R: Summarizing Nonparametric Kernel-Smoothed Stratified...

summary.kernel_sievePH {sievePH}

R Documentation

Summarizing Nonparametric Kernel-Smoothed Stratified Mark-Specific Proportional Hazards Model Fits

Description

summary method for an object of class kernel_sievePH.

Usage

## S3 method for class 'kernel_sievePH'
summary(
  object,
  contrast = c("te", "hr", "loghr"),
  sieveAlternative = c("twoSided", "oneSided"),
  confLevel = 0.95,
  ...
)

## S3 method for class 'summary.kernel_sievePH'
print(x, digits = 4, ...)

Arguments

`object`	an object of class `kernel_sievePH`, a result of a call to `kernel_sievePH` and `kernel_sievePHaipw`.
`contrast`	a character string specifying the treatment effect parameter of interest. The default value is `"te"` (treatment efficacy); other options are `"hr"` (hazard ratio) and `"loghr"` (log hazard ratio).
`sieveAlternative`	a character string specifying the alternative hypothesis for the sieve tests, which can be either `"twoSided"` (default) or `"oneSided"`.
`confLevel`	the confidence level (0.95 by default) of reported confidence intervals
`...`	further arguments passed to or from other methods
`x`	an object of class `summary.kernel_sievePH`, usually a result of a call to `summary.kernel_sievePH`
`digits`	the number of significant digits to use when printing (4 by default)

Details

print.summary.kernel_sievePH prints a formatted summary of results. Inference about coefficients in the kernel-smoothed mark-specific proportional hazards model is tabulated. Additionally, a summary is generated from the tests of two relevant null hypotheses: (1) {H_0: HR(v)=1 for all v}, and (2) {H_0: HR(v)=HR for all v}. For the tests of (2), sieveAlternative controls the choice of the alternative hypothesis.

Value

An object of class summary.kernel_sievePH, which is a list with the following components:

estBeta: a data frame summarizing point estimates and standard errors of the mark-specific coefficients for treatment.
HRunity.2sided: a data frame with test statistics (first row) and corresponding p-values (second row) for testing H_{10}: HR(v) = 1 vs. H_{1a}: HR(v) \neq 1 for any v \in [a, b] (general alternative). TSUP1 is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. Tint1 is a generalization of the integration-based Cramer-von Mises test.
HRunity.1sided: a data frame with test statistics (first row) and corresponding p-values (second row) for testing H_{10}: HR(v) = 1 vs. H_{1m}: HR(v) \leq 1 with strict inequality for some v \in [a, b] (monotone alternative). TSUP1m is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. Tint1m is a generalization of the integration-based Cramer-von Mises test.
HRconstant.2sided: a data frame with test statistics (first row) and corresponding p-values (second row) for testing H_{20}: HR(v) does not depend on v \in [a, b] vs. H_{2a}: HR depends on v \in [a, b] (general alternative). TSUP2 is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. Tint2 is a generalization of the integration-based Cramer-von Mises test. This component is available if sieveAlternative="twoSided".
HRconstant.1sided: a data frame with test statistics (first row) and corresponding p-values (second row) for testing H_{20}: HR(v) does not depend on v \in [a, b] vs. H_{2m}: HR increases as v increases \in [a, b] (monotone alternative). TSUP2m is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. Tint2m is a generalization of the integration-based Cramer-von Mises test. This component is available if sieveAlternative="oneSided".
te: a data frame summarizing point and interval estimates of the mark-specific treatment efficacy on the grid of mark values defined by nvgrid spanning from the minimum and maximum of the mark (available if contrast="te"). The confidence level is specified by confLevel.
hr: a data frame summarizing point and interval estimates of the mark-specific hazard ratio on the grid of mark values defined by nvgrid spanning from the minimum and maximum of the mark (available if contrast="hr"). The confidence level is specified by confLevel.
loghr: a data frame summarizing point and interval estimates of the mark-specific log hazard ratio on the grid of mark values defined by nvgrid spanning from the minimum and maximum of the mark (available if contrast="loghr"). The confidence level is specified by confLevel.

References

Gilbert, P. B. and Sun, Y. (2015). Inferences on relative failure rates in stratified mark-specific proportional hazards models with missing marks, with application to human immunodeficiency virus vaccine efficacy trials. Journal of the Royal Statistical Society Series C: Applied Statistics, 64(1), 49-73.

Sun, Y. and Gilbert, P. B. (2012). Estimation of stratified mark‐specific proportional hazards models with missing marks. Scandinavian Journal of Statistics, 39(1), 34-52.

Examples

set.seed(20240410)
beta <- 2.1
gamma <- -1.3
n <- 200
tx <- rep(0:1, each = n / 2)
tm <- c(rexp(n / 2, 0.2), rexp(n / 2, 0.2 * exp(gamma)))
cens <- runif(n, 0, 15)
eventTime <- pmin(tm, cens, 3)
eventInd <- as.numeric(tm <= pmin(cens, 3))
alpha <- function(b){ log((1 - exp(-2)) * (b - 2) / (2 * (exp(b - 2) - 1))) }
mark0 <- log(1 - (1 - exp(-2)) * runif(n / 2)) / (-2)
mark1 <- log(1 + (beta - 2) * (1 - exp(-2)) * runif(n / 2) / (2 * exp(alpha(beta)))) /
  (beta - 2)
mark <- ifelse(eventInd == 1, c(mark0, mark1), NA)
# the true TE(v) curve underlying the data-generating mechanism is:
# TE(v) = 1 - exp{alpha(beta) + beta * v + gamma}

# a binary auxiliary covariate
A <- sapply(exp(-0.5 - 0.2 * mark) / (1 + exp(-0.5 - 0.2 * mark)),
            function(p){ ifelse(is.na(p), NA, rbinom(1, 1, p)) })
linPred <- 1 + 0.4 * tx - 0.2 * A
probs <- exp(linPred) / (1 + exp(linPred))
R <- rep(NA, n)
while (sum(R, na.rm = TRUE) < 10){
  R[eventInd == 1] <- sapply(probs[eventInd == 1],
                             function(p){ rbinom(1, 1, p) })
}
# a missing-at-random mark
mark[eventInd == 1] <- ifelse(R[eventInd == 1] == 1, mark[eventInd == 1], NA)

# AIPW estimation; auxiliary covariate is used (not required)
fit <- kernel_sievePHaipw(eventTime, eventInd, mark, tx, aux = A,
                          auxType = "binary", formulaMiss = ~ eventTime,
                          formulaAux = ~ eventTime + tx + mark,
                          tau = 3, tband = 0.5, hband = 0.3, nvgrid = 20,
                          nboot = 20)
sfit <- summary(fit)
# print the formatted summary
sfit
# treatment efficacy estimates on the grid
sfit$te

[Package sievePH version 1.1 Index]