**nawtilus** provides a procedure for the navigated weighting (NAWT) proposed by Katsumata (2020), which estimates a pre-specified parameter of interest (e.g., the average treatment effects or the average treatment effects on the treated) with the inverse probability weighting where propensity scores are estimated using estimating equations suitable for the parameter of interest. It also provides several tools for summarizing and checking the estimation results, including a covariate balance check and an inverse probability weights plot.

Katsumata, Hiroto. 2020. “Navigated Weighting to Improve Inverse Probability Weighting for Missing Data Problems and Causal Inference.” Working Paper, arxiv:2005.10998.

Katsumata, Hiroto. 2020. nawtilus: Navigated Weighting for the Inverse Probability Weighting. R package version 0.1.4. https://CRAN.R-project.org/package=nawtilus.

You can install the released version of nawtilus from CRAN with:

And the development version from GitHub with:

This example shows how to use **nawtilus** for estimation of parameter of interest.

First, load the package and make toy data.

```
# Load the package
library(nawtilus)
# Make toy data
# ATT estimation
# True ATT is 10
tau <- 10
set.seed(12345)
n <- 1000
X <- matrix(rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 4)
prop <- 1 / (1 + exp(X[, 1] - 0.5 * X[, 2] + 0.25 * X[, 3] + 0.1 * X[, 4]))
treat <- rbinom(n, 1, prop)
y <- 210 + 27.4 * X[, 1] + 13.7 * X[, 2] + 13.7 * X[, 3] + 13.7 * X[, 4] +
tau * treat + rnorm(n)
# Data frame
df <- data.frame(X, treat, y)
colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y")
```

Then, specify a model for propensity score estimation.

Fit the model for the average treatment effects on the treated (ATT) estimation using `nawt()`

with the default setting (a power weighting function with α = 2).

```
# Power weighting function with alpha = 2
fit <- nawt(formula = formula_c, outcome = "y", estimand = "ATT",
method = "score", data = df, alpha = 2)
#> [1] "Estimate weights for the ATT estimation by (weighted) score conditions"
```

You can summarize the results easily with `summary()`

.

```
summary(fit)
#>
#> Call:
#> nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score",
#> data = df, alpha = 2)
#>
#> ATT estimates: 10.54
#>
#> Coefficients:
#> Estimate Std..Error z.value Pr...z..
#> est 10.54356 1.19535 8.8205 0.000e+00 ***
#> (Intercept) 0.01142 0.07642 0.1494 8.812e-01
#> x1 -1.05398 0.12718 -8.2871 2.220e-16 ***
#> x2 0.43165 0.09211 4.6860 2.786e-06 ***
#> x3 -0.21745 0.08829 -2.4629 1.378e-02 *
#> x4 0.12933 0.09039 1.4308 1.525e-01
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Effective N for the propensity score estimation: 610.16
#> Effective N for the ATT estimation:
#> treatment: 475
#> control: 156.68
```

Note that the estimated coefficients except for `est`

are for the propensity score estimation.

Check covariate balance between the treatment and control groups before and after the NAWT with `cbcheck()`

.

```
oldpar <- par(no.readonly = TRUE) # Just for adjusting plot margins
par(mar = c(5.1, 5.1, 4.1, 2.1)) # Just for adjusting plot margins
cbcheck(fit)
```

Let’s compare the inverse probability weights estimated by the nawt with those estimated by the standard logistic regression with `plot()`

.

Finally, check the weights used in propensity score estimation and distribution of the estimated propensity scores in the NAWT with `plot_omega()`

.