testcov2 {MDCcure} | R Documentation |
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 forz
.
References
Park, T., Saho, X. & Yao, S. (2015). Partial martingale difference correlation. Electronic Journal of Statistics, 9, 1492–1517. 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.