SumStat_cl {PSweight}

Calculate summary statistics for propensity score weighting with clustering (for binary treatment only)

Description

SumStat_cl is used to generate distributional plots of the estimated propensity scores and balance diagnostics after propensity score weighting with two-level data.

Usage

SumStat_cl(
  ps.formula = NULL,
  trtgrp = NULL,
  data = NULL,
  weight = "overlap",
  delta = 0,
  nAGQ = 1L
)

Arguments

ps.formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the propensity score model to be fitted. Additional details of model specification are given under "Details".

trtgrp

an optional character defining the "treated" population for estimating the average treatment effect among the treated (ATT). Only necessary if weight = "treated". This option can also be used to specify the treatment (in a two-treatment setting). Default value is the last group in the alphebatic order.

data

an data frame containing the variables in the propensity score model. If not found in data, the variables are taken from environment(formula).

weight

a character or vector of characters including the types of weights to be used. "IPW" specifies the inverse probability weights for estimating the average treatment effect among the combined population (ATE). "treated" specifies the weights for estimating the average treatment effect among the treated (ATT). "overlap" specifies the (generalized) overlap weights for estimating the average treatment effect among the overlap population (ATO), or population at clinical equipoise. "matching" specifies the matching weights for estimating the average treatment effect among the matched population (ATM). "entropy" specifies the entropy weights for the average treatment effect of entropy weighted population (ATEN). Default is "overlap".

delta

trimming threshold for estimated (generalized) propensity scores. Should be no larger than 1 / number of treatment groups. Default is 0, corresponding to no trimming.

nAGQ

integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation. Please refer to lme4 package for more details.

Details

A typical form for ps.formula is treatment ~ terms+1|clusters where treatment is the treatment variable, terms is a series of terms which specifies a linear predictor for treatment, and clusters is the cluster indicator. The current version supports two-level models and the random-effects term is required to be the last piece in the formula. ps.formula specifies a mixed-effects logistic regression model for estimating propensity scores. The treatment group corresponds to the last group in the alphebatic order, unless otherwise specified by trtgrp.

Current version of PSweight allows for five types of propensity score weights used to estimate ATE ("IPW"), ATT ("treated"), and ATO("overlap"), ATM ("matching") and ATEN ("entropy"). These weights are members of a larger class of balancing weights defined in Li, Morgan, and Zaslavsky (2018). When there is a practical violation of the positivity assumption, delta defines the symmetric propensity score trimming rule following Crump et al. (2009). With multiple treatments, delta defines the multinomial trimming rule introduced in Yoshida et al. (2019). The overlap weights can also be considered as a data-driven continuous trimming strategy without specifying trimming rules, see Li, Thomas and Li (2019). Additional details on balancing weights and generalized overlap weights for multiple treatment groups are provided in Li and Li (2019). For details about matching weights and entropy weights, please refer to Li and Greene (2013) and Zhou, Matsouaka and Thomas (2020).

Value

SumStat_cl returns a SumStat object including a list of the following value: treatment group, propensity scores, fitted propensity model, propensity score weights, effective sample sizes, and balance statistics. A summary of SumStat can be obtained with summary.SumStat.

trtgrp

a character indicating the treatment group.

propensity

a data frame of estimated propensity scores.

ps.fitObjects

the fitted propensity model details

ps.weights

a data frame of propensity score weights.

ess

a table of effective sample sizes. This serves as a conservative measure to characterize the variance inflation or precision loss due to weighting, see Li and Li (2019).

unweighted.sumstat

A list of tables including covariate means and variances by treatment group and standardized mean differences.

ATE.sumstat

If "IPW" is included in weight, this is a list of summary statistics using inverse probability weighting.

ATT.sumstat

If "treated" is included in weight, this is a list of summary statistics using the ATT weights.

ATO.sumstat

If "overlap" is included in weight, this is a list of summary statistics using the overlap weights.

ATM.sumstat

If "matching" is included in weight, this is a list of summary statistics using the matching weights.

ATEN.sumstat

If "entropy" is included in weight, this is a list of summary statistics using the entropy weights.

trim

If delta > 0, this is a table summarizing the number of observations before and after trimming.

References

Crump, R. K., Hotz, V. J., Imbens, G. W., Mitnik, O. A. (2009). Dealing with limited overlap in estimation of average treatment effects. Biometrika, 96(1), 187-199.

Li, L., Greene, T. (2013). A weighting analogue to pair matching in propensity score analysis. The International Journal of Biostatistics, 9(2), 215-234.

Li, F., Morgan, K. L., Zaslavsky, A. M. (2018). Balancing covariates via propensity score weighting. Journal of the American Statistical Association, 113(521), 390-400.

Li, F., Thomas, L. E., Li, F. (2019). Addressing extreme propensity scores via the overlap weights. American Journal of Epidemiology, 188(1), 250-257.

Li, F., Li, F. (2019). Propensity score weighting for causal inference with multiple treatments. The Annals of Applied Statistics, 13(4), 2389-2415.

Zhou, Y., Matsouaka, R. A., Thomas, L. (2020). Propensity score weighting under limited overlap and model misspecification. Statistical Methods in Medical Research 29(12), 3721-3756.

Li, F., Zaslavsky, A. M., & Landrum, M. B. (2013). Propensity score weighting with multilevel data. Statistics in Medicine, 32(19), 3373-3387.

Examples

data("psdata_cl")
# the propensity model
# ps.formula<-trt~cov1+cov2+cov3+cov4+cov5+cov6+(1|clt)

# using SumStat to estimate propensity scores
# msstat <- SumStat_cl(ps.formula, trtgrp="1", data=psdata_cl,
#   weight=c("IPW","overlap","treated","entropy","matching"))
#summary(msstat)