generalized propensity score in r

A. Estimate propensity scores for multivariate continuous exposure by assuming joint normal conditional densities. ), 28(3), 387395. In the presence of missing data, the following value(s) for missing are allowed: First, for each variable with missingness, a new missingness indicator variable is created which takes the value 1 if the original covariate is NA and 0 otherwise. For binary treatments, the output of the call to glm(). My expectation is that age is probably related in a non-linear fashion to the probability of getting job training treatment, so I used a generalized additive model to allow for this. Naimi, A. I., Moodie, E. E. M., Auger, N., & Kaufman, J. S. (2014). Multivariate Behavioral Research, 46(3), 399424. The literature has a range of (conflicting) views on estimating uncertainty of statistics estimated after propensity score matching or weighting. For binary treatments, link can be any of those allowed by binomial(). As you go through model validation, statistical approach peer review, and customer review, adjustments are made to the analysis which require a fresh look at your approach to the question at hand. Using a t-distribution can be useful when extreme outcome values are observed (Naimi et al., 2014). The method argument in glm() is renamed to glm.method. Our results indicate that under other circumstances, the technique is doubly frail.. n by p_j designating values of the confounders for each exposure The missing values in the covariates are then replaced with 0s (this value is arbitrary and does not affect estimation). The package does not include built-in methods for estimating propensity scores; rather, it relies upon existing generalized linear modeling machinery in R. Thus, our first step in analyzing the ECLS-K data was to estimate propensity scores using a logistic regression model with one main effect for each covariate. Other arguments to density() can be specified to refine the density estimation parameters. doi:10.1093/biomet/asn055, Austin, P. C. (2011). Journal of Causal Inference, 3(1), 25-40. For binary treatments, additional arguments to glm() can be specified as well. The generalized propensity score in the M -dimensional continuous treatment is specified as follows. If its a good model, youre fine. For example, if density = "dt_2" is specified, the density used will be that of a t-distribution with 2 degrees of freedom. For ordinal treatments, the output of the call to MASS::polr(). Then the generalized propensity score is R = r (Z, X). Creating a control group by matching has the distressing side-effect of throwing away large amounts of the data, because the control group is shrunk down to the same size as the treatment group. doi:10.3102/1076998609359785, - SAEM logistic regression for missing data, Jiang, W., Josse, J., & Lavielle, M. (2019). In this video, Dr. Walter Leite, Ph.D., demonstrates how to estimate generalized propensity scores for multiple treatment versions using multinomial logistic. The generalized propensity score is an extension of Assessing covariate balance when using the generalized propensity score with quantitative or continuous exposures Stat Methods Med Res. For more information, see the Extended Description below or the main paper: Yang, S., Imbens G. W., Cui, Z., Faries, D. E., & Kadziola, Z. doi:10.1002/sim.5753, Hong, G. (2012). Matching on generalized propensity scores with continuous exposures. Version: . For example, government programs to help individuals or firms are typically not allocated at random, but go to those with higher need, or higher potential to make something out of the assistance. 2015), and empirical likelihoods If blank, dnorm() is used as recommended by Robins et al. A logical extension to the multivariate exposure would be to define our domain as the product of the range of each exposure. Id probably do it both ways and if there are wildly different results Id worry, treating that as a diagnostic warning. You dont need to limit yourself to simple comparisons, although in principle they should work. confounders for all exposures. The extension of propensity score methods to quantitative exposures has been referred to as the generalized propensity score (GPS). From this perspective, matching is a preprocessor, which can be used to prepare the data for subsequent analysis with something such as a regression model.. See get_w_from_ps() for details. In addition, kernel density estimation can be used instead of assuming a specific density for the numerator and denominator of the generalized propensity score by setting use.kernel = TRUE . either a list of numeric matrices of length m of dimension For multinomial treatments with link = "br.logit", the output of the call to brglm2::brmultinom(). 2) A Stata package for the application of semiparametric estimators of dose-response functions (2014). (Zhu et al. percentile as trim_quantile=q. This page explains the details of estimating weights from generalized linear model-based propensity scores by setting method = "ps" in the call to weightit() or weightitMSM(). Yet their applications to evaluations of multi-valued and multiple t Marginal mean weighting through stratification: a generalized method for evaluating . Biometrika, 96(1), 187-199. The GBM parameter defaults are those found in Zhu, Coffman, & Ghosh (2015). To solve this dimensionality problem, generalized propensity score (GPS) is proposed. Assume that we have a set of continuous exposures, D, of length m where each element is a matrix of dimension n\times p_{j}. This controversy could be resolved if an estimator were available that was guaranteed to be consistent whenever at least one of the two models was correct. (2017) recently. Robins, J. M., Hernn, M. (2000). With link = "logit", the option use.mclogit = TRUE can be specified to request that mclogit::mblogit() from the mclogit package is used instead, which can be faster and is recommended. Generalized propensity scores for multiple continuous treatment variables. Details We developed an innovative approach for estimating causal effects using observational data in set-tings with continuous exposures, and introduce a new framework for GPS caliper matching. Li, F., Morgan, K. L., & Zaslavsky, A. M. (2018). Propensity score analysis (PSA) is widely used in medical literature to account for confounders. In causal inference for binary treatments, the propensity score is defined as the probability of receiving the treatment given covariates. Denote any possible vector of covariates determining treatment by z and define the M -variate conditional joint density of t 1, , t M given z as g ( t, z) = f T i | Z i ( t | z). The Annals of Applied Statistics, 13(4), 23892415. In our case since the bivariate exposure is assumed to be bivariate normal, we can break both the numerator and denominator into full conditional densities knowing that each univariate conditional expression will remain normally distributed. The upshot of this is that we need to take care when defining the domain of our exposure when estimating the mvGPS. Usage The Toolkit for Weighting and Analysis of Nonequivalent Groups (twang) is an R package that implements propensity score estimation via GBM using one (or all) of four different stopping rules for selecting the optimal GBM iteration described above (e.g., mean standardized bias, maximum standardized bias, mean KS, or maximum KS across the pretreatment covariates). Let r (t, x) be the conditional density of the treatment given the covariates: (2) r t x = f T X t X = x. However, in practice, observational analyses require large administrative databases or surveys, which inevitably will have missingness in the covariates. This method can be used with binary, multinomial, and continuous treatments. When exposure is bivariate, the resulting dose-response function is a surface. I use the method described by Austin and Small as the complex bootstrap, which involves resampling from the original data and performing the propensity modelling and matching for each resample. The mean of the dose-response equation is shown below. exposure of length p_{j} for j=1,\dots,m. doi:10.1214/19-AOAS1282, Yoshida, K., Hernndez-Daz, S., Solomon, D. H., Jackson, J. W., Gagne, J. J., Glynn, R. J., & Franklin, J. M. (2017). Matching is based on propensity scores estimated with logistic regression. In addition, kernel density estimation can be used instead of assuming a specific density for the numerator and denominator of the generalized propensity score by setting use.kernel = TRUE. to be multivariate normal as well. That gives us a result of $960 (output not shown). In the presence of time-varying treatment or exposure, the conventional method m Propensity score analysis for time-dependent exposure Ann Transl Med. Then, the GPS is R = r (T, X). For continuous treatments, link can be any of those allowed by gaussian(). MatchIt includes a subsample of the original data consisting Copyright 2022 | MH Corporate basic by MH Themes, Counterfactuals and Causal Inference: Methods and Principles for Social Research, Daniel E. Ho, Kosuke Imai, Gary King, Elizabeth A. Stuart (2011). This method can be used with binary, multinomial, and continuous treatments. 8, pp. A tutorial on propensity score estimation for multiple treatments using generalized boosted models The use of propensity scores to control for pretreatment imbalances on observed variables in non-randomized or observational studies examining the causal effects of treatments or interventions has become widespread over the past decade. The final identifying assumption, positivity, is our focus when defining estimable regions for multivariate exposure. The GPS is constructed using the conditional concerned about the effect of extreme weights. Weights can also be computed using marginal mean weighting through stratification for the ATE, ATT, and ATC. For example, in an incomplete article by Posner and Ash (there may be a complete version somewhere else): While this method can be shown to have nice mathematical properties, it does not work well in practice. doi:10.1093/biomet/asn055, Austin, P. C. (2011). The function ris de ned up to almost everywhere equivalence. I call this similar because the uncertainty around all these estimates is huge, which Ill demonstrate further down the post. Matching weights to simultaneously compare three treatment groups: Comparison to three-way matching. Lee BK, Lessler J, Stuart EA (2011). Posted on April 8, 2017 by Peter's stats stuff - R in R bloggers | 0 Comments. Marginal structural models and causal inference in epidemiology. This method can be used with binary, multinomial, and continuous treatments. For binary and multinomial treatments, a binomial or multinomial regression model is used to estimate the propensity scores as the predicted probability of being in each treatment given the covariates. Journal of Educational and Behavioral Statistics, 35(5), 499531. This page explains the details of estimating weights from SuperLearner-based propensity scores by setting method = "super" in the call to weightit () or weightitMSM (). Robins, J. M., Hernn, M. ., & Brumback, B. default is 0.99. Logistic regression with missing covariates Parameter estimation, model selection and prediction within a joint-modeling framework. univariate conditional densities, i.e.. mvGPS=f_{D_{m}\mid \mathbf{C}_{m}, D_{m-1},\dots,D_{1}}\times\cdots\times f_{D_{1}\mid\mathbf{C}_{1}}. 2011). robust regression with data weighted by inverse propensity of treatment; robust regression with the original data. logical indicator for whether C is a single matrix of common This function extends ps in twang to continuous treatments. Description: This project is to make resources (data and code) for the book "Practical Propensity Score Methods Using R" (by Walter Leite, published by Sage Publications in 2017) freely available, and to update these resources as research on propensity score analysis progresses. No additional covariates are created. Computational Statistics & Data Analysis, 106907. doi:10.1016/j.csda.2019.106907, Li, F., & Li, F. (2019). See get_w_from_ps() for details. Any of the methods allowed in the method argument of polr() can be supplied to link. To estimate the ATE, you compute each unit's weight as the inverse of the probability of being in the group they are in. No additional covariates are created. (see previous post on propensity score analysis for further details). Continuous Treatments For continuous treatments, the generalized propensity score is estimated using linear regression. w=\frac{f_{\mathbf{D}}}{f_{\mathbf{D}\mid \mathbf{C}_{1},\dots,\mathbf{C}_{m}}}. 2007, W aernbaum 2012). (2019) for information on this method. Checking balance as shown above is one of the key diagnostics to determining the legitimacy of this assumption in practice. plot = TRUE can be specified to plot the density for the numerator and denominator, which can be helpful in diagnosing extreme weights. Balance analysis prior to the implementation of propensity scores 3. The covariates output in the resulting weightit object will be the original covariates with the NAs. 5, 6. COVARIATE BALANCING PROPENSITY SCORE 157 of these promising methods, however, presume the accurate estimation of the un-known generalized propensity score. Heres code that bootstraps four of the methods of estimating treatment effect above: Those are big confidence intervals - reflecting the small sample size and the difficulty of picking up an impact of an intervention amongst all the complexities of income determinants. By standard results on Intuitively, treatment cases that resemble the controls are interesting and given more weight, and control cases that look like they should have got the treatment are interesting and get more weight. 42, No. For continuous treatments, a generalized linear model is used to estimate generalized propensity scores as the conditional density of treatment given the covariates. Note that trimming is applied at Multivariate Generalized Propensity Score Description. have been shown to balance confounders and return unbiased estimated of the 2018). (2000). fit the model without weights. doi:10.1515/ijb-2012-0030, Crump, R. K., Hotz, V. J., Imbens, G. W., & Mitnik, O. Assessing covariate balance when using the generalized propensity score with quantitative or continuous exposures. In most cases, the generalized propensity score model performs comparably to the Oracle model. Ignored if use.kernel = TRUE (described below). The generalized propensity score (GPS) method allows a flexible modeling of the exposure-response function within a potential outcomes approach to causal inference. These The proposed balance diagnostics seem therefore appropriate to assess balance for the generalized propensity score (GPS) under multiple imputation. For methods other than mvGPS which can only estimate univariate continuous exposure, each exposure is fit separately so that weights are generated for both exposures. So here is my robust M estimator regression, using inverse propensity of treatment as weights, where propensity of treatment was modelled earlier as a generalized additive model on all explanatory variables and non-linearly with age: This gives a treatment estimate of $910 and I think its my best point estimate so far. Weights are constructed as. In practice which would I do? Journal of Educational and Behavioral Statistics, 35(5), 499531. prefix can be added (e.g., "br.logit"); this changes the fitting method to the bias-corrected generalized linear models implemented in the brglm2 package. For continuous treatments in the presence of missing data with missing = "saem", additional arguments are passed to miss.lm and predict.miss.lm. Under inverse probability of treatment weighting, proposed by Imbens in 2000, observations that receive the treatment are given weight of \frac{1}{p} and those that did not receive the treatment are given weight of \frac{1}{1-p}, where p is the probability of getting the treatment. Propensity scores are an alternative method to estimate the effect of receiving treatment when random assignment of treatments to subjects is not feasible. If TRUE, uses kernel density estimation through the density() function to estimate the numerator and denominator densities for the weights. Kennedy et al. The International Journal of Biostatistics, 9(2). p that represents common confounders for all exposures. Journal of the Royal Statistical Society: Series B, 79(4), 1229-1245. The value of the inverse of the propensity score will be extremely high, asymptotically infinity. Thanks again for this! w = f(D2|D1)f(D1)/f(D2|D1,C2,C3)f(D1|C1,C2). The generalized propensity score model performs substantially better than both the Local only and the Naive models, although, intuitively, the Local only model does show reasonable direct effect estimates. A., Almirall, D., Slaughter, M. E., Ramchand, R., & Burgette, L. F. (2013). It includes updated code and data for the examples in the book "Practical Propensity Score Methods Using R" (by Walter Leite, published by Sage . For longitudinal treatments, the weights are the product of the weights estimated at each time point. The original methods papers that introduced the GPS considered continuous outcomes such as labor earnings, 5, 6 medical expenditures, 4 and birth weight. Finally, we want to check that these weights are properly reducing the bias when we estimate the exposure treatment effect. (2020) < arXiv:2008.13767 >. This page explains the details of estimating weights from generalized linear model-based propensity scores by setting method = "ps" in the call to weightit() or weightitMSM(). Warning messages may appear otherwise about non-integer successes, and these can be ignored. The missing values in the covariates are then replaced with 0s (this value is arbitrary and does not affect estimation). Converting predicted probabilities into weights is straightforward. Balancing covariates via propensity score weighting. 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