Table 3.

Table 3a: Analytical approach and validation of two assumptions for IV (studies are arranged by quality score)
Author	Analytical approach	Assumption 1: IV is associated with treatment assignment	Assumption 2: IV is not associated with measured and unmeasured confounders and is only associated with the outcome through treatment assignment	Quality of IV
				Score	Reason for the score
Bosco et al. [16]	2 stage model: First step: using logistic regression to estimate the probability of receiving treatment. Second step: using survival analysis to estimated the risk of breast cancer recurrence by including the probability of receiving treatment from the first step	They used linear regression to test the strength of association between IV and treatment assignment (coefficient=23.7%) and reported that the strength of IV was comparable to strength from another study using similar IV (coefficient = 23%).	IV reduced imbalance for some patient characteristics and increased the imbalance for others. This implied that IV was still associated with measured and unmeasured confounders.	1	Did not meet the second assumption
Brookhart et al. [15]	2 stage least square (2SLS)	The authors reported difference in treatment assignment between the two levels of the IV. For physician whose last prescription was COX-2, the probability that the physician's next prescription would be COX-2 was 77%. For physician whose last prescription was non-selective NSAID, the probability was 55%.	IV was weakly associated with observed characteristics implying that it might be associated with unobservables. The authors mentioned that the IV might be associated with the outcome through other paths besides treatment and acknowledged this limitation.	1	Did not meet the second assumption
Cain et al. [39]	Point estimates for both probability of treatment assignment and outcome were computed by pooled logistic regression. Bootstrapping sample 500 times was used to estimate confidence interval.	Compare difference in treatment rate before and after the calendar period. They also stated that this assumption was well documented.	They used inverse probability of calendar period weighs to relax the third assumption.	1	Did not assess the second assumption
Costanzo et al. [29]	2 stage IV analysis, bootstrapping for confidence interval	Propensity score was highly associated with treatment assignment.	Measured confounders should be balanced among patients with similar propensity score.	1	Propensity score only balanced measured confounders

Table 3b: Analytical approach and validation of two assumptions for IV (studies are arranged by quality score)
Dudl et al. [17]	Not abstracted due to unclear description of method	Facility use rates from 32% in the lowest-using quintile of facilities to 49.1% in the highest using quintile	IV reduced imbalance of patient characteristics. However, unmeasured facility-level confounder might still bias the results.	1	Did not meet the second assumption
Groenwold et al. [18]	Linear regression to estimate the difference in outcome and difference in vaccination rate between the two IV categories. Bootstrapping for confidence interval	History of gout was associated with vaccination (OR=1.56; 95%CI 1.23-1.97)	All 4 IVs were significantly associated with patient characteristics indicating weak IVs.	1	Did not meet the second assumption
		History of orthopedic morbidity was associated with vaccination (OR=1.16; 95CI 1.10-1.22)
		History of antacid medication was associated with vaccination (RD=18.1%; 95CI 6.1%-10.1%)
		Vaccination rates among GP group practices ranged from 68.1-77.9%
Rascati et al. [37]	2 stage model: First stage: using probit regression to estimate the probability of receiving treatment Second stage: using OLS regression to estimate the hospital cost or total schizo-related cost	In the first stage the IV was significantly associated with treatment assignment (Marginal effect = -0.0074; P<0.0001)	NA	1	No discussion of the second assumption
Setoguchi et al. [22]	2SLS	Instrument was associated with treatment assignment (OR=6.1 95% CI 5.8-6.4)	NA	1	No discussion of the second assumption
Yoo et al. [27]	BVP/2SLS reported BVP results	They stated that they examined F-statistic using pseudo-R square in BVP model. But no detailed data were reported.	NA	1	No discussion of the second assumption

Table 3c: Analytical approach and validation of two assumptions for IV (studies arranged by quality score)
Earle et al. [8]	Difference between survival in the highest and the lowest quintiles of HCSAs/difference in the probability of receiving treatment between the two Bootstrapping for confidence interval	HCSA was highly correlated with the likelihood of receiving chemotherapy.(F statistic= 7792, R square = 0.71)	They compared the observable characteristics between HCSAs with the highest and lowest prevalence of chemotherapy and found the IV reduced imbalance of observed characteristics.	2	Assessed both assumptions
Goldman et al. [32]	Bivariate probit (BVP)	The authors showed that the IV predicted the use of HAART. Average predicted probability of HAART receipt in return to work sample ranged from 31% in non-coverage group to 38% in coverage group. It ranged from 33% to 46% in the remaining employed sample and ranged from 34% to 44% in the hours of work sample.	They argued that patients have little influence on state policy, so state policy instrument is exogenous.	2	Assessed the first assumption and discussed the rationale for the second assumption
	2SLS
Ikeda et al. [33]	2SLS	The authors reported there was an association between the IV and treatment assignment (OR for IV = 47.7)	The authors reported that there was no significant difference in SBP among regions with different treatment rates.	2	Assessed both assumptions
Lu-Yao et al. [19]	Difference between survival in highest and the lowest quintiles of HSAs/difference in the probability of receiving treatment between the two Bootstrapping for confidence interval	The authors reported that PADT use varied by HSAs. (31%-53%)	They presented data showing that measured confounders were balanced by IV.	2	Assessed both assumptions
Park et al. [31]	2SLS	They provided Chow F-statistics in the first stage model and reported that IV was significantly associated with treatment assignment. (F=11.98, P<0.001)	They reported that imbalance was reduced by IV in some important confounders such as severity and comorbidity. But it was increased in other variables such as race. They used Hausman test statistic to examine that IV had no direct and indirect effect on the outcome through an unmeasured confounder.	2	Assessed both assumptions

Table 3d: Analytical approach and validation of two assumptions for IV (studies arranged by quality score)
Ramirez et al. [20]	2 stage model: First stage: using linear mixed model to estimate the probability of receiving rosiglitazone Second stage: survival analysis to estimate the risk of cardiovascular hospitalization by including probability of treatment from the first stage	They reported that IV explained the variation of treatment assignment. (R square = 0.166 for facility and case-mix variable; R square = 0.031 for case-mix variable alone.	Patient characteristics were balanced by the IV. (Table 3)	2	Assessed both assumptions
Salkever et al. [34]	2 stage generalized least square	Four IVs were significantly associated with treatment assignment in the first stage. Total R square was 0.29.	Sargan test for over-identification.	2	Assessed both assumptions
Salkever et al. [35]	BVP	IVs were significantly associated with treatment assignment for patient younger than 45yrs (P<0.05 for 3 out of 4 IVs) but not for patients older than 44yrs.	Including the instruments in the hospitalization regression and compute relevant test statistics based on likelihood ratios	2	Assessed both assumptions
Schneeweiss et al. [36]	2SLS	They reported that aprotinin utilization varied by surgeons	They argued that patients were not likely to choose their surgeon on the basis of the surgeon's preference for a specific antifibrinolytic agent implying patient characteristics would be independent of surgeon preference.	2	Assessed both assumptions
Schneeweiss et al. [21]	2SLS	Instrument was associated with treatment assignment (OR=6.1 95% CI 5.8-6.4)	Imbalance of study variables was reduced by IV.	2	Assessed both assumptions
Schneeweiss et al. [23]	2SLS	Physicians with different preference of NSAID varied by their COX-2 inhibitor utilizations.	Imbalance of study variables was reduced by IV.	2	Assessed both assumptions
Shetty et al. [24]	3 stage least square (3SLS)	They provided argument that release of the WHI data affected the use of HRT.	In the limitation section, they discussed that unmeasured confounders were not likely to affect the results.	2	Assessed both assumptions
Stuart et al. [25]	2 stage residual inclusion (2SRI)	They reported the drug coverage was significantly associated with treatment assignment. (t=6.993, p <0.001)	Residual derived from first stage was significant in the second stage indicating regression model biased and 2SRI was unbiased by unmeasured confounders.	2	Assessed both assumptions

Table 3e: Analytical approach and validation of two assumptions for IV (studies arranged by quality score)
Tentori et al. [30]	A facilities propensity to prescribe VD was modeled as the adjusted proportion of patients on VD at a facility, estimated by linear mixed regression. And 2 IVs were further adjusted in Cox model to predict patient's risk of mortality.	Propensity to prescribe was associated with VD.	They reported that imbalance of patient characteristics was reduced by IV.	2	Assessed both assumptions
Wang et al. [26]	2sls	They argued that antipsychotic prescriptions varied by physicians. But no data were reported.	For confounder between the treatment and the outcome: They reported that imbalanced of measured confounders was reduced by IV. This was validated in another study (ref 4). For confounder between the IV and the outcome: Exclusion criteria were tested by examining the association between physician preference of antipsychotics and hazard concomitant prescription of Tricycle antidepressant (TCA) and long-acting benzodiazepine. This was validated in another study (ref 4) There was no association when they restricted ample to primary physicians.	2	Assessed both assumptions
Zeliadt et al. [28]	2SRI	Reported change of the use of olanzapine before and after March 2000 and reported the first stage F-statistic = 27.63 (P<0.05)	Discussed that timing of approval is not associated with physician behavior patterns or other unmeasured variables.	2	Assessed both assumptions
Zhang et al. [38]	Difference between survival in highest and the lowest HCSAs/difference in the proportion of receiving treatment between the two was used as iV estimate. And they used bootstrapping 1000 samples to estimate confidence interval.	They used linear model to estimate the association between IV and treatment assignment and reported F-statistic was greater than 10.	Imbalance of patient characteristics was reduced by IV.	2	Assessed both assumptions