JMcmprsk (version 0.9.10)

linearTest: Linear hypothesis testing of joint models

Description

Joint modelling for longitutal and censored data with competing risks

Usage

linearTest(
  object,
  coeff = c("beta", "gamma", "alpha"),
  La = "identity",
  Lb = "identity",
  Lg = "identity",
  Ca = 0,
  Cb = 0,
  Cg = 0,
  digits = 4,
  ...
)

Arguments

object

The JMcmprsk object returned by either jmo or jmc function.

coeff

Types of coefficients selected for Wald. Note "alpha" is only avaiable to jmo type JMcmprsk object.

La

Linear contrast of the fixed effects of non-proportional odds covariates * (# of levels of the outcome - 2) in the longitudinal part. Default is "identity", i.e., all the fixed effects equal to zero. Otherwise, La must be a matrix.

Lb

Linear contrast of the fixed effects of proportional odds covariates in the longitudinal part. Default is "identity", i.e., all the fixed effects equal to zero. Otherwise, Lb must be a matrix.

Lg

Linear contrast of the fixed effects of covariates * # of competing risks in the survival part. Default is "identity", i.e., all the fixed effects equal to zero. Otherwise, Lg must be a matrix.

Ca

The hypothesized value of linear combination of the fixed effects of non-proportional odds covariates * (# of levels of the outcome - 2) in the longitudinal part. Default is 0. Otherwise, Ca must be a number / vector.

Cb

The hypothesized value of linear combination of the fixed effects of proportional odds covariates in the longitudinal part. Default is 0. Otherwise, Cb must be a number / vector.

Cg

The hypothesized value of linear combination of the fixed effects of covariates * # of competing risks in the survival part. Default is 0. Otherwise, Cg must be a number / vector.

digits

number of digits to be printed out.

...

further arguments passed to or from other methods.

Value

Return a Wald test statistic and the p value

beta	The Wald test for fixed effects for the longitutal part,i.e. \(\beta\) in jmo or jmc output.
gamma	The Wald test for fixed effects for the survival part,i.e. \(\gamma\) in jmo or jmc output.
alpha	The Wald test for non-proportional odds covariates,i.e. \(\alpha\) in jmo output.

Details

Wald test statistic is used for hypothesis testing on multiple parameters:

\(H_0: L\theta = C\) vs: \(H_1: L\theta \neq C\)

The test statistic is:

\((L\hat{\theta} - C)'(L\hat{V_{\theta}}L)^{-1}(L\hat{\theta} - C) \sim \chi_q^2,\)

where \(\hat{V_{\theta}}\) is the estimate of covariance of the parameter \(\theta\) and q is the rank of the linear contrast \(L\).