# prop_spline_est: The propensity-spline prediction estimator In causaldrf: Tools for Estimating Causal Dose Response Functions

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```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.

`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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50``` ```## 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) ```

### Example output ```
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causaldrf documentation built on May 2, 2019, 5:14 a.m.