A Shiny app for multiple RMTL-based tests

Description

This function provides a shiny app for performing multiple RMTL-based tests. Here, the asymptotic or permutation tests can be applied.

Usage

GFDrmtlGUI()

Details

Note that the calculations for the permutation test may take a while, especially with stepwise extension.

Value

No return value, called for side effects.

Function to perform multiple RMTL-based tests

Description

Linear hypotheses of the restricted mean time losts (RMTLs) of k different groups in a competing risks setup can be tested simultaneously. Therefore, the multivariate distribution of local Wald-type test statistics is approximated by (1) estimating the covariance between the test statistics (method = "asymptotic") or (3) a permutation approach with Bonferroni-correction (method = "permutation"), respectively. Hence, adjusted p-values can be obtained.

Usage

RMTL.test(
  time = NULL,
  status = NULL,
  group = NULL,
  formula = NULL,
  event = NULL,
  data = NULL,
  hyp_mat,
  hyp_vec = NULL,
  M = NULL,
  tau,
  method = c("permutation", "asymptotic"),
  stepwise = FALSE,
  alpha = 0.05,
  Nres = 4999,
  seed = 1
)

Arguments

Details

The restricted mean time lost (RMTL) of group i and event m is defined as

\mu_{im} := \int\limits_0^{\tau} F_{im}(t) \mathrm{d}t

for all i\in\{1,...,k\}, m\in\{1,...,M\}, where F_{im} denotes the cumulative incidence function of group i and event m. Let

\boldsymbol{\mu} := (\mu_{11},\mu_{12},...,\mu_{kM})^{\prime}

be the vector of the RMTLs and

\widehat{\boldsymbol{\mu}} := (\widehat{\mu}_{11},\widehat{\mu}_{12},...,\widehat{\mu}_{kM})^{\prime}

be the vector of their estimators. Let \mathbf{H}_{\ell} \in {\rm I\!R}^{r_{\ell}\times kM} with \mathrm{rank}(\mathbf{H}_{\ell}) >0 and \mathbf{c}_{\ell} \in {\rm I\!R}^{r_{\ell}} for all \ell\in\{1,...,L\}. We are considering the multiple testing problem with null and alternative hypotheses

\mathcal{H}_{0,\ell}: \mathbf{H}_{\ell} \boldsymbol\mu = \mathbf{c}_{\ell} \quad \mathrm{vs.} \quad \mathcal{H}_{1,\ell}: \mathbf{H}_{\ell} \boldsymbol\mu \neq \mathbf{c}_{\ell}, \qquad \mathrm{for }\: \ell\in\{1,...,L\}.

For the permutation test, the matrices additionally need to fulfill \mathbf{H}_{\ell}(\mathbf{1}_k\otimes \mathbf{e}_m) = \mathbf{0}_{r_{\ell}} for all m, \ell, where \mathbf{1}_k\in {\rm I\!R}^{k}, \mathbf{e}_m \in {\rm I\!R}^{M}, \mathbf{0}_{r_{\ell}} \in {\rm I\!R}^{r_{\ell}} denote the vector of ones, the mth unit vector and the vector of zeros, respectively.

For the argument hyp_mat, the options "Dunnett" and "Tukey" create the cause-wise many-to-one and all-pairs comparisons, respectively, as described in Example 3 of Munko et al. (2024) and the options "2by2" and "2by2 cause-wisely" create the hypothesis matrices as described in Example 4 of Munko et al. (2024).

If stepwise = TRUE, the closed testing procedure is applied. In this case, no confidence intervals can be computed for the linear combinations but potentially more tests can reject.

Note that the calculations for the permutation test may take a while.

Value

A list of class GFDrmst containing the following components:

References

Munko, M., Dobler, D., Ditzhaus, M. (2024). Multiple tests for restricted mean time lost with competing risks data, arXiv preprint (arXiv:2409.07917). doi:10.48550/arXiv.2409.07917

Examples

library(mstate)
data("ebmt2")

# multiple asymptotic tests
out <- RMTL.test(time = ebmt2$time,
                 status = ebmt2$status,
                 group = ebmt2$match,
                 hyp_mat = "Dunnett",
                 tau = 120,
                 method = "asymptotic")
summary(out)
plot(out)

## or, equivalently,
out <- RMTL.test(formula = "time ~ match",
                 event = "status",
                 data = ebmt2,
                 hyp_mat = "Dunnett",
                 tau = 120,
                 method = "asymptotic")
summary(out)
plot(out)


# multiple permutation tests
# this may take a few minutes
out_perm <- RMTL.test(formula = "time ~ match",
                      event = "status",
                      data = ebmt2,
                      hyp_mat = "Dunnett",
                      tau = 120,
                      method = "permutation",
                      Nres = 999)
summary(out_perm)
plot(out_perm)