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Editor's Notes

• #3: Stata ivreg2
• #6: Directed acyclic graph (DAG)
• #7: ��Ҫ���ȿ�������������ǥ�˺���뤳�Ȥ��Ǥ���С����Ή������������������ɷ֤Ȥ����v�ˤĤ��ƤϿ��]���ʤ��Ȥ�褯�ʤ롣 ��äơ��������������m�äϡ���Ҫ��u���}��������ϤϤ�����y�Ǥ���ȷ֤��롣���y���{���OӋ���ޤ����� x��z�����v��������Standard error���󤭤��ʤäƤ��ޤ��� Z��u�����v�Ϥ鷺���Ǥ⤢��С�IV�˴󤭤ʆ��}�Ȥʤ롣(p521. Wooldridge2013 & Turkington) �य�Έ��ϡ�x��z�����v�S����0.2δ���Ǥ��뤬��z��u�����v�S�����󤭤���С�IV����OLS�η����Х��������٤ʤ����⤷��ʤ���
• #8: Exogenous=error�����v���ʤ���������ϗ��^�Ǥ��ʤ��� IV=endogenous���h�����������v����
• #12: Davies 2013, p366 Table 5. A minority (n = 25, 28%) reported partial F-statistics or partial r2 of the association of the instruments with the exposures. Under monotonicity, studies identify a weighted average of local average treatment effects. This causal parameter is the effect of treatment on those persons whose treatment decision was affected by the instrumental variable. The assumption of no effect modification by the instrument among the treated identifies the average effect of treatment on the treated subpopulation. (Davies 2013 p365) intention-to-treat�νY���Ȥ��`����(Davies 2013 p365) Standard output from techniques such as two-stage least squares report standard errors that are valid under conditional homoscedasticity. If the variance of the error terms is heteroskedastic (eg, if the outcome is binary in a linear effects model), then the estimates of the confidence intervals may be biased. Therefore, studies should use heteroscedasticity robust standard errors (sandwich estimators). (Davies 2013 p365)
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• #14: It is generally accepted that F-test values <10 indicate weak instruments.[10] 10. Staiger D, Stock JH. Instrumental variables regression with weak instruments. Econometrica 1997; 65:557�C586. From the supplementary data of Mojtabai R, Crum RM. Cigarette smoking and onset of mood and anxiety disorders. Am J Public Health 2013; 103(9): 1656-65. ���ʤϡ� Staiger and Stock (1997) ����һ�λ�Ŀ���ƶ��Dz��������΂S���������Ȥ������o���h��ʶ������r�ˡ�F-statistics��10���¤Ǥ���нU�Y�Ĥ�weak���ȕ����������stock and yogo (2005)���a�㤷����Τ��٩`���ˤʤäƤ��� Checklist: Davies 2013, p366 A minority (n = 25, 28%) reported partial F-statistics or partial r2 of the association of the instruments with the exposures. ����: Davies 2013, p360 The F-statistic indicated that the instrumental variable results did not suffer from weak instruments.[46] Test of weak identification Kleibergen-Paap Wald statistic, robust to heteroskedasticity.
• #15: The observed baseline covariables were strongly associated with prescriptions (Table 1).(���� Davies 2013 p356)
• #16: Palmer p231 There are two commonly used tests of over-identification; the Hansen test and the Sargan test.[39,48]Rejection of an over-identification test is taken to indicate that at least one of the instruments is not valid (i.e., it does not give the same estimate as the other instruments).[49] p235 The Hausman tests suggest that the IV estimates using multiple instruments differ from the OLS estimate. ����������2��Ŀ������ 116. Hansen LP. Large sample properties of generalized method of moments estimators. Econometrica. 1982;50:1029�C1054. 117. Sargan J. The estimation of economic relationships using instrumental variables. Econometrica. 1958;26:393�C415. It should be recalled that it is still necessary to assume that at least one instrument is exogenous. This means that if none of the instruments is exogenous, the Sargan, Hansen and Basmann statistics will be biased and inconsistent and can erroneously fail to reject the null hypothesis (Murray, 2006a).
• #17: All combinations of surrogate instruments, prescriptions, and outcomes had one or more events (Table 2)(���� Davies 2013 p357)
• #18: Standard output from techniques such as two-stage least squares report standard errors that are valid under conditional homoscedasticity. If the variance of the error terms is heteroskedastic (eg, if the outcome is binary in a linear effects model), then the estimates of the confidence intervals may be biased. Therefore, studies should use heteroscedasticity robust standard errors (sandwich estimators). (Davies 2013 p365)
• #19: Davies 2013, p366 A minority (n = 25, 28%) reported partial F-statistics or partial r2 of the association of the instruments with the exposures. Under monotonicity, studies identify a weighted average of local average treatment effects. This causal parameter is the effect of treatment on those persons whose treatment decision was affected by the instrumental variable. The assumption of no effect modification by the instrument among the treated identifies the average effect of treatment on the treated subpopulation. (Davies 2013 p365) intention-to-treat�νY���Ȥ��`����(Davies 2013 p365) Standard output from techniques such as two-stage least squares report standard errors that are valid under conditional homoscedasticity. If the variance of the error terms is heteroskedastic (eg, if the outcome is binary in a linear effects model), then the estimates of the confidence intervals may be biased. Therefore, studies should use heteroscedasticity robust standard errors (sandwich estimators). (Davies 2013 p365)
• #20: intention-to-treat�νY���Ȥ��`����(Davies 2013 p365) Two options are the average treatment effect in the population and the local average treatment effect (LATE ) in the subpopulation of ��compliers.�� For nondichotomous instruments, LATE -like effects are weighted averages of the effect in multiple subgroups. Because ��compliers�� cannot be identified, the LATE is a causal effect in an unknown subset of the population, for example, if one found a beneficial effect of treatment, it is unclear who the ��compliers�� would be who would have this benefit. Because the average treatment effect and the LATE will generally differ, investigators should be explicit about their reasons for choosing one over the other; only 61% of studies in our review were explicit.(Swanson 2013 p372)
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• #23: Monotonicity is generally implausible for the commonly proposed preference-based instruments. (Swanson 2013, p373.)
• #24: Monotonicity is generally implausible for the commonly proposed preference-based instruments. (Swanson 2013, p373.)
• #25: Monotonicity is generally implausible for the commonly proposed preference-based instruments. (Swanson 2013, p373.) Whether estimating bounds or effects (see below), one needs to decide the causal effect of interest. Two options are the average treatment effect in the population and the local average treatment effect (LATE) in the subpopulation of ��compliers.�� For Davies et al, ��compliers�� are patients who would be prescribed a selective NSAID had they seen a physician who preferred selective NSAIDs, but would be prescribed a nonselective NSAID had they seen a physician who preferred nonselective NSAIDs. For nondichotomous instruments, LATE -like effects are weighted averages of the effect in multiple subgroups. Because ��compliers�� cannot be identified, the LATE is a causal effect in an unknown subset of the population, for example, if one found a beneficial effect of treatment, it is unclear who the ��compliers�� would be who would have this benefit. Because the average treatment effect and the LATE will generally differ, investigators should be explicit about their reasons for choosing one over the other; only 61% of studies in our review were explicit.(Swanson 2013, p372.) Homogeneity If interest is in the average treatment effect, the untestable fourth condition for point estimation may be either condition (4c) of identical (ie, constant) treatment effect for all individuals in the population��generally impossible for dichotomous outcomes and highly unlikely for others��or the weaker homogeneity condition (4h) of no additive effect modification across levels of the instrument within the treated and the untreated (no effect modification only in the treated would allow valid estimation of the effect in the treated). The next step in the flowchart is to assess this homogeneity condition (4h) using subject-matter knowledge. ����: Davies p361 Limitations of instrumental variable analysis are its imprecision and the large sample sizes required, as well as the unverifiable assumptions required for point identification.
• #30: intention-to-treat�νY���Ȥ��`����(Davies 2013 p365) Two options are the average treatment effect in the population and the local average treatment effect (LATE ) in the subpopulation of ��compliers.�� For nondichotomous instruments, LATE -like effects are weighted averages of the effect in multiple subgroups. Because ��compliers�� cannot be identified, the LATE is a causal effect in an unknown subset of the population, for example, if one found a beneficial effect of treatment, it is unclear who the ��compliers�� would be who would have this benefit. Because the average treatment effect and the LATE will generally differ, investigators should be explicit about their reasons for choosing one over the other; only 61% of studies in our review were explicit.(Swanson 2013 p372) ������ ���񷽷��ι�(no effect modification) ? Under the no-effect-modification assumption, ��0 is equal to the average effect of prescription on those prescribed, E[Y(1) ? Y(0)|X = 1]. If no-effect-modification assumption also holds for the untreated, then the average causal effect is identified. However, as the prescriptions are binary, it is impossible for no-effect-modification assumption to hold simultaneously for those prescribed and not prescribed.[33] Assuming no effect modification, we further specified multiple previous prescriptions as instruments and used the generalized method of moments estimator to estimate weighted averages of the effect of prescription on those prescribed.[38,44] The size of bias is a decreasing function of the strength of association of Z and X, and the proportion of the patients with Z = 0 who were not prescribed COX-2s.
• #35: *Studies that used instruments from multiple categories were counted more than once. Percentages are based on 187 total instrumental variable comparative effectiveness research studies. ? ��Treatment�� refers to instrument assignment to treatment group rather than actual receipt of treatment.
• #38: 65 instrumental variable CER studies that used 1 of the 4 most common instruments and a mortality outcome to determine whether the authors discussed or controlled for the potential instrument�Coutcome confounders. None of the studies in our review controlled for all potential instrument�Coutcome confounders we identified in the literature. Most (39 of 65 [60%]) used data from only administrative databases, such as electronic medical records and insurer claims. * Analysis was limited to studies that used 1 of the 4 most commonly used instruments and a mortality outcome (see Supplement 3). Studies that used 1 of the 4 instruments appear in multiple columns. ? Studies that used procedure or facility volume as an instrument or independent variable were removed from the denominator.
• #39: 65 instrumental variable CER studies that used 1 of the 4 most common instruments and a mortality outcome to determine whether the authors discussed or controlled for the potential instrument�Coutcome confounders.