Effect modification in HIV treatment (ACTG175)

library(dScoreTest)

We use hte_test_conditional() to look for effect modifiers in treating HIV, using the AIDS Clinical Trials Group (ACTG) Protocol 175 data (Hammer et al., 1996), available from the R package speff2trial. This is a randomized trial that compares treatments for HIV among adults with CD4 T-cell counts between 200 and 500 cells per \(\text{mm}^3\). We consider two treatment arms: monotherapy with didanosine (\(T=0\)) versus combination therapy with zidovudine and didanosine (\(T=1\)), which have 561 and 522 patients respectively. We study the CD4 count at \(20 \pm 5\) weeks as the continuous outcome \(Y\), with higher values indicating better health.

There are 12 baseline covariates. Here, we look at potential effect modification by homosexual activity (binary) and baseline CD4 count (continuous).

data(ACTG175, package = "speff2trial")

covs <- c(
    "age", "wtkg", "karnof", "cd40", "cd80", "gender",
    "homo", "race", "symptom", "drugs", "str2", "hemo"
)
label_list <- c(
    cd40 = "CD4", homo = "Homosexual activity", age = "Age", wtkg = "Weight",
    str2 = "Antiretroviral history", race = "Race", hemo = "Hemophilia",
    symptom = "Symptomatic", cd80 = "CD8", karnof = "Karnofsky score",
    drugs = "IV drug use", gender = "Gender"
)

dat <- ACTG175[ACTG175$arms %in% c(1, 3), ]
Z  <- dat[, covs]
Tr <- as.integer(dat$arms == 1)
y  <- dat$cd420

For a covariate \(Z_i\), we use hte_test_conditional(y, Tr, Z, S = i) to test the conditional hypothesis \(H_0(\{i\})\): the conditional treatment effect \[ \tau(Z) := \mathbb{E}[Y(t=1) - Y(t=0) \mid Z]\] does not depend on \(Z_i\), while holding all the remaining covariates fixed. Although here \(S\) is chosen to be a singleton, the method is also applicable where \(S\) is a group of covariates. The test involves a random sample split, so we repeat it a number of times and combine the p-values by their harmonic mean, which controls the type-I error if the \(\alpha\) level is small in the sense that \(\text{Type-I error} / \alpha \to 1\) holds as \(\alpha \to 0\) under the null, even when the \(p\)-values are computed on the same sample and are therefore dependent.

hmean <- function(p) length(p) / sum(1 / p)

n.reps <- 10
covariates.of.interest <- c("homo", "cd40")

set.seed(42)
results <- do.call(rbind, lapply(covariates.of.interest, function(cov) {
    cov.idx <- which(covs == cov)
    p.vals <- replicate(n.reps, hte_test_conditional(y, Tr, Z, S = cov.idx)$p.val)
    data.frame(covariate = cov, label = label_list[[cov]],
              n.reps = n.reps, harmonic.p = hmean(p.vals))
}))
rownames(results) <- NULL
results
#>   covariate               label n.reps harmonic.p
#> 1      homo Homosexual activity     10 0.02219521
#> 2      cd40                 CD4     10 0.02535719

Both covariates come back with harmonic p-values below the conventional 0.05 threshold, suggesting that both homosexual activity and baseline CD4 count may modify the effect of combination therapy versus monotherapy on CD4 count at 20 weeks. This is only a preview with 10 reps per covariate, so the harmonic-mean estimate is still noisy; a production run would use many more reps for a stable estimate.