Propensity score interval matching: using bootstrap confidence intervals for accommodating estimation errors of propensity scores

BMC Medical Research Methodology

Haiyan Bai¹  Wei Pan² 

[1] Department of Educational and Human Sciences, University of Central Florida, Orlando 32816, FL, USA;School of Nursing, Duke University, DUMC 3322, 307 Trent Drive, Durham 27710, NC, USA

关键词: Causal inference;    Confidence intervals;    The bootstrap;    Caliper matching;    Nearest neighbour matching;    Propensity score matching;    Propensity score methods;    Observational studies;   

Others  :  1222444
DOI  :  10.1186/s12874-015-0049-3

 received in 2014-11-08, accepted in 2015-07-13,  发布年份 2015

【 摘 要 】

Background

Propensity score methods have become a popular tool for reducing selection bias in making causal inference from observational studies in medical research. Propensity score matching, a key component of propensity score methods, normally matches units based on the distance between point estimates of the propensity scores. The problem with this technique is that it is difficult to establish a sensible criterion to evaluate the closeness of matched units without knowing estimation errors of the propensity scores.

Methods

The present study introduces interval matching using bootstrap confidence intervals for accommodating estimation errors of propensity scores. In interval matching, if the confidence interval of a unit in the treatment group overlaps with that of one or more units in the comparison group, they are considered as matched units.

Results

The procedure of interval matching is illustrated in an empirical example using a real-life dataset from the Nursing Home Compare, a national survey conducted by the Centers for Medicare and Medicaid Services. The empirical example provided promising evidence that interval matching reduced more selection bias than did commonly used matching methods including the rival method, caliper matching. Interval matching’s approach methodologically sounds more meaningful than its competing matching methods because interval matching develop a more “scientific” criterion for matching units using confidence intervals.

Conclusions

Interval matching is a promisingly better alternative tool for reducing selection bias in making causal inference from observational studies, especially useful in secondary data analysis on national databases such as the Centers for Medicare and Medicaid Services data.

【 授权许可】

   
2015 Pan and Bai.

【 图 表 】

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

【 参考文献 】

• [1]Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983; 70(1):41-55.
• [2]Propensity score analysis: Fundamentals and developments. The Guilford Press, New York, NY; 2015.
• [3]McCaffrey DF, Ridgeway G, Morral AR. Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychological methods. 2004; 9(4):403-425.
• [4]Cochran WG, Rubin DB. Controlling bias in observational studies: A review. Sankhyā: The Indian Journal of Statistics, Series A. 1973; 35(4):417-446.
• [5]Efron B, Tibshirani RJ. An introduction to the bootstrap. CRC Press LLC, New York, NY; 1998.
• [6]Design for Nursing Home Compare five-star quality rating system: Technical users’ guide. http://www. cms.gov/Medicare/Provider-Enrollment-and-Certification/CertificationandComplianc/Downloads/usersguide.pdf webcite
• [7]Ho DE, Imai K, King G, Stuart EA: Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political Analysis 2007.
• [8]Rosenbaum PR, Rubin DB. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician. 1985; 39(1):33-38.
• [9]Austin PC. Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies. Pharmaceutical statistics. 2011; 10(2):150-161.
• [10]Rosenbaum PR. Optimal matching for observational studies. Journal of the American Statistical Association. 1989; 84(408):1024-1032.
• [11]Gu XS, Rosenbaum PR. Comparison of multivariate matching methods: Structures, distances, and algorithms. Journal of Computational and Graphical Statistics. 1993; 2(4):405-420.
• [12]Ho DE, Imai K, King G, Stuart EA. MatchIt: Nonparametric preprocessing for parametric causal inference. Journal of Statistical Software. 2011; 42(8):1-28.
• [13]Austin PC. An Introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivariate behavioral research. 2011; 46(3):399-424.
• [14]Bai H. A comparison of propensity score matching methods for reducing selection bias. International Journal of Research & Method in Education. 2011; 34(1):81-107.
• [15]Guo S, Barth RP, Gibbons C. Propensity score matching strategies for evaluating substance abuse services for child welfare clients. Children and Youth Services Review. 2006; 28(4):357-383.
• [16]Lutfiyya MN, Gessert CE, Lipsky MS. Nursing home quality: A comparative analysis using CMS Nursing Home Compare data to examine differences between rural and nonrural facilities. Journal of the American Medical Directors Association. 2013; 14(8):593-598.
• [17]Rural–urban continuum codes. http://www. ers.usda.gov/data-products/rural-urban-continuum-codes/documentation.aspx webcite
• [18]Brookhart MA, Schneeweiss S, Rothman KJ, Glynn RJ, Avorn J, Stürmer T. Variable selection for propensity score models. Am J Epidemiol. 2006; 163(12):1149-1156.
• [19]Don’t be loopy: Re-sampling and simulation the SAS® way. http://www2. sas.com/proceedings/forum2007/183-2007.pdf webcite
• [20]Local and global optimal propensity score matching. http://www2. sas.com/proceedings/forum2007/185-2007.pdf webcite
• [21]Caliendo M, Kopeinig S. Some practical guidance for the implementation of propensity score matching. Journal of Economic Surveys. 2008; 22(1):31-72.
• [22]Rubin DB. Multivariate matching methods that are equal percent bias reducing, II: Maximums on bias Rreduction for fixed sample sizes. Biometrics. 1976; 32(1):121-132.
• [23]Rubin DB. Multivariate matching methods that are equal percent bias reducing, I: Some examples. Biometrics. 1976; 32(1):109-120.