logrank.maxtest: Maximum combination (MaxCombo) log-rank test

In nph: Planning and Analysing Survival Studies under Non-Proportional Hazards

Maximum combination (MaxCombo) log-rank test

Description

Calculates a MaxCombo test for the comparison of two groups based on the maximum of test statistics of a set of weighted log-rank tests

Usage

logrank.maxtest(
  time,
  event,
  group,
  alternative = c("two.sided", "less", "greater"),
  rho = c(0, 0, 1),
  gamma = c(0, 1, 0),
  event_time_weights = NULL,
  algorithm = mvtnorm::GenzBretz(maxpts = 50000, abseps = 1e-05, releps = 0)
)

Arguments

time	Vector of observed event/censored times
event	logical vector or numeric vector with entries 0 or 1, indicating if an event was observed (TRUE or 1) or the time is censored (FALSE or 0)
group	Vector of group allocations
alternative	Either of "two.sided","less" or "greater", specifies if two-sided or respective one-sided p-values are calculated. In any case the z test statistic of each included weighted log-rank test is based on the (weighted) sum of expected minus observed events in the group corresponding to the first factor level of group. Hence a small value of the test statistic corresponds to a lower (weighted average) hazard rate in the first group.
rho	Vector of parameter values rho for a set of weighting functions in the rho-gamma family
gamma	Vector of parameter values gamma for a set of weighting functions in the rho-gamma family
event_time_weights	Optional matrix, each column containing a different weighting vector for the event times. These weight vectors need to have one entry per event time (not per event, as multiple events may occur at the same time) and must be sorted by increasing event time.
algorithm	algorithm for the multivariate normal integration to be used in pmvnorm.

Details

To perform a maximum-type combination test, a set of m different weight functions w_1(t), …, w_m(t) is specified and the correspondingly weighted logrank statistics z_1,…,z_m are calculated. The maximum test statistic is z_{max}=\max_{i=1,…,m} z_i. If at least one of the selected weight functions results in high power, we may expect a large value of z_{max}. Under the least favorable configuration in H_0, approximately (Z_1,…,Z_m)\sim N_m({0},{Σ}). The p-value of the maximum test, P_{H_0}(Z_{max}>z_{max})=1-P(Z_1 ≤q z_{max},…,Z_m ≤q z_{max}), is calculated based on this multivariate normal approximation via numeric integration. The integration is done using pmvnorm. The default settings in logrank.maxtest correspond to greater precision than the original default of pmvnorm. Precision can be set via the argument algorithm. Lower precision settings may speed up caclulation.

The multivariate normal approach automatically corrects for multiple testing with different weights and does so efficiently since the correlation between the different tests is incorporated in {Σ}. For actual calculations, {Σ} is replaced by an estimate.

Value

A list with elements:

pmult

The two sided p-value for the null hypothesis of equal hazard functions in both groups, based on the multivariate normal approximation for the z-statistics of differently weighted log-rank tests.

p.Bonf

The two sided p-value for the null hypothesis of equal hazard functions in both groups, based on a Bonferroni multiplicity adjustment for differently weighted log-rank tests.

tests

Data frame with z-statistics and two-sided unadjusted p-values of the individual weighted log-rank tests

korr

Estimated correlation matrix for the z-statistics of the differently weighted log-rank tests.

Author(s)

Robin Ristl, [e-mail]

References

Robin Ristl, Nicolas Ballarini, Heiko Götte, Armin Schüler, Martin Posch, Franz König. Delayed treatment effects, treatment switching and heterogeneous patient populations: How to design and analyze RCTs in oncology. Pharmaceutical statistics. 2021; 20(1):129-145.

Pranab Ghosh, Robin Ristl, Franz König, Martin Posch, Christopher Jennison, Heiko Götte, Armin Schüler, Cyrus Mehta. Robust group sequential designs for trials with survival endpoints and delayed response. Biometrical Journal. First published online: 21 December 2021

Tarone RE. On the distribution of the maximum of the logrank statistic and the modified wilcoxon statistic. Biometrics. 1981; 37:79-85.

Lee S-H. On the versatility of the combination of the weighted log-rank statistics. Comput Stat Data Anal. 2007; 51(12):6557-6564.

Karrison TG et al. Versatile tests for comparing survival curves based on weighted log-rank statistics. Stata J. 2016; 16(3):678-690.

See Also

logrank.test

Examples

A <- pop_pchaz(Tint = c(0, 90, 1500),
  lambdaMat1 = matrix(c(0.2, 0.1, 0.4, 0.1), 2, 2) / 365,
 lambdaMat2 = matrix(c(0.5, 0.2, 0.6, 0.2), 2, 2) / 365,
 lambdaProg = matrix(c(0.5, 0.5, 0.4, 0.4), 2, 2) / 365,
 p = c(0.8, 0.2), 
 timezero = FALSE, discrete_approximation = TRUE)
B <- pop_pchaz(Tint = c(0, 90, 1500),
  lambdaMat1 = matrix(c(0.2, 0.1, 0.4, 0.1), 2, 2) / 365,
 lambdaMat2 = matrix(c(0.5, 0.1, 0.6, 0.1), 2, 2) / 365,
 lambdaProg = matrix(c(0.5, 0.5, 0.04, 0.04), 2, 2) / 365,
 p = c(0.8, 0.2), 
 timezero = FALSE, discrete_approximation = TRUE)
dat <- sample_fun(A, B, r0 = 0.5, eventEnd = 30,
  lambdaRecr = 0.5, lambdaCens = 0.25 / 365,
 maxRecrCalendarTime = 2 * 365,
 maxCalendar = 4 * 365)
logrank.maxtest(dat$y, dat$event, dat$group)

nph documentation built on May 17, 2022, 1:06 a.m.