imtp

Non-Parametric Causal Effects Based on Incremental Propensity Score Interventions

An implementation of the incremental propensity score intervention estimator described in Kennedy (2019). The UI is implemented in the same manner as the lmtp package and provides a compliment to the main objective of lmtp for when treatment/exposure is binary.

Are incremental propensity score interventions MTPs?

Yes! A modified treatment policy is simply an intervention that can be written as a function of the natural value of exposure. Using this defintion, an incremenental propensity score intervention may be defined as a modified treatment policy. See Example 3 in Non-parametric causal effects based on longitudinal modified treatment policies for more details.

Installation

You can install the development version of imtp from GitHub with:

devtools::install_github("mtpverse/imtp")

Example

library(imtp)

n <- 1000
W <- matrix(rnorm(n*3), ncol = 3)
A <- rbinom(n, 1, 1/(1 + exp(-(.2*W[,1] - .1*W[,2] + .4*W[,3]))))
Y <- A + 2*W[,1] + W[,3] + W[,2]^2 + rnorm(n)
R <- rbinom(n, 1, 0.9)
tmp <- data.frame(W, A, R, Y = ifelse(R == 1, Y, NA_real_))

imtp_tmle(tmp, "A", "Y", paste0("X", 1:3), cens = "R", delta = 2, outcome_type = "continuous")
#> IPSI Estimator: TMLE
#>          delta: 2
#> 
#> Population intervention estimate
#>       Estimate: 1.6243
#>     Std. error: 0.107
#>         95% CI: (1.4145, 1.834)

deltas <- seq(0.1, 2, length.out = 5)
fits <- lapply(deltas, function(d) imtp_tmle(tmp, "A", "Y", paste0("X", 1:3), cens = "R", delta = d, outcome_type = "continuous"))
imtp_simul(fits)
#>      theta mult.conf.low mult.conf.high
#> 1 1.064633     0.9057856       1.223480
#> 2 1.313744     1.1279433       1.499544
#> 3 1.461470     1.2513807       1.671560
#> 4 1.569143     1.3432812       1.795005
#> 5 1.630143     1.3904212       1.869865

References

Edward H. Kennedy (2019) Nonparametric Causal Effects Based on Incremental Propensity Score Interventions, Journal of the American Statistical Association, 114:526, 645-656, DOI: 10.1080/01621459.2017.1422737

Kwangho Kim and Edward H. Kennedy and Ashley I. Naimi (2019) Incremental Intervention Effects in Studies with Many Timepoints, Repeated Outcomes, and Dropout, arXiv: 1907.04004

Iván Díaz, Nicholas Williams, Katherine L. Hoffman & Edward J. Schenck (2021) Non-parametric causal effects based on longitudinal modified treatment policies, Journal of the American Statistical Association, DOI: 10.1080/01621459.2021.1955691