Incorporate the third contrast of a three-level categorical predictor into the odds ratio summary plot of a logistic regression model

In any regression model, by default, a 3-level categorical predictor generates only 2 contrasts. For example, if race was a predictor in the model and had the levels Black, Caucasian, and Other, and Caucasian was the reference level, only the contrasts of Caucasian:Black and Caucasian:Other would be calculated. It would be useful to be able to incorporate the third contrast Black:Other into the desired output.

In this specific example, the desired output is an odds ratio (OR) plot that is generated by the Design package's plot.summary.Design() function when based on a logistic regression model (defined using the Design pacage's lrm() function).

For this example, let's use our old standby -- the samplefile.txt data file.

• samplefile.txt:

Let's first load the necessary packages, read in our data file, and make some changes to our data frame -- add some variable labels, level labels, and units. library(Hmisc) library(Design)

x<-read.table("samplefile.txt", header=TRUE) x<-upData(x, labels=c(age="Age", race="Race", sex="Sex", weight="Weight", visits="No. of Visits", tx="Treatment"), levels=list(sex=c("Female", "Male"), race=c("Black", "Caucasian", "Other"), tx=c("Drug X", "Placebo")), units=c(age="years", weight="lbs.")) contents(x)

Now let's create a binary outcome based on the number of visits --- we're interested in what predicts a patient will have more than 10 visits. x$gt10visits <- factor(ifelse(x$visits <= 10, 0, 1), labels = c("<= 10 visits", "> 10 visits")) describe(x$gt10visits)

Now let's fit the logistic regression model: m1 <- lrm(gt10visits ~ age + race + sex + weight + tx, data = x)

Because we're going to be summarizing and plotting our lrm model, we need to define the datadist (i.e., data distribution --- the ranges, levels, etc.) of our data. dd <- datadist(x) options(datadist = "dd") NOTE, these two lines of code must be executed when using the Design package's summary.Design(), plot.Design(), and plot.summary.Design() functions (as well as others) to summarize of plot any of the Design package's modeling functions (e.g., ols(), lrm(), and cph()).

Let's plot the model: plot(summary(m1))

Let's make some changes to the previous default plot: plot(summary(m1, # use variable labels instead of variable names # --> must have variable labels defined # ---> NOTE: vnames= is a summary.Design argument vnames = "labels"), # plot only the 95% CI of the ORs # ---> * must specify both q= and col= * q = 0.95, col = "gray", # Plot on the X beta scale but label with anti-logs log = TRUE)

Based on the plot, we notice that only two of the three race contrasts have been included. Let's work on incorporating the third race contrast into the plot: # Problem: By default, for a 3-level categorical variable, # summary generates ORs for 2 comparisons # (all to reference level) # Desire: Include the additional contrast # (i.e., for race, Black:Other) # Solution: Expand the matrix of ORS generated by summary.Design # that is used by plot.summary.Design to include # the additional contrast # Step 1: Assign the summary including the two default race contrasts m1summ <- summary(m1, vnames = "labels") # Step 2: Assign the summary of the third race contrast # --> Only need the first two rows race3contrast <- summary(m1, est.all = FALSE, race = "Other", vnames = "labels")[1:2,] # Step 3: Splice together the two summaries # --> insert the third race contrast after the first two expandedsumm <- rbind(m1summ[1:8, ], race3contrast, m1summ[9:10,]) # Step 4: Modify the attributes of expandedsumm # --> Class of expandedsumm must be "summary.Design" # in order for plot to be correct # --> right now, class(expandedsumm) = "matrix" # --> however, class(m1summ) = "summary.Design", so # use its attributes as a template str(m1summ) attributes(m1summ) # Step 4a: Assign the attributes of m1summ summattr <- attributes(m1summ) # Step 4b: Modify the dimnames of summattr to include # the third race contrast (i.e., use the dimnames of expandedsumm) summattr$dimnames <- attr(expandedsumm, "dimnames") # NOTE: the attributes() function returns all attributes of an object # while the attr() function allows you to extract specific (one or more) # attributes from an object # NOTE: attr(expandedsumm, "dimnames") <==> attributes(expandedsumm)$dimnames # Step 4c: Modify the dimensions of summattr to match those of expandedsumm summattr$dim <- attr(expandedsumm, "dim") # Step 4d: Assign the attributes of expandedsumm to summattr attributes(expandedsumm) <- summattr

# Create the OR plot based on the expanded summary plot(expandedsumm, q = 0.95, col = "gray", log = TRUE)