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Variance-Covariance Matrix and Confidence Intervals for coxph_mpl Fits

vcov.coxph_mpl.Rd

Extract the estimated variance-covariance matrix of a fitted coxph_mpl model, and the Wald confidence intervals that follow from it.

Usage

# S3 method for class 'coxph_mpl'
vcov(
  object,
  parameters = c("Beta", "Theta"),
  se = c("M2QM2", "M2HM2", "H"),
  ...
)

# S3 method for class 'coxph_mpl'
confint(
  object,
  parm,
  level = 0.95,
  parameters = c("Beta", "Theta"),
  se = c("M2QM2", "M2HM2", "H"),
  ...
)

Arguments

object

A fitted model of class "coxph_mpl".

parameters

Parameter block of interest: "Beta" for the regression coefficients or "Theta" for the baseline hazard parameters. Default "Beta".

se

Inference method, matching the choices offered by [summary.coxph_mpl()] and [predict.coxph_mpl()]: one of "M2QM2", "M2HM2" or "H". Default "M2QM2".

...

Additional arguments passed to methods.

parm

Parameters to report an interval for, given as names or as indices into the selected block. Defaults to all of them.

level

Confidence level. Default 0.95.

Value

vcov returns a symmetric matrix with one row and column per parameter in the selected block. confint returns a matrix with two columns giving the lower and upper limits.

Details

coxph_mpl estimates the regression coefficients \(\boldsymbol\beta\) and the baseline hazard parameters \(\boldsymbol\theta\) jointly, and stores the covariance of the whole \((\boldsymbol\beta, \boldsymbol\theta)\) vector. vcov returns one diagonal block of it, so vcov(fit) is the \(p \times p\) matrix a reader of coef(fit) expects. The cross-block covariances between \(\boldsymbol\beta\) and \(\boldsymbol\theta\) are not discarded, only unreported here; they are available as fit$covar[[se]].

Rows and columns for baseline parameters that were driven to the boundary (at or below min.theta, see [coxph_mpl.control()]) are zero, as are all entries when the covariance could not be inverted; in the latter case the matrix is filled with NA and the intervals follow suit.

confint forms symmetric Wald intervals on the scale the parameters were estimated on, so for regression coefficients they are intervals for \(\beta\), not for the hazard ratio; exponentiate to obtain the latter.

See also

[coxph_mpl()], [coef.coxph_mpl()], [summary.coxph_mpl()]

Examples

if (FALSE) { # \dontrun{
data(bcos2)
fit <- coxph_mpl(Surv(left, right, type = "interval2") ~ treatment,
                 data = bcos2, basis = "msplines")
vcov(fit)
confint(fit)
exp(confint(fit))          # hazard ratio scale
} # }