testDensRatioGOF {sievePH}

Goodness-of-Fit Test of the Validity of a Univariate or Multivariate Mark Density Ratio Model

Description

testDensRatioGoF implements the complete-case goodness-of-fit test of Qin and Zhang (1997) for evaluating the validity of the specified mark density ratio model used for modeling a component of the mark-specific hazard ratio model in Juraska and Gilbert (2013). Multivariate marks are accommodated. Subjects who experienced the event of interest but their mark is missing are discarded.

Usage

testDensRatioGOF(
  eventInd,
  mark,
  tx,
  DRcoef = NULL,
  DRlambda = NULL,
  iter = 1000
)

Arguments

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. For subjects with a right-censored time-to-event, the value(s) in mark should be set to NA.

tx

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

DRcoef

a numeric vector of the coefficients \phi in the weight function g(v, \phi) = \exp\{\phi^T (1, v)\} in the density ratio model. If NULL (default), the maximum profile likelihood estimates (Qin, 1998) of the coefficients are computed.

DRlambda

the Lagrange multiplier in the profile score functions for \phi (that arises by profiling out the nuisance parameter). If NULL (default), the maximum profile likelihood estimate (Qin, 1998) of the Lagrange multiplier is computed.

iter

the number of bootstrap iterations (1000 by default)

Details

testDensRatioGoF performs a goodness-of-fit test for the exponential form of the weight function, i.e., g(v, \phi) = \exp\{\phi^T (1, v)\}. Other weight functions are not considered.

Value

Returns a list containing the following components:

• teststat: the value of the Kolmogorov-Smirnov-type test statistic

• pval: the bootstrap p-value from the Kolmogorov-Smirnov-type test of validity of the mark density ratio model

• DRcoef: the input object if different from NULL or a numeric vector of estimates of coefficients \phi in the weight function g(v, \phi) in the density ratio model

• DRlambda: the input object if different from NULL or an estimate of the Lagrange multiplier in the profile score functions for \phi

References

Qin, J., & Zhang, B. (1997). A goodness-of-fit test for logistic regression models based on case-control data. Biometrika, 84(3), 609-618.

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.

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)

# test goodness-of-fit for a univariate mark
testDensRatioGOF(eventInd, mark1, tx, iter=15)

# test goodness-of-fit for a bivariate mark
testDensRatioGOF(eventInd, data.frame(mark1, mark2), tx, iter=15)