Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies
In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity‐score matching is increasingly being used to estimate the effects of exposures using observational data....
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| Published in | Pharmaceutical statistics : the journal of the pharmaceutical industry Vol. 10; no. 2; pp. 150 - 161 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
01.03.2011
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1539-1604 1539-1612 1539-1612 |
| DOI | 10.1002/pst.433 |
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| Abstract | In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity‐score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity‐score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre‐specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means. Copyright © 2010 John Wiley & Sons, Ltd. |
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| AbstractList | In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity‐score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity‐score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre‐specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means. Copyright © 2010 John Wiley & Sons, Ltd. In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity-score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity-score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre-specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means.In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity-score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity-score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre-specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means. In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity-score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity-score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre-specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means. |
| Author | Austin, Peter C. |
| AuthorAffiliation | a Institute for Clinical Evaluative Sciences Toronto, Ont., Canada b Dalla Lana School of Public Health Sciences, University of Toronto Ont., Canada c Department of Health Management, Policy and Evaluation, University of Toronto Ont., Canada |
| AuthorAffiliation_xml | – name: b Dalla Lana School of Public Health Sciences, University of Toronto Ont., Canada – name: a Institute for Clinical Evaluative Sciences Toronto, Ont., Canada – name: c Department of Health Management, Policy and Evaluation, University of Toronto Ont., Canada |
| Author_xml | – sequence: 1 givenname: Peter C. surname: Austin fullname: Austin, Peter C. email: peter.austin@ices.on.ca organization: Institute for Clinical Evaluative Sciences, Toronto, Ont., Canada |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/20925139$$D View this record in MEDLINE/PubMed |
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| References | Austin PC. The performance of different propensity score methods for estimating marginal odds ratios. Statistics in Medicine. 2007; 26:3078-3094. Sinclair JC, Bracken MB. Clinically useful measures of effect in binary analyses of randomized trials. Journal of Clinical Epidemiology 1994; 47:881-889. Greenland S. Interpretation and choice of effect measures in epidemiologic analyses. American Journal of Epidemiology 1987; 125:761-768. Austin PC. The relative ability of different propensity-score methods to balance measured covariates between treated and untreated subjects in observational studies. Medical Decision Making 2009; 29:661-677. Lee DS, Austin PC, Rouleau JL, Liu PP, Naimark D, Tu JV. Predicting mortality among patients hospitalized for heart failure: derivation and validation of a clinical model. Journal of the American Medical Association 2003; 290:2581-2587. Jaeschke R, Guyatt G, Shannon H, Walter S, Cook D, Heddle N. Basis statistics for clinicians 3: assessing the effects of treatment: measures of association. Canadian Medical Association Journal 1995; 152:351-357. Cochran WG, Rubin DB. Controlling bias in observational studies: a review. Sankhya: The Indian Journal of Statistics 1973;35:416-466. Cohen J. Statistical Power Analysis for the Behavioral Sciences (2nd edn). Lawrence Erlbaum Associates Publishers: Hillsdale NJ, 1988. Austin PC. Some methods of propensity-score matching had superior performance to others: results of an empirical investigation and Monte Carlo simulations. Biometrical Journal 2009; 51:171-184. DOI: 10.1002/bimj.200810488. Rosenbaum PR, Rubin DB. Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association 1984; 79:516-524. Austin PC. Propensity-score matching in the cardiovascular surgery literature from 2004 to 2006: a systematic review and suggestions for improvement. Journal of Thoracic and Cardiovascular Surgery 2007; 134:1128-1135. Austin PC. Type I error rates, coverage of confidence intervals, and variance estimation in propensity-score matched analyses. The International Journal of Biostatistics 2009; 5(1). Article 13. DOI: 10.2202/1557-4679.1146. Austin PC. The performance of different propensity score methods for estimating difference in proportions (risk differences or absolute risk reductions) in observational studies. Statistics in Medicine 2010; DOI: 10.1002/sim.3854. Imbens GW. Nonparametric estimation of average treatment effects under exogeneity: a review. The Review of Economics and Statistics 2004; 86:4-29. Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika 1983; 70:41-55. Austin PC. Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Statistics in Medicine 2009; 28:3083-3107. Austin PC. A critical appraisal of propensity score matching in the medical literature from 1996 to 2003. Statistics in Medicine 2008; 27:2037-2049. Agresti A, Min Y. Effects and non-effects of paired identical observations in comparing proportions with binary matched-pairs data. Statistics in Medicine 2004; 23:65-75. Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. British Medical Journal 1995; 310:452-454. Austin PC, Stafford J. The performance of two data-generation processes for data with specified marginal treatment odds ratios. Communications in Statistics-Simulation and Computation 2008; 37:1039-1051. Austin PC, Mamdani MM. A comparison of propensity score methods: a case-study estimating the effectiveness of post-AMI statin use. Statistics in Medicine 2006; 25:2084-2106. Austin PC. A report card on propensity-score matching in the cardiology literature from 2004 to 2006: results of a systematic review. Circulation: Cardiovascular Quality and Outcomes 2008; 1:62-67. Rosenbaum PR, Rubin DB. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician 1985; 39:33-38. Schechtman E. Odds ratio, relative risk, absolute risk reduction, and the number needed to treat-which of these should we use? Value in Health 2002; 5:431-436. Austin PC. A data-generation process for data with specified risk differences or numbers needed to treat. Communications in Statistics-Simulation and Computation 2010; 39:563-577. Stürmer T, Joshi M, Glynn RJ, Avorn J, Rothman KJ, Schneeweiss S. A review of the application of propensity score methods yielded increasing use, advantages in specific settings, but not substantially different estimates compared with conventional multivariable methods. Journal of Clinical Epidemiology 2006; 59:437-447. Flury BK, Riedwyl H. Standard distance in univariate and multivariate analysis. The American Statistician 1986; 40:249-251. Tu JV, Donovan LR, Lee DS, Austin PC, Ko DT, Wang JT, Newman AM. Quality of Cardiac Care in Ontario-Phase 1. Report 1. Institute for Clinical Evaluative Sciences: Toronto, 2004. Austin PC, Grootendorst P, Normand SLT, Anderson GM. Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: a Monte Carlo study. Statistics in Medicine 2007; 26:754-768. 2004; 86 1987; 125 2010 1973; 35 2010; 39 2002; 5 2004; 23 2006; 59 2008; 37 1994; 47 2003; 290 2004 1995; 310 1983; 70 2008; 1 1995; 152 2009; 29 2009; 28 1985; 39 2007; 134 2009; 51 1986; 40 2006; 25 2008; 27 1984; 79 2009; 5 2007; 26 1988 e_1_2_7_5_2 e_1_2_7_4_2 e_1_2_7_3_2 e_1_2_7_2_2 e_1_2_7_9_2 e_1_2_7_8_2 e_1_2_7_7_2 e_1_2_7_6_2 e_1_2_7_19_2 e_1_2_7_18_2 e_1_2_7_17_2 e_1_2_7_16_2 e_1_2_7_15_2 e_1_2_7_13_2 e_1_2_7_12_2 e_1_2_7_11_2 e_1_2_7_10_2 Tu JV (e_1_2_7_26_2) 2004 e_1_2_7_27_2 e_1_2_7_28_2 e_1_2_7_29_2 Jaeschke R (e_1_2_7_14_2) 1995; 152 Cochran WG (e_1_2_7_23_2) 1973; 35 e_1_2_7_25_2 e_1_2_7_24_2 e_1_2_7_30_2 e_1_2_7_21_2 e_1_2_7_20_2 Cohen J (e_1_2_7_22_2) 1988 12201860 - Value Health. 2002 Sep-Oct;5(5):431-6 19197955 - Biom J. 2009 Feb;51(1):171-84 7730891 - J Clin Epidemiol. 1994 Aug;47(8):881-9 17976439 - J Thorac Cardiovasc Surg. 2007 Nov;134(5):1128-35 19757444 - Stat Med. 2009 Nov 10;28(25):3083-107 18038446 - Stat Med. 2008 May 30;27(12):2037-49 20031790 - Circ Cardiovasc Qual Outcomes. 2008 Sep;1(1):62-7 20108233 - Stat Med. 2010 Sep 10;29(20):2137-48 16220490 - Stat Med. 2006 Jun 30;25(12):2084-106 7828099 - CMAJ. 1995 Feb 1;152(3):351-7 14695640 - Stat Med. 2004 Jan 15;23(1):65-75 16632131 - J Clin Epidemiol. 2006 May;59(5):437-47 3551588 - Am J Epidemiol. 1987 May;125(5):761-8 19684288 - Med Decis Making. 2009 Nov-Dec;29(6):661-77 20949126 - Int J Biostat. 2009;5(1):Article 13 16783757 - Stat Med. 2007 Feb 20;26(4):754-68 17187347 - Stat Med. 2007 Jul 20;26(16):3078-94 14625335 - JAMA. 2003 Nov 19;290(19):2581-7 7873954 - BMJ. 1995 Feb 18;310(6977):452-4 |
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Sankhya: The Indian Journal of Statistics 1973;35:416-466. – reference: Sinclair JC, Bracken MB. Clinically useful measures of effect in binary analyses of randomized trials. Journal of Clinical Epidemiology 1994; 47:881-889. – reference: Flury BK, Riedwyl H. Standard distance in univariate and multivariate analysis. The American Statistician 1986; 40:249-251. – reference: Austin PC. A data-generation process for data with specified risk differences or numbers needed to treat. Communications in Statistics-Simulation and Computation 2010; 39:563-577. – reference: Austin PC, Grootendorst P, Normand SLT, Anderson GM. Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: a Monte Carlo study. Statistics in Medicine 2007; 26:754-768. – reference: Austin PC. Some methods of propensity-score matching had superior performance to others: results of an empirical investigation and Monte Carlo simulations. Biometrical Journal 2009; 51:171-184. DOI: 10.1002/bimj.200810488. – reference: Austin PC. A report card on propensity-score matching in the cardiology literature from 2004 to 2006: results of a systematic review. Circulation: Cardiovascular Quality and Outcomes 2008; 1:62-67. – reference: Rosenbaum PR, Rubin DB. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician 1985; 39:33-38. – reference: Imbens GW. Nonparametric estimation of average treatment effects under exogeneity: a review. The Review of Economics and Statistics 2004; 86:4-29. – reference: Austin PC. The performance of different propensity score methods for estimating difference in proportions (risk differences or absolute risk reductions) in observational studies. Statistics in Medicine 2010; DOI: 10.1002/sim.3854. – reference: Austin PC. The performance of different propensity score methods for estimating marginal odds ratios. Statistics in Medicine. 2007; 26:3078-3094. – reference: Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika 1983; 70:41-55. – reference: Rosenbaum PR, Rubin DB. Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association 1984; 79:516-524. – reference: Stürmer T, Joshi M, Glynn RJ, Avorn J, Rothman KJ, Schneeweiss S. A review of the application of propensity score methods yielded increasing use, advantages in specific settings, but not substantially different estimates compared with conventional multivariable methods. Journal of Clinical Epidemiology 2006; 59:437-447. – reference: Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. British Medical Journal 1995; 310:452-454. – reference: Austin PC, Stafford J. The performance of two data-generation processes for data with specified marginal treatment odds ratios. Communications in Statistics-Simulation and Computation 2008; 37:1039-1051. – reference: Austin PC. A critical appraisal of propensity score matching in the medical literature from 1996 to 2003. Statistics in Medicine 2008; 27:2037-2049. – reference: Austin PC, Mamdani MM. A comparison of propensity score methods: a case-study estimating the effectiveness of post-AMI statin use. Statistics in Medicine 2006; 25:2084-2106. – reference: Austin PC. Propensity-score matching in the cardiovascular surgery literature from 2004 to 2006: a systematic review and suggestions for improvement. Journal of Thoracic and Cardiovascular Surgery 2007; 134:1128-1135. – reference: Schechtman E. Odds ratio, relative risk, absolute risk reduction, and the number needed to treat-which of these should we use? Value in Health 2002; 5:431-436. – reference: Tu JV, Donovan LR, Lee DS, Austin PC, Ko DT, Wang JT, Newman AM. Quality of Cardiac Care in Ontario-Phase 1. Report 1. Institute for Clinical Evaluative Sciences: Toronto, 2004. – reference: Agresti A, Min Y. Effects and non-effects of paired identical observations in comparing proportions with binary matched-pairs data. Statistics in Medicine 2004; 23:65-75. – reference: Greenland S. Interpretation and choice of effect measures in epidemiologic analyses. American Journal of Epidemiology 1987; 125:761-768. – reference: Lee DS, Austin PC, Rouleau JL, Liu PP, Naimark D, Tu JV. Predicting mortality among patients hospitalized for heart failure: derivation and validation of a clinical model. Journal of the American Medical Association 2003; 290:2581-2587. – reference: Austin PC. Type I error rates, coverage of confidence intervals, and variance estimation in propensity-score matched analyses. 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| Title | Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies |
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