A Primer on Inverse Probability of Treatment Weighting and Marginal Structural Models

Emerging adulthood researchers are often interested in the effects of developmental tasks. The majority of transitions that occur during the period of early/emerging adulthood are not randomized; therefore, their effects on developmental trajectories are subject to potential bias due to confounding. Traditionally, confounding has been addressed using regression adjustment; however, there are viable alternatives, such as propensity score matching and inverse probability of treatment weighting. Propensity scores are probabilities of selecting treatment given values on observed covariates. Inverse probability of treatment weights are also based on estimated probabilities of treatment selection and can be used to create so-called pseudo-populations in which confounders and treatment are unrelated to each other. In longitudinal models, such weighting can occur at multiple time points. This article provides a primer on these weighting methods and illustrates their application to studies of emerging adulthood. We provide annotated computer code for both SPSS and R, for both binary and continuous treatments.

[1]  J. Pearl Remarks on the method of propensity score , 2009, Statistics in medicine.

[2]  Bianca L. De Stavola,et al.  Gformula: Estimating Causal Effects in the Presence of Time-Varying Confounding or Mediation using the G-Computation Formula , 2011 .

[3]  Arvid Sj Propensity scores and M-structures , 2009 .

[4]  S. Murphy,et al.  Assessing the Total Effect of Time-Varying Predictors in Prevention Research , 2006, Prevention Science.

[5]  B L De Stavola,et al.  Methods for dealing with time‐dependent confounding , 2013, Statistics in medicine.

[6]  R. D'Agostino Adjustment Methods: Propensity Score Methods for Bias Reduction in the Comparison of a Treatment to a Non‐Randomized Control Group , 2005 .

[7]  J. Robins A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[8]  D. Rubin,et al.  Using Multivariate Matched Sampling and Regression Adjustment to Control Bias in Observational Studies , 1978 .

[9]  S. Greenland Quantifying Biases in Causal Models: Classical Confounding vs Collider-Stratification Bias , 2003, Epidemiology.

[10]  Jasjeet S. Sekhon,et al.  Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The Matching Package for R , 2008 .

[11]  P. J. Huber The behavior of maximum likelihood estimates under nonstandard conditions , 1967 .

[12]  S. Cole,et al.  Illustrating bias due to conditioning on a collider. , 2010, International journal of epidemiology.

[13]  J. Pearl,et al.  Causal diagrams for epidemiologic research. , 1999, Epidemiology.

[14]  Mark J. van der Laan,et al.  tmle : An R Package for Targeted Maximum Likelihood Estimation , 2012 .

[15]  Noboru Murata,et al.  Boosting Algorithm , 2008, Computer Vision.

[16]  Jin Tian,et al.  Graphical Models for Inference with Missing Data , 2013, NIPS.

[17]  D. McCaffrey,et al.  Propensity score estimation with boosted regression for evaluating causal effects in observational studies. , 2004, Psychological methods.

[18]  Judea Pearl,et al.  Letter to the Editor: Remarks on the Method of Propensity Score , 2009 .

[19]  J. Robins,et al.  Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. , 2000, Epidemiology.

[20]  Wei Zhong,et al.  Assessing mediation using marginal structural models in the presence of confounding and moderation. , 2012, Psychological methods.

[21]  J. Haukoos,et al.  The Propensity Score. , 2015, JAMA.

[22]  Joseph Kang,et al.  Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data , 2007, 0804.2958.

[23]  F. Thoemmes,et al.  Personality traits and living arrangements in young adulthood: selection and socialization. , 2014, Developmental psychology.

[24]  Rajeev Dehejia,et al.  Propensity Score-Matching Methods for Nonexperimental Causal Studies , 2002, Review of Economics and Statistics.

[25]  T. Lancaster,et al.  Instrumental variables and inverse probability weighting for causal inference from longitudinal observational studies , 2004, Statistical methods in medical research.

[26]  Debashis Ghosh,et al.  A Boosting Algorithm for Estimating Generalized Propensity Scores with Continuous Treatments , 2015, Journal of causal inference.

[27]  K. Mohan,et al.  Graphical Representation of Missing Data Problems , 2015 .

[28]  F. Thoemmes,et al.  A Systematic Review of Propensity Score Methods in the Social Sciences , 2011, Multivariate behavioral research.

[29]  M. J. van der Laan,et al.  Statistical Applications in Genetics and Molecular Biology Super Learner , 2010 .

[30]  J. Brian Gray,et al.  Applied Regression Including Computing and Graphics , 1999, Technometrics.

[31]  Norman Rose,et al.  A Cautious Note on Auxiliary Variables That Can Increase Bias in Missing Data Problems , 2014, Multivariate behavioral research.

[32]  D. Rubin Using Propensity Scores to Help Design Observational Studies: Application to the Tobacco Litigation , 2001, Health Services and Outcomes Research Methodology.

[33]  H. White A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[34]  Marco Caliendo,et al.  Some Practical Guidance for the Implementation of Propensity Score Matching , 2005, SSRN Electronic Journal.

[35]  G. Shaw,et al.  Maternal pesticide exposure from multiple sources and selected congenital anomalies. , 1999 .

[36]  Joshua D. Angrist,et al.  Mostly Harmless Econometrics: An Empiricist's Companion , 2008 .

[37]  T. Therneau,et al.  The Basics of Propensity Scoring and Marginal Structural Models , 2013 .

[38]  D. Rubin,et al.  Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome , 1983 .

[39]  D. Rubin Causal Inference Using Potential Outcomes , 2005 .

[40]  J. Schafer,et al.  Average causal effects from nonrandomized studies: a practical guide and simulated example. , 2008, Psychological methods.

[41]  W. G. Cochran,et al.  Controlling Bias in Observational Studies: A Review. , 1974 .

[42]  William R Shadish,et al.  Propensity Scores , 2005, Evaluation review.

[43]  J M Robins,et al.  Identifiability, exchangeability, and epidemiological confounding. , 1986, International journal of epidemiology.

[44]  Peter C Austin,et al.  A critical appraisal of propensity‐score matching in the medical literature between 1996 and 2003 , 2008, Statistics in medicine.

[45]  A. Vinokur,et al.  Two years after a job loss: long-term impact of the JOBS program on reemployment and mental health. , 2000, Journal of occupational health psychology.

[46]  Catherine P. Bradshaw,et al.  The use of propensity scores to assess the generalizability of results from randomized trials , 2011, Journal of the Royal Statistical Society. Series A,.

[47]  D. Rubin,et al.  Estimation of causal effects of binary treatments in unconfounded studies with one continuous covariate , 2017, Statistical methods in medical research.

[48]  Elizabeth A Stuart,et al.  Matching methods for causal inference: A review and a look forward. , 2010, Statistical science : a review journal of the Institute of Mathematical Statistics.

[49]  Onyebuchi A Arah,et al.  Bias Formulas for Sensitivity Analysis of Unmeasured Confounding for General Outcomes, Treatments, and Confounders , 2011, Epidemiology.

[50]  T. VanderWeele Sensitivity Analysis: Distributional Assumptions and Confounding Assumptions , 2008, Biometrics.

[51]  J. Sterne,et al.  G-estimation of Causal Effects, Allowing for Time-varying Confounding , 2002 .

[52]  P. Austin An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies , 2011, Multivariate behavioral research.

[53]  R. Berk Regression Analysis: A Constructive Critique , 2003 .

[54]  J. Robins,et al.  Marginal Structural Models and Causal Inference in Epidemiology , 2000, Epidemiology.

[55]  P. Rosenbaum The Consequences of Adjustment for a Concomitant Variable that Has Been Affected by the Treatment , 1984 .

[56]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[57]  Elizabeth A Stuart,et al.  Improving propensity score weighting using machine learning , 2010, Statistics in medicine.

[58]  Ulrich Trautwein,et al.  Military Training and Personality Trait Development , 2012, Psychological science.

[59]  G. King,et al.  Causal Inference without Balance Checking: Coarsened Exact Matching , 2012, Political Analysis.

[60]  Gary King,et al.  The Dangers of Extreme Counterfactuals , 2006, Political Analysis.

[61]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[62]  Stephen R Cole,et al.  Constructing inverse probability weights for marginal structural models. , 2008, American journal of epidemiology.

[63]  Daniel Westreich,et al.  Propensity score estimation: neural networks, support vector machines, decision trees (CART), and meta-classifiers as alternatives to logistic regression. , 2010, Journal of clinical epidemiology.

[64]  K. Imai,et al.  Covariate balancing propensity score , 2014 .

[65]  Ronald B. Geskus,et al.  ipw: An R Package for Inverse Probability Weighting , 2011 .

[66]  S. Vansteelandt,et al.  On regression adjustment for the propensity score , 2014, Statistics in medicine.

[67]  Tyler J VanderWeele,et al.  A marginal structural model analysis for loneliness: implications for intervention trials and clinical practice. , 2011, Journal of consulting and clinical psychology.

[68]  Mark J. van der Laan,et al.  Targeted Maximum Likelihood Estimation: A Gentle Introduction , 2009 .