cvmf {modeLLtest}

Cross-Validated Median Fit (CVMF) Test

Description

Applies cross-validated log-likelihood to test between partial likelihood maximization (PLM) and the iteratively reweighted robust (IRR) method of estimation for a given application of the Cox model. For more, see: Desmarais, B. A., & Harden, J. J. (2012). Comparing partial likelihood and robust estimation methods for the Cox regression model. Political Analysis, 20(1), 113-135. doi: 10.1093/pan/mpr042

Usage

cvmf(
  formula,
  data,
  method = c("exact", "approximate", "efron", "breslow"),
  trunc = 0.95,
  subset,
  na.action,
  f.weight = c("linear", "quadratic", "exponential"),
  weights,
  singular.ok = TRUE
)

Arguments

formula

A formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function from the survival package.

data

A data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model or in the subset and the weights argument.

method

A character string specifying the method for tie handling in coxph(). If there are no tied death times all the methods are equivalent. Following the coxph function in the survival package, the Efron approximation is used as the default. The survival package justifies this due to the Efron method being is more accurate when dealing with tied death times, and is as efficient computationally than the common Breslow method. The "exact partial likelihood" is equivalent to a 'conditional logistic model, and is appropriate when the times are a small set of discrete values. This argument does not exist in the coxr function in the coxrobust package. For coxr, method is based on a smooth modification of the partial likelihood. See documentation from survival package for more on coxph method and coxrobust package for coxr method.

trunc

A value that determines the trimming level for the robust estimator. The default is 0.95. Roughly, quantile of the sample T_i exp(\beta'Z_i). It is an argument in the coxr function in the coxrobust package.

subset

Expression indicating which subset of the rows of data should be used in the fit. All observations are included by default.

na.action

A missing-data filter function, applied to the model.frame, after any subset argument has been used.

f.weight

A type of weighting function for coxr in the coxrobust package. The default is quadratic. See coxr documentation for more.

weights

A vector of case weights for coxph in the survival package. See coxph documentation for more.

singular.ok

Logical value indicating how to handle collinearity in the model matrix. If TRUE, the program will automatically skip over columns of the X matrix that are linear combinations of earlier columns. In this case the coefficients for such columns will be NA, and the variance matrix will contain zeros. For ancillary calculations, such as the linear predictor, the missing coefficients are treated as zeros.

Details

This function implements the cross-validated median fit (CVMF) test. The function cvmf() tests between the partial likelihood maximization (PLM) and the iteratively reweighted robust (IRR) method of estimation for a given application of the Cox model. The Cox model is a partial parametric model that does not make assumptions about the baseline hazard. It can be estimated via PLM, the standard estimator, or IRR, a robust estimator that identifies and downweights outliers. The choice between the two methods involves a trade-off between bias and efficiency. PLM is more efficient, but biased under specification problems. IRR reduces bias, but results in high variance due to the loss of efficiency. The cvmf() function returns an object to identify the prefered estimation method.

See also coxph, coxr, Surv

Value

An object of class cvmf computed by the cross-validated median fit test (CVMF) to test between the PLM and IRR methods of estimating the Cox model. See cvmf_object for more details.

References

Desmarais, B. A., & Harden, J. J. (2012). Comparing partial likelihood and robust estimation methods for the Cox regression model. Political Analysis, 20(1), 113-135. doi: 10.1093/pan/mpr042

Examples

  set.seed(12345)
  x1 <- rnorm(100)
  x2 <- rnorm(100)

  x2e <- x2 + rnorm(100, 0, 0.5)

  y <- rexp(100, exp(x1 + x2))
  y <- survival::Surv(y)

  dat <- data.frame(y, x1, x2e)
  form <- y ~ x1 + x2e

  results <- cvmf(formula = form, data = dat)