Local Control Phase Two:  CONFIRM
 

This phase is devoted to confirming that an observed LTD distribution is indeed “Salient” (Statistically Meaningful.)

The LC approach assumes that making many "local" comparisons of outcomes between treated and control patients who are otherwise very similar will yield results that are more scientifically objective and relevant than a single, global comparison.  Luckily, there is a way to at least partially verify this premise!

Via patient clustering in X-space, LC determines which treated patients are directly compared to which control patients.  What would result from such comparisons if all observed X-characteristics were actually irrelevant (unrelated to treatment choices and their resulting outcomes)?  Well, the results would then be purely random ...as if there weren't any available X-characteristics to distinguish one patient from another.  This situation is easily simulated by simply ignoring all observed X-values and randomly assigning the treated and control patients to the same number of clusters, of the same sizes, and with the same within-cluster treatment/control fractions as the given clustering.  The resulting simulated distribution is called the “artificial” LTD distribution.

Why SHOULD these two distributions (observed and artificial) be different?  Well, whenever treatment imbalance and X-variable confounding are present, comparisons made within random (artificial) subgroups are BIASED  ...just like the overall comparison between full treatment cohorts.  Again, by making only the most clearly relevant patient comparisons, the observed LTD distribution will be UNBIASED ...unless key unmeasured confounders exist.

If the observed and artificial LTD distributions are NOT CLEARLY DIFFERENT, essentially nothing interesting has been accomplished via LC clustering!  If they are DIFFERENT, the observed LTD Distribution is said to be SALIENT!

The following graphs compare the right- and left-hand tails of these two distributions (observed LTD => solid and artificial LTD => dashed) for the six-month-mortality example considered earlier.  The full range of possible LTD rates is -1.00 to +1.00.  For example, a value of -1 results when all of the treated patients within an informative cluster survive while all of the control patients within that same cluster die within six months.

The observed LTD distribution has a thinner extreme right-hand tail (favorable to control) than the artificial LTD distribution, but the distributions cross at a LTD of approximately +0.1.

The observed LTD distribution has a heavier left-hand tail (favorable to treatment) than the artificial LTD distribution.

The observed LTD distribution is clearly salient in this example.  We conclude that LC adjustment for treatment imbalance and X-variable confounding reduces bias here and makes the treatment-versus-control comparison at least slightly more favorable to treatment.