# Graphic for data and loess-based estimate of effect size after propensity score adjustment Plots data points using propesity scores vs. the response, separately for treatment and control groups; points are distinguished by both type and color for the two groups. Also shows (non-linear, loess-based) regression curves for both groups. The loess regresion curves are then used to derive an overall estimate of effect size (based on number and/or location of strata as set by the user). Several other statistics are also provided, for both description and inference. Graphic motivated by a suggestion of R. L. Obenchain. ```r loess.psa( response, treatment = NULL, propensity = NULL, family = "gaussian", span = 0.7, degree = 1, minsize = 5, xlim = c(0, 1), colors = c("dark blue", "dark green", "blue", "dark green"), legend.xy = "topleft", legend = NULL, int = 10, lines = TRUE, strata.lines = TRUE, rg = TRUE, xlab = "Estimated Propensity Scores", ylab = "Response", pch = c(16, 1), ... ) ``` ## Arguments - `response`: Either a numeric vector containing the response of interest in a propensity score analysis, or a three column array containing response, treatment and strata. - `treatment`: Binary variable of same length as `response`; 0 for 'control,' 1 for 'treatment.' - `propensity`: Numeric vector of estimated propensity scores. - `family`: Passed to loess. Either `"gaussian"` (default) or `"symmetric"`. - `span`: Parameter passed to loess governing degree of smoothing. Default = 0.7. - `degree`: Parameter passed to loess governing degree of polynomials used. Default = 1 - `minsize`: Integer. Determines the minimum number of observations in each stratum treatment group allowed. If one of the treatment groups in a given statum does not meet this minsize, then all observations in this stratum are ignored as far as the effect size calculation is concerned. - `xlim`: Binary vector `(min, max)` providing the horizontal axis minimum and maximum. Default is `c(0, 1)`. - `colors`: List of four colors used for control points, treatment points, control loess line, treatment loess line respectively. Default = `c("seagreen3", "goldenrod1", "seagreen4", "goldenrod3")`. - `legend.xy`: Coordinates for legend box, see `legend`. Default = `"topleft"`. - `legend`: Binary character vector containing the text of the legend. Default is taken from `treatment`. - `int`: Integer or ordered vector. If an integer is used, it represents the maximum number of equally sized strata. Alternatively, it may be a vector of cuts of the unit interval. Lower and upper ends need not be included. See examples. Default = 10. - `lines`: Logical; fitted loess values are plotted by default as points. If true, values are plotted as two lines. - `strata.lines`: Logical; default = `TRUE`. Creates light vertical lines that delineate strata. - `rg`: Logical; if `TRUE` (default) then rug plots are given for treatment and control propensity score and response distributions. - `xlab`: X axis label, default = `"Estimated Propensity Scores"`. - `ylab`: Y axis label, default = `"Response"`. - `pch`: Character types for plotted points, default = `c(16, 1)`. Note: must be of length 2 to allow different plotting points for each treatment. - ``...``: Optional parameters passed to points command. ## Returns In addition to the plot, the function returns a list with the following components: - **ATE**: Estimated effect size based upon (number of) strata defined by `int`; that is, this is the Average Treatment Effect, after propensity-based adjustment. - **se.wtd**: Weighted standard error based on pooling of within-strata variance estimates. - **CI.95**: Approximate 95% confidence interval for the overall effect size (conditional on the specification of `int`). - **summary.strata**: A table with rows corresponding to strata; first two columns show counts (by statum) for both control and treatment; followed by mean differences for all strata. for control and treatment, followed by mean differences for all strata. The weighted average difference yields the effect size noted above. ## Examples ```r #Artificial example where ATE should be 1 over all of (0,1). response1 <- c(rep(1, 100), rep(2, 100), rep(3, 100)) + rnorm(300, 0, .5) response0 <- c(rep(0, 100), rep(1, 100), rep(2, 100)) + rnorm(300, 0, .5) response <- c(response1, response0) treatment <- c(rep(1, 300), rep(0, 300)) propensity <- rep(seq(.01, .99, (.98/299)), 2) a <- data.frame(response, treatment, propensity) loess.psa(a, span = .15, degree = 1, int = c(0, .33, .67, 1)) #Artificial example where estimates are unstable with varying #numbers of strata. Note: sometimes get empty treatment/strata error. rr <- c(rnorm(150, 3, .75), rnorm(700, 0, .75), rnorm(150, 3, .75), rnorm(150, -3, .75), rnorm(700, 0, .75), rnorm(150, -3, .75)) tt <- c(rep(1, 1000),rep(0, 1000)) pp <- NULL for(i in 1:1000){pp <- c(pp, rnorm(1, 0, .05) + .00045*i + .25)} for(i in 1:1000){pp <- c(pp, rnorm(1, 0, .05) + .00045*i + .4)} a <- data.frame(rr, tt, pp) loess.psa(a, span=.5, cex = .6) #Using strata of possible interest as determined by loess lines. data(lindner) attach(lindner) lindner.ps <- glm(abcix ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc, data = lindner, family = binomial) loess.psa(log(cardbill), abcix, lindner.ps$fitted, int = c(.37, .56, .87, 1), lines = TRUE) abline(v=c(.37, 56, .87)) ``` ## See Also `circ.psa` ## Author(s) James E. Helmreich James.Helmreich@Marist.edu Robert M. Pruzek RMPruzek@yahoo.com

loess.psa function