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CPS1113 Madhu Mazumdar et al.
                  patients’ chances of receiving a drain and is not directly associated with the
                  outcome, blood transfusion, except through its association with the treatment,
                  CWD. Patients undergoing a procedure performed by surgeons in the ≥80th
                  percentile of drain usage were labeled as ‘receiving a drain’; the rest were
                  labeled as ‘not receiving a drain’ (i.e. treatment allocation according to the IV
                  and not actual drain use; cut-off of 80% chosen to match observered drain
                  utilization).
                      Assessing  the  first  assumption  –  that  the  IV  is  associated  with  the
                  likelihood of actually receiving a drain – is straightforward. The study showed
                  a  significant  correlation  between  the  IV  and  treatment  variable  (r=0.78,
                  P<0.0001). The second assumption, i.e., the IV is independent of (unobserved)
                  confounders, cannot be assessed directly, but the relationship between the IV
                  and observed confounders can  suggest whether the second assumption is
                  violated.  This  relationship  can  be  calculated  by  comparing  covariate
                  differences between IV-based treatment allocation groups (see Table 1 for a
                  simplified  selection).  Compared  to  the  original  cohort  where  groups  were
                  compared based on actual drain use, characteristics of patients and hospitals
                  appear  to  be  more  balanced  between  groups  created  by  the  IV,  as
                  demonstrated by standardized differences of <0.111,12 This is what would be
                  expected in an RCT.
                      To assess the validity of the third assumption (the IV is associated with
                  the  outcome  only  through  treatment),  we  need  to  explore  whether  other
                  treatments that may influence the outcome are given concomitantly with drain
                  use. For example, patients taking anticoagulants may be at increased risk of
                  bleeding and subsequent blood transfusion. Therefore, the third assumption
                  would  be  violated  if  the  IV  is  associated  with  anticoagulant  usage,  a
                  confounder. In our example, the correlation between anticoagulant usage and
                  the  percentage  of  drain  utilization  was  not  significant  (r=0.0048,  P=0.12),
                  suggesting that the third assumption holds.
                      After checking the validity of assumptions underlying the chosen IV, we
                  applied a 2SLS technique to estimate the effect of drains on blood transfusion
                  risk.  In  the  first  stage,  each  patient’s  probability  of  receiving  a  drain  was
                  predicted from the IV, adjusted for all observed confounders. Then the odds
                  of  blood  transfusion  was  calculated based on  the  estimated  probability  of
                  receiving a drain, again adjusted for all observed confounders except for the
                  IV.  Patients  receiving  drains  (allocation  based  on  the  IV)  had  significantly
                  higher odds of blood transfusion (OR: 1.61, 95% CI; 1.37-1.91). This finding
                  was consistent across all methods examined by Chan et al.

                  2.  Discussion and Conclusion
                      Double-blind  RCTs,  the  gold  standard,  are  not  always  feasible.
                  Alternatively, administrative databases (e.g., electronic medical records, claims,


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