sievePH {sievePH}

Semiparametric Estimation of Coefficients in a Mark-Specific Proportional Hazards Model with a Multivariate Continuous Mark, Fully Observed in All Failures

Description

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.

Usage

sievePH(eventTime, eventInd, mark, tx, strata = NULL)

Arguments

eventTime

a numeric vector specifying the observed right-censored time to the event of interest

eventInd

a numeric vector indicating the event of interest (1 if event, 0 if right-censored)

mark

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 eventInd = 1. For subjects with eventInd = 0, the value(s) in mark should be set to NA.

tx

a numeric vector indicating the treatment group (1 if treatment, 0 if placebo)

strata

a numeric vector specifying baseline strata (NULL by default). If specified, a stratified Cox model is fit for estimating the marginal hazard ratio (i.e., a separate baseline hazard is assumed for each stratum). No stratification is used in estimation of the mark density ratio.

Details

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 survival package. Both estimators are consistent and asymptotically normal. The joint asymptotic distribution of the estimators is detailed in Juraska and Gilbert (2013).

Value

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 \phi in the weight function g(v, \phi) in the density ratio model

• DRlambda: an estimate of the Lagrange multiplier in the profile score functions for \phi (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 survival package

• cov: the estimated joint covariance matrix of DRcoef and logHR

• coxphFit: an object returned by the call of coxph()

• 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

References

Juraska, M. and Gilbert, P. B. (2013), Mark-specific hazard ratio model with multivariate continuous marks: an application to vaccine efficacy. Biometrics 69(2):328–337.

Qin, J. (1998), Inferences for case-control and semiparametric two-sample density ratio models. Biometrika 85, 619–630.

See Also

summary.sievePH, plot.summary.sievePH, testIndepTimeMark and testDensRatioGOF

Examples

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)