iptw_est {causaldrf}

The inverse probability of treatment weighting (iptw) estimator

Description

The iptw method or importance weighting method estimates the ADRF by weighting the data with stabilized or non-stabilized weights.

Usage

iptw_est(Y,
         treat,
         treat_formula,
         numerator_formula,
         data,
         degree,
         treat_mod,
         link_function,
         ...)

Arguments

Y

is the the name of the outcome variable contained in data.

treat

is the name of the treatment variable contained in data.

treat_formula

an object of class "formula" (or one that can be coerced to that class) that regresses treat on a linear combination of X: a symbolic description of the model to be fitted.

numerator_formula

an object of class "formula" (or one that can be coerced to that class) that regresses treat on a linear combination of X: a symbolic description of the model to be fitted. i.e. treat ~ 1.

data

is a dataframe containing Y, treat, and X.

degree

is 1 for linear and 2 for quadratic outcome model.

treat_mod

a description of the error distribution to be used in the model for treatment. Options include: "Normal" for normal model, "LogNormal" for lognormal model, "Sqrt" for square-root transformation to a normal treatment, "Poisson" for Poisson model, "NegBinom" for negative binomial model, "Gamma" for gamma model, "Binomial" for binomial model, "Ordinal" for ordinal model, "Multinomial" for multinomial model.

link_function

specifies the link function between the variables in numerator or denominator and exposure, respectively. For treat_mod = "Gamma" (fitted using glm) alternatives are "log" or "inverse". For treat_mod = "Binomial" (fitted using glm) alternatives are "logit", "probit", "cauchit", "log" and "cloglog". For treat_mod = "Multinomial" this argument is ignored, and multinomial logistic regression models are always used (fitted using multinom). For treat_mod = "Ordinal" (fitted using polr) alternatives are "logit", "probit", "cauchit", and "cloglog".

...

additional arguments to be passed to the low level treatment regression fitting functions.

Details

This method uses inverse probability of treatment weighting to adjust for possible biases. For more details see Schafer and Galagate (2015) and Robins, Hernan, and Brumback (2000).

Value

iptw_est returns an object of class "causaldrf", a list that contains the following components:

param

parameter estimates for a iptw fit.

t_mod

the result of the treatment model fit.

num_mod

the result of the numerator model fit.

weights

the estimated weights.

weight_data

the weights.

out_mod

the outcome model.

call

the matched call.

References

Schafer, J.L., Galagate, D.L. (2015). Causal inference with a continuous treatment and outcome: alternative estimators for parametric dose-response models. Manuscript in preparation.

van der Wal, Willem M., and Ronald B. Geskus. "IPW: an R package for inverse probability weighting." Journal of Statistical Software 43.13 (2011): 1-23.

Robins, James M and Hernan, Miguel Angel and Brumback, Babette. Marginal structural models and causal inference in epidemiology. Epidemiology 11.5 (2000): 550–560.

Zhu, Yeying and Coffman, Donna L and Ghosh, Debashis. A Boosting Algorithm for Estimating Generalized Propensity Scores with Continuous Treatments. Journal of Causal Inference 3.1 (2015): 25–40.

See Also

iptw_est, ismw_est, reg_est, aipwee_est, wtrg_est, etc. for other estimates.

t_mod, overlap_fun to prepare the data for use in the different estimates.

Examples

## Example from Schafer (2015).

example_data <- sim_data

iptw_list <- iptw_est(Y = Y,
              treat = T,
              treat_formula = T ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
              numerator_formula = T ~ 1,
              data = example_data,
              degree = 1,
              treat_mod = "Normal")

sample_index <- sample(1:1000, 100)

plot(example_data$T[sample_index],
      example_data$Y[sample_index],
      xlab = "T",
      ylab = "Y",
      main = "iptw estimate")

abline(iptw_list$param[1],
        iptw_list$param[2],
        lty=2,
        lwd = 2,
        col = "blue")

legend('bottomright',
        "iptw estimate",
        lty=2,
        lwd = 2,
        col = "blue",
        bty='Y',
        cex=1)

rm(example_data, iptw_list, sample_index)


## Example from van der Wal, Willem M., and Ronald B. Geskus. (2011)
#Simulate data with continuous confounder and outcome, binomial exposure.
#Marginal causal effect of exposure on outcome: 10.
n <- 1000
simdat <- data.frame(l = rnorm(n, 10, 5))
a.lin <- simdat$l - 10
pa <- exp(a.lin)/(1 + exp(a.lin))
simdat$a <- rbinom(n, 1, prob = pa)
simdat$y <- 10*simdat$a + 0.5*simdat$l + rnorm(n, -10, 5)
simdat[1:5,]
temp_iptw <- iptw_est(Y = y,
                      treat = a,
                      treat_formula = a ~ l,
                      numerator_formula = a ~ 1,
                      data = simdat,
                      degree = 1,
                      treat_mod = "Binomial",
                      link_function = "logit")


temp_iptw[[1]]  # estimated coefficients