sievePH implements the semiparametric estimation method of Juraska and Gilbert (2013) for the multivariate mark-
specific hazard ratio in the competing risks failure time analysis framework. It employs (i) the semiparametric
method of maximum profile likelihood estimation in the treatment-to-placebo mark density
ratio model (Qin, 1998) and (ii) the ordinary method of maximum partial likelihood estimation of the overall log hazard ratio in the Cox model.
sievePH requires that the multivariate mark data are fully observed in all failures.
sievePH(eventTime, eventInd, mark, tx)
a numeric vector specifying the observed right-censored time to the event of interest
a numeric vector indicating the event of interest (1 if event, 0 if right-censored)
either a numeric vector specifying a univariate continuous mark or a data frame specifying a multivariate continuous mark.
No missing values are permitted for subjects with
a numeric vector indicating the treatment group (1 if treatment, 0 if placebo)
sievePH considers data from a randomized placebo-controlled treatment efficacy trial with a time-to-event endpoint.
The parameter of interest, the mark-specific hazard ratio, is the ratio (treatment/placebo) of the conditional mark-specific hazard functions.
It factors as the product of the mark density ratio (treatment/placebo) and the ordinary marginal hazard function ignoring mark data.
The mark density ratio is estimated using the method of Qin (1998), while the marginal hazard ratio is estimated using
coxph() in the
Both estimators are consistent and asymptotically normal. The joint asymptotic distribution of the estimators is detailed in Juraska and Gilbert (2013).
An object of class
sievePH which can be processed by
summary.sievePH to obtain or print a summary of the results. An object of class
sievePH is a list containing the following components:
DRcoef: a numeric vector of estimates of coefficients φ in the weight function g(v, φ) in the density ratio model
DRlambda: an estimate of the Lagrange multiplier in the profile score functions for φ (that arises by profiling out the nuisance parameter)
DRconverged: a logical value indicating whether the estimation procedure in the density ratio model converged
logHR: an estimate of the marginal log hazard ratio from
coxph() in the
cov: the estimated joint covariance matrix of
coxphFit: an object returned by the call of
nPlaEvents: the number of events observed in the placebo group
nTxEvents: the number of events observed in the treatment group
mark: the input object
tx: the input object
Juraska, M. and Gilbert, P. B. (2013), Mark-specific hazard ratio model with multivariate continuous marks: an application to vaccine efficacy. Biometrics 69(2):328<e2><80><93>337.
Qin, J. (1998), Inferences for case-control and semiparametric two-sample density ratio models. Biometrika 85, 619<e2><80><93>630.
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n <- 500 tx <- rep(0:1, each=n/2) tm <- c(rexp(n/2, 0.2), rexp(n/2, 0.2 * exp(-0.4))) cens <- runif(n, 0, 15) eventTime <- pmin(tm, cens, 3) eventInd <- as.numeric(tm <= pmin(cens, 3)) mark1 <- ifelse(eventInd==1, c(rbeta(n/2, 2, 5), rbeta(n/2, 2, 2)), NA) mark2 <- ifelse(eventInd==1, c(rbeta(n/2, 1, 3), rbeta(n/2, 5, 1)), NA) # fit a model with a univariate mark fit <- sievePH(eventTime, eventInd, mark1, tx) # fit a model with a bivariate mark fit <- sievePH(eventTime, eventInd, data.frame(mark1, mark2), tx)
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