Logrank-type test for comparing recurrent event marginal means between groups

Tests whether the marginal mean number of recurrent events differs across groups (strata), extending the classical logrank test to the setting of recurrent events with a competing terminal event. The test statistic is $$z = \int_0^\tau w(s)\bigl[d\hat\mu_1(s) - d\hat\mu_2(s)\bigr],$$ where $w(s)$ is a weight function and $\hat\mu_j(s)$ is the estimated marginal mean for group $j$. Variance is estimated robustly via the influence functions of Ghosh and Lin (2000).

Usage

test_logrankRecurrent(
  recurrent,
  death,
  weight = c("I", "II"),
  km = TRUE,
  start = 0,
  stop = NULL,
  at.risk = 5,
  cluster.id = NULL,
  ...
)

Arguments

recurrent: Either a "recurrent" object returned by recurrent_marginal, or a "phreg" object for the recurrent event model (in which case death must also be supplied).
death: A "phreg" object for the terminal event model. Required when recurrent is a "phreg" object; ignored otherwise.
weight: Character string specifying the weight scheme: "I", "II", or "III". Default is "I".
km: Logical. If TRUE (default), the Kaplan-Meier estimator is used for the survival probability $S(t)$; otherwise the Nelson-Aalen estimator is used.
start: Left truncation time for the integration. Default is 0.
stop: Right truncation time for the integration. Defaults to the last observed jump time.
at.risk: Minimum combined risk-set size below which the weight is set to zero. Default is 5.
cluster.id: Optional vector of cluster identifiers for aggregating influence functions across clusters before forming the test statistic.
...: Currently unused.

Value

An object of class "estimate" (from the lava package) with the following components:

coef: The weighted difference in marginal means between groups.
se: Robust standard error of the test statistic.
lower, upper: 95% confidence interval bounds.
p.value: Two-sided p-value for the null hypothesis of no difference.

The object also carries an iid attribute containing the subject-level influence function decomposition of the test statistic, which can be used for further inference or combination with other estimators.

Details

Three weight schemes are available:

"I": (Default) $w(t) = R_1(t) R_2(t) / (R_1(t) + R_2(t))$, where $R_j(t) = Y_j(t) / \hat S_j(t-)$. Analogous to the standard logrank weight.
"II": $w(t) = Y_j(t)$, the raw risk-set size. Equivalent to using observed counts without survival adjustment.
"III": A modified weight incorporating the cumulative incidence, analogous to Gray's test for competing risks.

References

Ghosh, D. and Lin, D. Y. (2000). Nonparametric analysis of recurrent events and death. Biometrics, 56, 554–562.

Author

Thomas Scheike

Examples

data(hfactioncpx12)
hf <- hfactioncpx12

## Test using two separate phreg models
xr <- phreg(Surv(entry, time, status == 1) ~ strata(treatment) + cluster(id), data = hf)
dr <- phreg(Surv(entry, time, status == 2) ~ strata(treatment) + cluster(id), data = hf)
out <- test_logrankRecurrent(xr, dr, stop = 5)
summary(out)
#> Call: estimate.default(f = FALSE, contrast = contrast, vcov = vcov(object), 
#>     coef = p)
#> ────────────────────────────────────────────────────────────
#>    Estimate Std.Err   2.5% 97.5% P-value
#> p1    37.98   27.04 -15.01 90.97  0.1601
#> ────────────────────────────────────────────────────────────
#> Null Hypothesis: 
#>   [p1] = 0 
#>  
#> chisq = 1.9737, df = 1, p-value = 0.1601

## Equivalently, using a recurrent_marginal object directly
outN <- recurrent_marginal(Event(entry, time, status) ~ strata(treatment) + cluster(id),
                           data = hf, cause = 1, death.code = 2)
test_logrankRecurrent(outN)
#>    Estimate Std.Err   2.5% 97.5% P-value
#> p1    37.98   27.04 -15.01 90.97  0.1601
#> ────────────────────────────────────────────────────────────
#> Null Hypothesis: 
#>   [p1] = 0 
#>  
#> chisq = 1.9737, df = 1, p-value = 0.1601