testConstancy {pssmooth}

Testing of the Null Hypotheses of a Flat and a Constant Marginal Causal Effect Predictiveness Curve

Description

Computes a two-sided p-value either from the test of {H_0^1: mCEP(s_1)=CE for all s_1}, where CE is the overall causal treatment effect on the clinical endpoint, or from the test of {H_0^2: mCEP(s_1)=c for all s_1 in the interval limS1 and a specified constant c}, each against a general alternative hypothesis. The testing procedures are described in Juraska, Huang, and Gilbert (2018) and are based on the simultaneous estimation method of Roy and Bose (1953).

Usage

testConstancy(
  object,
  boot,
  contrast = c("te", "rr", "logrr", "rd"),
  null = c("H01", "H02"),
  overallPlaRisk = NULL,
  overallTxRisk = NULL,
  MCEPconstantH02 = NULL,
  limS1 = NULL
)

Arguments

object

an object returned by riskCurve

boot

an object returned by bootRiskCurve

contrast

a character string specifying the mCEP curve. It must be one of te (treatment efficacy), rr (relative risk), logrr (log relative risk), and rd (risk difference [placebo minus treatment]).

null

a character string specifying the null hypothesis to be tested; one of H01 and H02 as introduced above

overallPlaRisk

a numeric value of the estimated overall clinical endpoint risk in the placebo group. It is required when null equals H01.

overallTxRisk

a numeric value of the estimated overall clinical endpoint risk in the treatment group. It is required when null equals H01.

MCEPconstantH02

the constant c in the null hypothesis H_0^2. It is required when null equals H02.

limS1

a numeric vector of length 2 specifying an interval that is a subset of the support of S(1) and that is used in the evaluation of the null hypothesis H_0^2. If NULL (default), then H_0^2 is evaluated for all s_1.

Value

A numeric value representing the two-sided p-value from the test of either H_0^1 or H_0^2.

References

Juraska, M., Huang, Y., and Gilbert, P. B. (2020), Inference on treatment effect modification by biomarker response in a three-phase sampling design, Biostatistics, 21(3): 545-560, https://doi.org/10.1093/biostatistics/kxy074.

Roy, S. N. and Bose, R. C. (1953), Simultaneous condence interval estimation, The Annals of Mathematical Statistics, 24, 513-536.

See Also

riskCurve, bootRiskCurve and testEquality

Examples

n <- 500
Z <- rep(0:1, each=n/2)
S <- MASS::mvrnorm(n, mu=c(2,2,3), Sigma=matrix(c(1,0.9,0.7,0.9,1,0.7,0.7,0.7,1), nrow=3))
p <- pnorm(drop(cbind(1,Z,(1-Z)*S[,2],Z*S[,3]) %*% c(-1.2,0.2,-0.02,-0.2)))
Y <- sapply(p, function(risk){ rbinom(1,1,risk) })
X <- rbinom(n,1,0.5)
# delete S(1) in placebo recipients
S[Z==0,3] <- NA
# delete S(0) in treatment recipients
S[Z==1,2] <- NA
# generate the indicator of being sampled into the phase 2 subset
phase2 <- rbinom(n,1,0.4)
# delete Sb, S(0) and S(1) in controls not included in the phase 2 subset
S[Y==0 & phase2==0,] <- c(NA,NA,NA)
# delete Sb in cases not included in the phase 2 subset
S[Y==1 & phase2==0,1] <- NA
data <- data.frame(X,Z,S[,1],ifelse(Z==0,S[,2],S[,3]),Y)
colnames(data) <- c("X","Z","Sb","S","Y")
qS <- quantile(data$S, probs=c(0.05,0.95), na.rm=TRUE)
grid <- seq(qS[1], qS[2], length.out=3)

out <- riskCurve(formula=Y ~ S + factor(X), bsm="Sb", tx="Z", data=data, psGrid=grid)
boot <- bootRiskCurve(formula=Y ~ S + factor(X), bsm="Sb", tx="Z", data=data,
                      psGrid=grid, iter=2, seed=10)
fit <- glm(Y ~ Z, data=data, family=binomial)
prob <- predict(fit, newdata=data.frame(Z=0:1), type="response")

testConstancy(out, boot, contrast="te", null="H01", overallPlaRisk=prob[1],
              overallTxRisk=prob[2])
testConstancy(out, boot, contrast="te", null="H02", MCEPconstantH02=0, limS1=c(qS[1],1.5))