Local Control Phase Two:
Individual Local Treatment Differences (LTDs) are effect-size estimates observed within clusters of experimental units (patients) relatively well-matched in X-space. The resulting Distribution of effect-sizes across clusters (blocks) is then either Homogeneous (purely random, highly unpredictable except in mean-effect) or else Heterogeneous (partially predictable from patient baseline X-characteristics.)
The confirm phase of Local Control strategy is devoted to asking whether a given set of K clusters of sizes N1, N2, ..., NK yields a Heterogeneous LTD Distribution. In other words, the observed LTD distribution from those clusters is different in clearly visible and important ways from the corresponding NULL (purely random) LTD distribution that results when patient X-characteristics are assumed to be ignorable.
This NULL LTD distribution can be simulated to arbitrary precision by randomly permuting treated (t=1) and control (t=0) patients across the same number of clusters, of the same sizes, as the given clustering. Technically, a single random permutation of "Cluster ID Labels" across all N = N1 + N2 + ... + NK patients produces a set of K "random" LTD estimates. A total of R such independent replicates are merged to depict the full simulated random NULL distribution.
By making only the most clearly relevant X-variable comparisons, the observed LTD distribution will be relatively UNBIASED ...unless key unmeasured confounders exist.
If the observed LTD and random NULL LTD distributions are NOT clearly different, essentially nothing "interesting" has been accomplished via the current LC clustering!
EXAMPLE: Local Control (LC) "Confirm" graphic for 39,585 MDD Patients
Note that the top random NULL LTD distribution has a positive mean value and is fairly symmetric. In stark contrast, the observed LTD distribution has a negative mean value (an average savings of $635 per year on the New Treatment) and is highly skewed ...with a very long and highly desirable left-hand tail. For more detail on this example, see Obenchain and Young (2013) Journal of Statistical Theory and Practice 7: 456-469.
When the observed LTD effect-size distribution appears quite similar to its homogeneous NULL distrinution, observed local effects are best summarized by their global Average Treatment Effect (ATE); a traditional one-size-fits-all treatment policy is then justified.
In stark contrast, when the LTD distribution appears quite heterogeneous (as in the above example), it provides objective support for Individualized Medicine.
Guidelines for Interpretation of LC Confirm Phase Graphics (6-page PDF). View/Download