On meta-analytic assessment of surrogate outcomes

We discuss the strengths and weaknesses of the meta-analytic approach to estimating the effect of a new treatment on a true clinical outcome measure, \(T\) ⁠, from the effect of treatment on a surrogate response, \(S\) ⁠. The meta-analytic approach (see Daniels and Hughes (1997) 16, 1965–1982) uses data from a series of previous studies of interventions similar to the new treatment. The data are used to estimate relationships between summary measures of treatment effects on \(T\) and \(S\) that can be used to infer the magnitude of the effect of the new treatment on \(T\) from its effects on \(S\) ⁠. We extend the class of models to cover a broad range of applications in which the parameters define features of the marginal distribution of \((T,\ S)\) ⁠. We present a new bootstrap procedure to allow for the variability in estimating the distribution that governs the between-study variation. Ignoring this variability can lead to confidence intervals that are much too narrow. The meta-analytic approach relies on quite different data and assumptions than procedures that depend, for example, on the conditional independence, at the individual level, of treatment and \(T\) ⁠, given \(S\) (see Prentice (1989) 8, 431–440). Meta-analytic calculations in this paper can be used to determine whether a new study, based only on \(S\) ⁠, will yield estimates of the treatment effect on \(T\) that are precise enough to be useful. Compared to direct measurement on \(T\) ⁠, the meta-analytic approach has a number of limitations, including likely serious loss of precision and difficulties in defining the class of previous studies to be used to predict the effects on \(T\) for a new intervention.