prop_spline_est {causaldrf} R Documentation

## The propensity-spline prediction estimator

### Description

This method estimates the linear or quadratic parameters of the ADRF by estimating a least-squares fit on the basis functions which are composed of combinations of the covariates, propensity spline basis, and treatment values.

### Usage

```prop_spline_est(Y,
treat,
covar_formula = ~ 1,
covar_lin_formula = ~ 1,
covar_sq_formula = ~ 1,
data,
e_treat_1 = NULL,
degree = 1,
wt = NULL,
method = "same",
spline_df = NULL,
spline_const = 1,
spline_linear = 1,
spline_quad = 1)
```

### Arguments

 `Y` is the the name of the outcome variable contained in `data`. `treat` is the name of the treatment variable contained in `data`. `covar_formula` is the formula to describe the covariates needed to estimate the constant term: `~ X.1 + ....`. Can include higher order terms or interactions. i.e. `~ X.1 + I(X.1^2) + X.1 * X.2 + ....`. Don't forget the tilde before listing the covariates. `covar_lin_formula` is the formula to describe the covariates needed to estimate the linear term, t: `~ X.1 + ....`. Can include higher order terms or interactions. i.e. `~ X.1 + I(X.1^2) + X.1 * X.2 + ....`. Don't forget the tilde before listing the covariates. `covar_sq_formula` is the formula to describe the covariates needed to estimate the quadratic term, t^2: `~ X.1 + ....`. Can include higher order terms or interactions. i.e. `~ X.1 + I(X.1^2) + X.1 * X.2 + ....`. Don't forget the tilde before listing the covariates. `data` is a dataframe containing `Y`, `treat`, and `X`. `e_treat_1` a vector, representing the conditional expectation of `treat` from `T_mod`. Or, plug in gps estimates here to create splines from the gps values. `degree` is 1 for linear and 2 for quadratic outcome model. `wt` is weight used in lsfit for outcome regression. Default is wt = NULL. `method` is "same" if the same set of covariates are used to estimate the constant, linear, and/or quadratic term with no spline terms. If method = "different", then different sets of covariates can be used to estimate the constant, linear, and/or quadratic term. To use spline terms, it is necessary to set method = "different". covar_lin_formula and covar_sq_formula must be specified if method = "different". `spline_df` degrees of freedom. The default, spline_df = NULL, corresponds to no knots. `spline_const` is the number of spline terms to include when estimating the constant term. `spline_linear` is the number of spline terms to include when estimating the linear term. `spline_quad` is the number of spline terms to include when estimating the quadratic term.

### Details

This function estimates the ADRF by the method described in Schafer and Galagate (2015), that fits an outcome model using a function of the covariates and spline basis functions derived from the propensity function component.

### Value

`prop_spline_est` returns an object of class "causaldrf_lsfit", a list that contains the following components:

 `param` the estimated parameters. `out_mod` the result of the outcome model fit using lsfit. `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.

Little, Roderick and An, Hyonggin (2004). ROBUST LIKELIHOOD-BASED ANALYSIS OF MULTIVARIATE DATA WITH MISSING VALUES. Statistica Sinica. 14: 949–968.

Schafer, Joseph L, Kang, Joseph (2008). Average causal effects from nonrandomized studies: a practical guide and simulated example. Psychological methods, 13.4, 279.

### 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

t_mod_list <- t_mod(treat = T,
treat_formula = T ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
data = example_data,
treat_mod = "Normal")

cond_exp_data <- t_mod_list\$T_data
full_data <- cbind(example_data, cond_exp_data)

prop_spline_list <- prop_spline_est(Y = Y,
treat = T,
covar_formula = ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
covar_lin_formula = ~ 1,
covar_sq_formula = ~ 1,
data = example_data,
e_treat_1 = full_data\$est_treat,
degree = 1,
wt = NULL,
method = "different",
spline_df = 5,
spline_const = 4,
spline_linear = 4,
spline_quad = 4)

sample_index <- sample(1:1000, 100)

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

abline(prop_spline_list\$param,
prop_spline_list\$param,
lty = 2,
col = "blue",
lwd = 2)

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

rm(example_data, prop_spline_list, sample_index)
```

[Package causaldrf version 0.3 Index]