Local Control Phase One:
EXPLORE
The first phase of LC analysis starts with specifying the observed, numerical X-characteristics that will be used to Cluster patients. It is convenient to use a hierarchical clustering algorithm because the initial indicator of LC analysis sensitivity will be NCreq = number of clusters requested.
As illustrated below, the overall Clustering Dendrogram (tree) can then be cut to produce any desired number of clusters. Note that, as NCreq is systematically increased, within cluster treatment comparisons are forced to become more and more LOCAL (more fair and clearly relevant.)
The key graphical display examined by the health services researcher in Phase One of LC Analysis is called the "Unbiasing TRACE" display. As NCreq increases, this display shows how the implied "adjusted" Main-Effect of Treatment (i.e. the Overall MEAN of the LTD Distribution) changes.
When the treatment cohorts within an Observational Study suffer from Treatment Selection (Channeling) Bias and/or X-factor Confounding, this display will provide a clear indication of BIAS Reduction.
LC “Unbiasing” TRACE Display
LTD: Difference in Six-Month-Survival Rates
Across Cluster Weighted Average LTD Outcome
Plus Two Sigma Upper Limit for Average LTD
Minus Two Sigma Lower Limit for Average LTD
NCreq = Number of Clusters Requested
In the above TRACE, the "unadjusted" analysis (i.e. all patients within a single cluster) suggests that the "new" treatment provides only a 2.5% survival advantage over the "control" treatment. On the other hand, when between 600 and 900 clusters are requested, this same comparison is seen to result in a more than a 3.5% advantage for "new" over "control."
NOTE: Although it didn't happen here, it is also possible that the Plus-or-Minus Two Sigma BAND in the Unbiasing TRACE display ultimately starts to get wider and wider as NCreq increases. This happens when the smallest clusters become PURE (i.e. contain only Treated or only Control patients.) Such clusters are clearly UNINFORMATIVE about differences in outcome due to treatment! In other words, just as in Propensity Score matching methods, the data from patients who are least comparable to any patients within the other treatment cohort may be best "set aside" (not used) in the main LC Analysis.