Observational data are used to estimate associations of exposures with outcomes, but if exposures are not allocated randomly these associations may be confounded by associated characteristics.1–3 An approach to estimate causal effects in the presence of unmeasured confounding is instrumental variable analysis.4–7 Instrumental variables are defined by three assumptions: (1) relevance, that is, that the variable is associated with exposure; (2) exclusion restriction, that is, that the variable affects only the outcome through the likelihood of exposure; and (3) the instrument is independent of confounders.4,5 Without further assumptions, instrumental variables can generally estimate only the maximum and minimum values of the causal treatment effect consistent with the observed data. To estimate specific parameters (also referred to as point identification), such as the average treatment effect, stronger assumptions are required.5,8 Detailed reviews of instrumental variable methodology are available elsewhere,5,7–9 including use of Mendelian randomization10–12 and data from randomized controlled trials.13
For instrumental variables to provide meaningful evidence, authors must report sufficient information for readers and reviewers to assess, where possible, whether the instrumental variable assumptions are likely to hold. However, despite their increasing use in epidemiology14,15—and concerns that reporting is inadequate15—there are no specific recommendations for reporting of studies using instrumental variables.3 We build on previous findings15 by investigating the information provided in a broad range of clinical epidemiology studies using instrumental variables, including whether the point-identifying assumptions were specified. We propose a checklist of information to be reported by studies using instrumental variables.
We searched Embase and Medline for studies containing the term “instrumental variable$” published at any time up to October 2012. We included all articles with a clinical intervention and a clinical outcome. We excluded articles that (1) did not use instrumental variables; (2) had a nonclinical outcome or exposure, such as economic exposures or outcomes; (3) were analyses of randomized controlled trials; (4) were reviews or theoretical articles; or (5) were related publications from a single study. We extracted the following information from eligible studies: type of study, methods used to estimate the models, number of observations, whether the study discussed the identifying assumptions (ie, the relevance and exclusion restriction assumptions), and whether the authors tested the association of the instruments and observed confounders.
Our search returned 756 articles, of which 90 studies published since 1994 were eligible (eFigure, https://links.lww.com/EDE/A663). The number of studies using instrumental variables has increased markedly between 2003 and 2012 (Figure). Studies were published in general medical journals,16–24 economics and health services research journals,25–39 epidemiology journals,40–46 and a range of specialist journals (eTable 1, https://links.lww.com/EDE/A663).47–105 The most commonly studied exposures were surgical and pharmacological (eTable 2, https://links.lww.com/EDE/A663). Several sources of variation were used as instruments (Table 1). A minority (n = 25, 28%) reported partial F-statistics or partial r2 of the association of the instruments with the exposures, with partial F-test statistics ranging from 4.21 to 32,266.* Others (n = 39, 43%) reported other measures, such as the C-statistic or the risk difference of exposure by level of the instrument.† To quantify the association between instrument and exposure, six reported both partial F-statistics and risk differences.44,83,86,91,92,103 The remaining studies (n = 20, 22%) reported neither the magnitude of the association nor a partial F-test.‡ The methods used to estimate the causal parameters and the target parameters estimated are shown in Tables 2 and 3, respectively.
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FIGURE: Cumulative number of studies listed in Medline and Embase that used non-genetic instrumental variable analysis for medical research over time.
TABLE 1: Type of Instrumental Variable in 90 Studies
TABLE 2: Estimation Methods Used in 90 Instrumental Variable Studies
TABLE 3: Target Parameter in 90 Studies Using Instrumental Variables
Some studies reported calculating standard errors that were valid under homoskedasticy (Table 4). Of these, a minority used two-stage least squares. Methods used to allow for heteroscedasticity included nonparametric bootstraps, clustered robust standard errors, sandwich estimators, generalized estimated equations, or generalized method of moments. A minority (n = 15, 17%) of studies reported the selection model equation (also known as the first-stage regression). The association of observed covariates with the instruments was reported by 44 (49%) studies and a minority (n = 20, 22%) of studies used multiple instruments in a single model.
TABLE 4: Methods Used to Estimate Standard Errors and Reported Information in 90 Studies Using Instrumental Variables
Overall, we found that although the number of studies using instrumental variables is increasing, many did not report enough information to determine whether the inferences the authors drew were supported by their evidence. We propose a checklist of information to guide instrumental variable studies (Table 5).
TABLE 5: Proposed Reporting Checklist for Authors, Editors, and Reviewers of Instrumental Variable Studies
Although estimation methods for instrumental variables are asymptotically unbiased, studies using small samples or weak instruments that explain little of the variation in the exposure can produce biased estimates of the causal parameters.106,107 The sample size required for a sufficiently powered instrumental variable analysis depends on the distributions of the outcomes, exposures, and instruments. All else being equal, the weaker the association of the instrument with the exposure, the larger the sample size required to detect a given effect size. Studies with insufficient observations are unlikely to provide evidence of clinically meaningful treatment effects or differences between the instrumental variable and conventional observational results.15
Reporting of the strength of the association between instrumental variables and exposures was frequently insufficient because the partial F-statistic or partial r2 were not provided. If studies do not report the strength of the association of instruments with exposure, it is not possible to tell whether the instrument is valid or whether weak instruments could bias the results toward the conventional observational estimates.106–109 Many studies reported the magnitude of the association of the instrument with exposure using either the risk difference in exposure by value of the instrumental variable or the C-statistic. However, these parameters do not incorporate information about the number of observations included in the analysis.
Although the associations of an instrument and the unobserved confounders cannot be estimated, the associations with observed potential confounding factors can be quantified and tested and should be reported. Of the 90 eligible studies, 44 reported the association of observed covariates with the instrumental variables, and of these studies, 15 performed no formal statistical tests.§ Of the studies that tested these associations, all except three23,30,45 found some evidence of associations of covariates with the instruments. This suggests that the instrumental variable assumptions are violated to some extent in each of these studies, and it is not possible to prove which approach (the instrumental variable or conventional results) would be more prone to bias.5 Furthermore, some studies used characteristics of the patients as instruments for their treatment; such characteristics are unlikely to be independent of the confounding variables.27,29,51,62
Ideally, studies should identify their results using the weakest set of assumptions possible. The studies used many different methods to estimate their results, and hence targeted different parameters. Structural mean models can estimate causal risk differences, risk ratios, or odds ratios under relatively weak semiparametric assumptions,5,8,110 although this comes at a cost of precision. Estimators with stronger assumptions, such as a fully specified parametric bivariate probit, may be more precise and can also identify causal risk differences, risk ratios, or odds ratios.7 If the assumptions underlying the bivariate probit do not hold in the data, then the bivariate probit estimates may be biased.111
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).112
In most epidemiologic studies, treatment effects are likely to be heterogeneous across the population. This is particularly true for studies with binary outcomes,5 which can be point-identified by assuming monotonicity or no effect modification.5,7 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.113 The assumption of no effect modification by the instrument among the treated identifies the average effect of treatment on the treated subpopulation (see Hernán and Robins5 for sufficient conditions and a detailed exposition of these issues). Even given identical observational and experimental samples in which the average treatment effects were identical, the parameters estimated by instrumental variables will not necessarily equal the intention-to-treat parameter found in a randomized controlled trial. This is true for two reasons: first, the persons who choose to be treated or are caused to change treatment may not be representative of the whole population; second, the intention-to-treat parameter is the difference in outcomes across two arms of a trial. If there has been noncompliance or incomplete follow-up, then the intention-to-treat estimate will generally be smaller than the average treatment effect in the population.13
Instrumental variables can estimate the causal effects of exposures in the presence of unmeasured or residual confounding.4,5,114,115 At present, the reporting of studies using instrumental variables is often inadequate to determine whether the instrumental variables were valid or whether the authors’ inferences are supported by the empirical evidence presented. Strong assumptions must be satisfied for instrumental variable studies to be valid and are not always met. Therefore, it is essential for studies to report tests of these assumptions, as readers will need to determine whether the bias because of residual confounding is likely to be smaller or greater than the bias because of violations of the exclusion restriction assumption, magnified by the weakness of the instruments.5 Studies using instrumental variables must report sufficient information for reviewers, readers, and editors to evaluate the extent to which the results provide evidence about the hypotheses being asked.
ACKNOWLEDGMENTS
We are grateful for comments and suggestions from Paul Clarke, Tom Palmer, Nic Timpson, and Vanessa Didelez.
* References 24–28, 30, 36, 37, 45, 46, 49, 51, 52, 57, 64, 72, 81, 82, 88, 89, 93, 94, 100, 101, 104.
Cited Here
† References 17–21, 23, 29, 31, 33, 40–42, 47, 48, 54–56, 59, 61–63, 65–68, 70, 71, 73–75, 77, 78, 80, 85, 87, 90, 96, 102.
Cited Here
‡ References 16, 22, 32, 34, 38, 39, 43, 50, 53, 58, 60, 69, 76, 79, 84, 95, 97–99.
Cited Here
§ References 18, 21, 33, 35, 41, 42, 44, 52, 74, 76, 85, 90–92, 101.
Cited Here
REFERENCES
1. McMahon AD. Approaches to combat with confounding by indication in observational studies of intended drug effects. Pharmacoepidemiol Drug Saf. 2003;12:551–558
2. Concato J, Shah N, Horwitz RI. Randomized, controlled trials, observational studies, and the hierarchy of research designs. N Engl J Med. 2000;342:1887–1892
3. Vandenbroucke JP, von Elm E, Altman DG, et al.STROBE Initiative. Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): explanation and elaboration. Epidemiology. 2007;18:805–835
4. Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables. J Am Stat Assoc. 1996;91:444–455
5. Hernán MA, Robins JM. Instruments for causal inference: an epidemiologist’s dream? Epidemiology. 2006;17:360–372
6. Basu A. Estimating decision-relevant comparative effects using instrumental variables. Stat Biosci. 2011;3:6–27
7. Clarke PS, Windmeijer F. Instrumental variable estimators for binary outcomes. J Am Statis Assoc. 2012;107:1638–1652
8. Clarke PS, Windmeijer F. Identification of causal effects on binary outcomes using structural mean models. Biostatistics. 2010;11:756–770
9. Greenland S. An introduction to instrumental variables for epidemiologists. Int J Epidemiol. 2000;29:722–729
10. Davey Smith G, Lawlor DA, Harbord R, et al. Association of C-reactive protein with blood pressure and hypertension: life course confounding and Mendelian randomization tests of causality. Arterioscler Thromb Vasc Biol. 2005;25:1051–1056
11. Timpson NJ, Wade KH, Smith GD. Mendelian randomization: application to cardiovascular disease. Curr Hypertens Rep. 2012;14:29–37
12. von Hinke Kessler Scholder S, Smith GD, Lawlor DA, Propper C, Windmeijer F. Mendelian randomization: the use of genes in instrumental variable analyses. Health Econ. 2011;20:893–896
13. Bang H, Davis CE. On estimating treatment effects under non-compliance in randomized clinical trials: are intent-to-treat or instrumental variables analyses perfect solutions? Stat Med. 2007;26:954–964
14. Aarstad J. Instrumental variables in epidemiological research: an assessment of the adoption rate and future trends. Int J Epidemiol. 2011;40:1738–1739
15. Chen Y, Briesacher BA. Use of instrumental variable in prescription drug research with observational data: a systematic review. J Clin Epidemiol. 2011;64:687–700
16. Lindenauer PK, Pekow PS, Lahti MC, Lee Y, Benjamin EM, Rothberg MB. Association of corticosteroid dose and route of administration with risk of treatment failure in acute exacerbation of chronic obstructive pulmonary disease. JAMA. 2010;303:2359–2367
17. Lu-Yao GL, Albertsen PC, Moore DF, et al. Survival following primary androgen deprivation therapy among men with localized prostate cancer. JAMA. 2008;300:173–181
18. McClellan M, McNeil BJ, Newhouse JP. Does more intensive treatment of acute myocardial infarction in the elderly reduce mortality? Analysis using instrumental variables. JAMA. 1994;272:859–866
19. Punglia RS, Saito AM, Neville BA, Earle CC, Weeks JC. Impact of interval from breast conserving surgery to radiotherapy on local recurrence in older women with breast cancer: retrospective cohort analysis. BMJ. 2010;340:c845
20. Schneeweiss S, Seeger JD, Landon J, Walker AM. Aprotinin during coronary-artery bypass grafting and risk of death. N Engl J Med. 2008;358:771–783
21. Stukel TA, Fisher ES, Wennberg DE, Alter DA, Gottlieb DJ, Vermeulen MJ. Analysis of observational studies in the presence of treatment selection bias: effects of invasive cardiac management on AMI survival using propensity score and instrumental variable methods. JAMA. 2007;297:278–285
22. Wang PS, Schneeweiss S, Avorn J, et al. Risk of death in elderly users of conventional vs. atypical antipsychotic medications. N Engl J Med. 2005;353:2335–2341
23. Xian Y, Holloway RG, Chan PS, et al. Association between stroke center hospitalization for acute ischemic stroke and mortality. JAMA. 2011;305:373–380
24. Tan HJ, Norton EC, Ye Z, Hafez KS, Gore JL, Miller DC. Long-term survival following partial vs radical nephrectomy among older patients with early-stage kidney cancer. JAMA. 2012;307:1629–1635
25. Beck CA, Penrod J, Gyorkos TW, Shapiro S, Pilote L. Does aggressive care following acute myocardial infarction reduce mortality? Analysis with instrumental variables to compare effectiveness in Canadian and United States patient populations. Health Serv Res. 2003;38(6 Pt 1):1423–1440
26. Brooks JM, Chrischilles EA, Scott SD, Chen-Hardee SS. Was breast conserving surgery underutilized for early stage breast cancer? Instrumental variables evidence for stage II patients from Iowa. Health Serv Res. 2003;38(6 Pt 1):1385–1402
27. Brown TT, Dela Cruz E, Brown SS. The effect of dental care on cardiovascular disease outcomes: an application of instrumental variables in the presence of heterogeneity and self-selection. Health Econ. 2011;20:1241–1256
28. Encinosa WE, Bernard D, Dor A. Does prescription drug adherence reduce hospitalizations and costs? The case of diabetes. Adv Health Econ Health Serv Res. 2010;22:151–173
29. Groenwold RH, Hak E, Klungel OH, Hoes AW. Instrumental variables in influenza vaccination studies: mission impossible? Value Health. 2010;13:132–137
30. Hadley J, Polsky D, Mandelblatt JS, et al.OPTIONS Research Team. An exploratory instrumental variable analysis of the outcomes of localized breast cancer treatments in a medicare population. Health Econ. 2003;12:171–186
31. Ho V, Hamilton BH, Roos LL. Multiple approaches to assessing the effects of delays for hip fracture patients in the United States and Canada. Health Serv Res. 2000;34:1499–1518
32. Kim HM, Eisenberg D, Ganoczy D, et al. Examining the relationship between clinical monitoring and suicide risk among patients with depression: matched case-control study and instrumental variable approaches. Health Serv Res. 2010;45(5 Pt 1):1205–1226
33. Landrum MB, Ayanian JZ. Causal effect of ambulatory specialty care on mortality following myocardial infarction: a comparison of propensity score and instrumental variable analyses. Health Serv Outcomes Res Methodol. 2001;2:221–245
34. Matsui H, Hashimoto H, Horiguchi H, Yasunaga H, Matsuda S. An exploration of the association between very early rehabilitation and outcome for the patients with acute ischaemic stroke in Japan: a nationwide retrospective cohort survey. BMC Health Serv Res. 2010;10:213
35. McConnell KJ, Newgard CD, Mullins RJ, Arthur M, Hedges JR. Mortality benefit of transfer to level I versus level II trauma centers for head-injured patients. Health Serv Res. 2005;40:435–457
36. Park TR, Brooks JM, Chrischilles EA, Bergus G. Estimating the effect of treatment rate changes when treatment benefits are heterogeneous: antibiotics and otitis media. Value Health. 2008;11:304–314
37. Posner MA, Ash AS, Freund KM, Moskowitz MA, Shwartz M. Comparing standard regression, propensity score matching, and instrumental variables methods for determining the influence of mammography on stage of diagnosis. Health Serv Outcomes Res Methodol. 2001;2:279–290
38. Yoo BK, Frick KD. The instrumental variable method to study self-selection mechanism: a case of influenza vaccination. Value Health. 2006;9:114–122
39. Bjorvatn A. Hospital readmission among elderly patients. Eur J Health Econ. 2012 September 18 [epub ahead of print]
40. Ahern TP, Pedersen L, Sværke C, Rothman KJ, Sørensen HT, Lash TL. The association between vitamin K antagonist therapy and site-specific cancer incidence estimated by using heart valve replacement as an instrumental variable. Am J Epidemiol. 2011;174:1382–1390
41. Bosco JL, Silliman RA, Thwin SS, et al. A most stubborn bias: no adjustment method fully resolves confounding by indication in observational studies. J Clin Epidemiol. 2010;63:64–74
42. Brookhart MA, Wang PS, Solomon DH, Schneeweiss S. Evaluating short-term drug effects using a physician-specific prescribing preference as an instrumental variable. Epidemiology. 2006;17:268–275
43. Cain LE, Cole SR, Greenland S, et al. Effect of highly active antiretroviral therapy on incident AIDS using calendar period as an instrumental variable. Am J Epidemiol. 2009;169:1124–1132
44. Rassen JA, Brookhart MA, Glynn RJ, Mittleman MA, Schneeweiss S. Instrumental variables II: instrumental variable application-in 25 variations, the physician prescribing preference generally was strong and reduced covariate imbalance. J Clin Epidemiol. 2009;62:1233–1241
45. Fang G, Brooks JM, Chrischilles EA. Comparison of instrumental variable analysis using a new instrument with risk adjustment methods to reduce confounding by indication. Am J Epidemiol. 2012;175:1142–1151
46. Huybrechts KF, Brookhart MA, Rothman KJ, et al. Comparison of different approaches to confounding adjustment in a study on the association of antipsychotic medication with mortality in older nursing home patients. Am J Epidemiol. 2011;174:1089–1099
47. Bond TC, Nissenson AR, Krishnan M, Wilson SM, Mayne T. Dialyzer reuse with peracetic acid does not impact patient mortality. Clin J Am Soc Nephrol. 2011;6:1368–1374
48. Bradbury BD, Do TP, Winkelmayer WC, Critchlow CW, Brookhart MA. Greater Epoetin alfa (EPO) doses and short-term mortality risk among hemodialysis patients with hemoglobin levels less than 11 g/dL. Pharmacoepidemiol Drug Saf. 2009;18:932–940
49. Brooks JM, McClellan M, Wong HS. The marginal benefits of invasive treatments for acute myocardial infarction: does insurance coverage matter? Inquiry. 2000;37:75–90
50. Dudl RJ, Wang MC, Wong M, Bellows J. Preventing myocardial infarction and stroke with a simplified bundle of cardioprotective medications. Am J Manag Care. 2009;15:e88–e94
51. Durham R, Pracht E, Orban B, Lottenburg L, Tepas J, Flint L. Evaluation of a mature trauma system. Ann Surg. 2006;243:775–783; discussion 783
52. Earle CC, Tsai JS, Gelber RD, Weinstein MC, Neumann PJ, Weeks JC. Effectiveness of chemotherapy for advanced lung cancer in the elderly: instrumental variable and propensity analysis. J Clin Oncol. 2001;19:1064–1070
53. Edidin AA, Ong KL, Lau E, Kurtz SM. Mortality risk for operated and nonoperated vertebral fracture patients in the medicare population. J Bone Miner Res. 2011;26:1617–1626
54. Flint AC, Kamel H, Navi BB, et al. Statin use during ischemic stroke hospitalization is strongly associated with improved poststroke survival. Stroke. 2012;43:147–154
55. Gillum LA, Johnston SC. Influence of physician specialty on outcomes after acute ischemic stroke. J Hosp Med. 2008;3:184–192
56. Gore JL, Litwin MS, Lai J, et al.Urologic Diseases in America Project. Use of radical cystectomy for patients with invasive bladder cancer. J Natl Cancer Inst. 2010;102:802–811
57. Hadley J, Yabroff KR, Barrett MJ, Penson DF, Saigal CS, Potosky AL. Comparative effectiveness of prostate cancer treatments: evaluating statistical adjustments for confounding in observational data. J Natl Cancer Inst. 2010;102:1780–1793
58. Kane RL, Chen Q, Finch M, Blewett L, Burns R, Moskowitz M. Functional outcomes of posthospital care for stroke and hip fracture patients under medicare. J Am Geriatr Soc. 1998;46:1525–1533
59. Kawaguchi T, Ieiri N, Yamazaki S, et al. Clinical effectiveness of steroid pulse therapy combined with tonsillectomy in patients with immunoglobulin A nephropathy presenting glomerular haematuria and minimal proteinuria. Nephrology (Carlton). 2010;15:116–123
60. Krishnan E, Baker JF, Furst DE, Schumacher HR. Gout and the risk of acute myocardial infarction. Arthritis Rheum. 2006;54:2688–2696
61. Lalani T, Cabell CH, Benjamin DK, et al.International Collaboration on Endocarditis-Prospective Cohort Study (ICE-PCS) Investigators. Analysis of the impact of early surgery on in-hospital mortality of native valve endocarditis: use of propensity score and instrumental variable methods to adjust for treatment-selection bias. Circulation. 2010;121:1005–1013
62. Marcin JP, Song J, Leigh JP. The impact of pediatric intensive care unit volume on mortality: a hierarchical instrumental variable analysis. Pediatr Crit Care Med. 2005;6:136–141
63. McGuire KJ, Bernstein J, Polsky D, Silber JH. The 2004 Marshall Urist award: delays until surgery after hip fracture increases mortality. Clin Orthop Relat Res. 2004:294–301
64. Newgard CD, Schmicker RH, Hedges JR, et al.Resuscitation Outcomes Consortium Investigators. Emergency medical services intervals and survival in trauma: assessment of the “golden hour” in a North American prospective cohort. Ann Emerg Med. 2010;55:235–246.e4
65. Newman TB, Vittinghoff E, McCulloch CE. Efficacy of phototherapy for newborns with hyperbilirubinemia: a cautionary example of an instrumental variable analysis. Med Decis Making. 2012;32:83–92
66. Pilote L, Beck CA, Eisenberg MJ, et al. Comparing invasive and noninvasive management strategies for acute myocardial infarction using administrative databases. Am Heart J. 2008;155:42–48
67. Pisoni RL, Arrington CJ, Albert JM, et al. Facility hemodialysis vascular access use and mortality in countries participating in DOPPS: an instrumental variable analysis. Am J Kidney Dis. 2009;53:475–491
68. Pracht EE, Tepas JJ 3rd, Langland-Orban B, Simpson L, Pieper P, Flint LM. Do pediatric patients with trauma in Florida have reduced mortality rates when treated in designated trauma centers? J Pediatr Surg. 2008;43:212–221
69. Pracht EE, Langland-Orban B, Flint L. Survival advantage for elderly trauma patients treated in a designated trauma center. J Trauma. 2011;71:69–77
70. Pratt N, Roughead EE, Ryan P, Salter A. Antipsychotics and the risk of death in the elderly: an instrumental variable analysis using two preference based instruments. Pharmacoepidemiol Drug Saf. 2010;19:699–707
71. Ramirez SP, Albert JM, Blayney MJ, et al. Rosiglitazone is associated with mortality in chronic hemodialysis patients. J Am Soc Nephrol. 2009;20:1094–1101
72. Rassen JA, Mittleman MA, Glynn RJ, Alan Brookhart M, Schneeweiss S. Safety and effectiveness of bivalirudin in routine care of patients undergoing percutaneous coronary intervention. Eur Heart J. 2010;31:561–572
73. Ryan JW, Peterson ED, Chen AY, et al.CRUSADE Investigators. Optimal timing of intervention in non-ST-segment elevation acute coronary syndromes: insights from the CRUSADE (Can Rapid risk stratification of Unstable angina patients Suppress ADverse outcomes with Early implementation of the ACC/AHA guidelines) Registry. Circulation. 2005;112:3049–3057
74. Salkever DS, Slade EP, Karakus M, Palmer L, Russo PA. Estimation of antipsychotic effects on hospitalization risk in a naturalistic study with selection on unobservables. J Nerv Ment Dis. 2004;192:119–128
75. Scales DC, Thiruchelvam D, Kiss A, Redelmeier DA. The effect of tracheostomy timing during critical illness on long-term survival. Crit Care Med. 2008;36:2547–2557
76. Schneeweiss S, Solomon DH, Wang PS, Rassen J, Brookhart MA. Simultaneous assessment of short-term gastrointestinal benefits and cardiovascular risks of selective cyclooxygenase 2 inhibitors and nonselective nonsteroidal antiinflammatory drugs: an instrumental variable analysis. Arthritis Rheum. 2006;54:3390–3398
77. Setoguchi S, Wang PS, Alan Brookhart M, Canning CF, Kaci L, Schneeweiss S. Potential causes of higher mortality in elderly users of conventional and atypical antipsychotic medications. J Am Geriatr Soc. 2008;56:1644–1650
78. Suaya JA, Stason WB, Ades PA, Normand SL, Shepard DS. Cardiac rehabilitation and survival in older coronary patients. J Am Coll Cardiol. 2009;54:25–33
79. Tentori F, Albert JM, Young EW, et al. The survival advantage for haemodialysis patients taking vitamin D is questioned: findings from the Dialysis Outcomes and Practice Patterns Study. Nephrol Dial Transplant. 2009;24:963–972
80. Venkitachalam L, Lei Y, Magnuson EA, et al.EVENT Registry Investigators. Survival benefit with drug-eluting stents in observational studies: fact or artifact? Circ Cardiovasc Qual Outcomes. 2011;4:587–594
81. Zeliadt SB, Potosky AL, Penson DF, Etzioni R. Survival benefit associated with adjuvant androgen deprivation therapy combined with radiotherapy for high- and low-risk patients with nonmetastatic prostate cancer. Int J Radiat Oncol Biol Phys. 2006;66:395–402
82. Brooks JM, Chrischilles EA, Landrum MB, et al. Survival implications associated with variation in mastectomy rates for early-staged breast cancer. Int J Surg Oncol. 2012;2012:127854
83. Federspiel JJ, Stearns SC, Sheridan BC, et al. Evaluating the effectiveness of a rapidly adopted cardiovascular technology with administrative data: the case of drug-eluting stents for acute coronary syndromes. Am Heart J. 2012;164:207–214
84. Flint AC, Kamel H, Navi BB, et al. Inpatient statin use predicts improved ischemic stroke discharge disposition. Neurology. 2012;78:1678–1683
85. Jacob BJ, Moineddin R, Sutradhar R, Baxter NN, Urbach DR. Effect of colonoscopy on colorectal cancer incidence and mortality: an instrumental variable analysis. Gastrointest Endosc. 2012;76:355–64.e1
86. Lopes AA, Tong L, Thumma J, et al. Phosphate binder use and mortality among hemodialysis patients in the Dialysis Outcomes and Practice Patterns Study (DOPPS): evaluation of possible confounding by nutritional status. Am J Kidney Dis. 2012;60:90–101
87. Lorch SA, Baiocchi M, Ahlberg CE, Small DS. The differential impact of delivery hospital on the outcomes of premature infants. Pediatrics. 2012;130:270–278
88. Mojtabai R. The public health impact of antidepressants: an instrumental variable analysis. J Affect Disord. 2011;134:188–197
89. Nelson RE, Nebeker JR, Hayden C, Reimer L, Kone K, Lafleur J. Comparing adherence to two different HIV antiretroviral regimens: an instrumental variable analysis. AIDS Behav. 2013;17:160–167
90. Saito AM, Landrum MB, Neville BA, Ayanian JZ, Earle CC. The effect on survival of continuing chemotherapy to near death. BMC Palliat Care. 2011;10:14
91. Slinin Y, Guo H, Li S, et al. Association of provider-patient visit frequency and patient outcomes on hemodialysis. J Am Soc Nephrol. 2012;23:1560–1567
92. Suh HS, Hay JW, Johnson KA, Doctor JN. Comparative effectiveness of statin plus fibrate combination therapy and statin monotherapy in patients with type 2 diabetes: use of propensity-score and instrumental variable methods to adjust for treatment-selection bias. Pharmacoepidemiol Drug Saf. 2012;21:470–484
93. Tentori F, Zhang J, Li Y, et al. Longer dialysis session length is associated with better intermediate outcomes and survival among patients on in-center three times per week hemodialysis: results from the Dialysis Outcomes and Practice Patterns Study (DOPPS). Nephrol Dial Transplant. 2012;27:4180–4188
94. Valenstein M, Kim HM, Ganoczy D, et al. Antidepressant agents and suicide death among US Department of Veterans Affairs patients in depression treatment. J Clin Psychopharmacol. 2012;32:346–353
95. van de Water W, Bastiaannet E, Dekkers OM, et al. Adherence to treatment guidelines and survival in patients with early-stage breast cancer by age at diagnosis. Br J Surg. 2012;99:813–820
96. Wisnivesky JP, Halm EA, Bonomi M, Smith C, Mhango G, Bagiella E. Postoperative radiotherapy for elderly patients with stage III lung cancer. Cancer. 2012;118:4478–4485
97. Schneeweiss S, Setoguchi S, Brookhart A, Dormuth C, Wang PS. Risk of death associated with the use of conventional versus atypical antipsychotic drugs among elderly patients. CMAJ. 2007;176:627–632
98. Hogan JW, Lancaster T. Instrumental variables and inverse probability weighting for causal inference from longitudinal observational studies. Stat Methods Med Res. 2004;13:17–48
99. Shetty KD, Vogt WB, Bhattacharya J. Hormone replacement therapy and cardiovascular health in the United States. Med Care. 2009;47:600–606
100. Buntin MB, Colla CH, Deb P, Sood N, Escarce JJ. Medicare spending and outcomes after postacute care for stroke and hip fracture. Med Care. 2010;48:776–784
101. Kuo YF, Montie JE, Shahinian VB. Reducing bias in the assessment of treatment effectiveness: androgen deprivation therapy for prostate cancer. Med Care. 2012;50:374–380
102. Kahn JM, Werner RM, David G, Ten Have TR, Benson NM, Asch DA. Effectiveness of long-term acute care hospitalization in elderly patients with chronic critical illness. Med Care. 2013;51:4–10
103. Hauck K, Zhao X. How dangerous is a day in hospital? A model of adverse events and length of stay for medical inpatients. Med Care. 2011;49:1068–1075
104. Mojtabai R. Does depression screening have an effect on the diagnosis and treatment of mood disorders in general medical settings? An instrumental variable analysis of the national ambulatory medical care survey. Med Care Res Rev. 2011;68:462–489
105. Pracht EE, Tepas JJ 3rd, Celso BG, Langland-Orban B, Flint L. Survival advantage associated with treatment of injury at designated trauma centers: a bivariate probit model with instrumental variables. Med Care Res Rev. 2007;64:83–97
106. Staiger D, Stock J. Instrumental variables regression with weak instruments. Econometrica. 1997;65:557–586
107. Bound J, Jaeger D, Baker R. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. J Am Statis Assoc. 1995;90:443–450
108. Stock J, Wright J, Yogo M. A survey of weak instruments and weak identification in generalized method of moments. J Bus Econ Statis. 2002;20:518–529
109. Stock J, Yogo M. Asymptotic distributions of instrumental variables statistics with many instruments. In: Andrews DWK, Stock JH, eds. Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg. Cambridge: Cambridge University Press. 2005:109–120
110. Clarke PS, Palmer TM, Windmeijer F Estimating Structural Mean Models with Multiple Instrumental Variables Using the Generalised Method of Moments. 2011 The Centre for Market and Public Organisation
111. Greene W Econometric Analysis. 2003 Upper Saddle River, NJ Prentice Hall
112. Wooldridge J Econometric Analysis of Cross Section and Panel Data. 2002 Cambridge, MA The MIT Press
113. Angrist JD, Imbens GW. Two-stage least squares estimation of average causal effects in models with variable treatment intensity. J Am Stat Assoc. 1995;90:431–442
114. Angrist JD, Graddy K, Imbens G. The interpretation of instrumental variables estimators in simultaneous equations models with an application to the demand for fish. Rev Econ Stud. 2000;67:499–527
115. Newhouse JP, McClellan M. Econometrics in outcomes research: the use of instrumental variables. Annu Rev Public Health. 1998;19:17–34
116. Hansen LP. Large sample properties of generalized method of moments estimators. Econometrica. 1982;50:1029–1054
117. Sargan J. The estimation of economic relationships using instrumental variables. Econometrica. 1958;26:393–415
