testcov2: Hypothesis test for association between covariate and cure...

In MDCcure: Martingale Dependence Tools and Testing for Mixture Cure Models

Hypothesis test for association between covariate and cure indicator adjusted by a second covariate

Description

Performs a permutation-based test assessing the association between a primary covariate (x) and the cure indicator, while adjusting for a secondary covariate (z). The test calculates the p-value via permutation using the partial martingale difference correlation.

Usage

testcov2(x, time, z, delta, P = 999, H = NULL)

Arguments

x	Numeric vector. The primary covariate whose association with the latent cure indicator is tested.
time	Numeric vector. Observed survival or censoring times.
z	Numeric vector. Secondary covariate for adjustment.
delta	Numeric vector. Censoring indicator (1 indicates event occurred, 0 indicates censored).
P	Integer. Number of permutations used to compute the permutation p-value. Default is 999.
H	Optional numeric. Bandwidth parameter (currently unused, reserved for future extensions).

Details

In order to test if the cure rate depends on the covariate \boldsymbol{X} given it depends on the covariate \boldsymbol{Z}. The hypotheses are

\mathcal{H}_0 : \mathbb{E}(\nu | \boldsymbol{X}) \equiv 1 - p(\boldsymbol{X}) \quad \text{a.s.} \quad \text{vs} \quad \mathcal{H}_1 : \mathbb{E}(\nu | \boldsymbol{X}) \not\equiv 1 - p(\boldsymbol{X}) \quad \text{a.s.}

The proxy of the cure rate under the null hypothesis \mathcal{H}_0 is obtained by:

\mathbb{I}(T > \tau) + (1-\delta)\mathbb{I}(T \leq \tau) \, \frac{1 - p(\boldsymbol{Z})}{1 - p(\boldsymbol{Z}) + p(\boldsymbol{Z})S_0(T|\boldsymbol{X,Z})}.

The statistic for testing the covariate hypothesis is based on partial martingale difference correlation and it is given by:

\text{pMDC}_n(\hat{\nu}_{\boldsymbol{H}}|\boldsymbol{X,Z})^2.

The null distribution is approximated using a permutation test.

Value

List with components:

statistic

Numeric. The test statistic value.

p.value

Numeric. The permutation p-value assessing the null hypothesis of no association between x and the latent cure indicator, adjusting for z.

References

Park, T., Saho, X. & Yao, S. (2015). Partial martingale difference correlation. Electronic Journal of Statistics, 9, 1492–1517. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/15-EJS1047")}

See Also

pmdc for the partial martingale difference correlation, pmdd for the partial martingale difference divergence, testcov for the test for one covariate.

MDCcure documentation built on Aug. 8, 2025, 6:10 p.m.