal to] 20%, 20%-60%, [greater than or equal to] 60%) and dichotomize outcome (into a cholesterol reduction of at least 20 units or not); see Table 1. From the tabulated data, we can estimate causal parameters when compliance is not an attribute under the assumption of monotone dose-response: increasing cholestyramine does not cause increased cholesterol. We show that changing the cutpoint for success leaves the qualitative results unaltered, and we derive a continuous efficacy measure. A similar statement on the compliance cutpoint needs more care (Sec. 5.3). Table 1. Observed LRC-CPPT Data: Compliance Cut-Offs at 20% and 60%
Treatment group Intake Success Failure % [less than or equal to] 20% 8 24 19.4 20%-60% 19 26 27.3 [is greater than] 60% 72 16 53.3 Placebo group Intake Success Failure % [less than or equal to] 20% 3 14 9.9 20%-60% 1 28 16.9 [is greater than] 60% 28 98 73.3
NOTE: Outcome is called success if cholesterol reduction of at least 20 units is observed.
1.2 Methodological Background
A traditional intention-to-treat analysis compares average observed responses in both groups and provides an unbiased estimator of the effect of treatment assignment. …