Pepe-Mori Test for Marginal Mean Comparison

Performs score-test type tests for proportionality of marginal means in competing risks data and recurrent events, as presented in Ghosh and Lin (2000). The test is based on an IPCW (Inverse Probability of Censoring Weighting) formulation.

Usage

test_marginalMean(
  formula,
  data,
  cause = 1,
  cens.code = 0,
  ...,
  death.code = 2,
  death.code.prop = NULL,
  time = NULL,
  beta = NULL
)

Arguments

formula: Formula with an Event object on the left-hand side and covariates (typically with strata() for group comparison) on the right. Can include cluster(id) for correlated data.
data: Data frame containing all variables referenced in the formula.
cause: Cause of interest (default 1).
cens.code: Censoring code (default 0).
...: Additional arguments passed to lower-level functions.
death.code: Code for death (terminating event, default 2).
death.code.prop: Code for other causes of death for Fine-Gray regression model.
time: Upper limit for Pepe-Mori and AUC integrals. If NULL, defaults to the maximum event time for the cause of interest.
beta: Starting values for the score test (default NULL, uses zeros).

Value

An object of class "marginalTest" containing:

pepe.mori: Pepe-Mori test results with compare p-value.
RatioAUC: Ratio of AUC test results with compare p-value.
difAUC: Difference of AUC test results with compare p-value.
prop.test: Proportionality test results.
score.test: Score test results (equivalent to Gray's test).
score.iid: Influence function for the score test.
time: Upper time limit used.
RAUCl, RAUCe: Raw and transformed AUC estimates.

Details

The function computes several tests:

Pepe-Mori Test: Tests for equality of marginal mean functions between groups.
Ratio of AUC: Compares the area under the curve of marginal means.
Difference of AUC: Tests for difference in areas under the curve.
Score Test: Tests for proportionality (equivalent to Gray's test for CIF).
Proportionality Test: Tests the proportional hazards assumption.

The Pepe-Mori test uses weights based on the number at risk in each group to construct a weighted integral of the difference in marginal means.

References

Ghosh, D. and Lin, D. Y. (2000). Nonparametric Analysis of Recurrent Events and Death. Biometrics, 56, 554–562.

Author

Thomas Scheike

Examples

data(bmt,package="mets")
bmt$time <- bmt$time+runif(nrow(bmt))*0.01
bmt$id <- 1:nrow(bmt)
dcut(bmt) <- age.f~age
     
fg=cifregFG(Event(time,cause)~tcell,data=bmt,cause=1)
 
## computing tests for difference  for CIF
pmt <- test_marginalMean(Event(time,cause)~strata(tcell)+cluster(id),data=bmt,cause=1,
       death.code=1:2,death.code.prop=2,cens.code=0,time=40)
#> Warning: IC does not have mean zero (max |mean|/rms = 0.11). Using lava.options(check.ic = FALSE) disables the warning globally.
summary(pmt) 
#> coeffients:
#>                            p-value
#> time                       40.0000
#> Pepe-Mori                   0.0203
#> Ratio-AUC                   0.0494
#> Proportionality             0.0500
#> Proportionality-score-test  0.0292
#> 
 
pmt$pepe.mori
#>                         Estimate Std.Err   2.5%  97.5% P-value
#> factor(strata__)tcell=1   -6.409   2.762 -11.82 -0.996 0.02031
#> ────────────────────────────────────────────────────────────
#> Null Hypothesis: 
#>   [factor(strata__)tcell=1] = 0 
#>  
#> chisq = 5.385, df = 1, p-value = 0.02031
pmt$RatioAUC
#>             Estimate Std.Err    2.5%     97.5% P-value
#> (Intercept)   -0.484  0.2463 -0.9667 -0.001352 0.04936
#> ────────────────────────────────────────────────────────────
#> Null Hypothesis: 
#>   [(Intercept)] = 0 
#>  
#> chisq = 3.863, df = 1, p-value = 0.04936
pmt$prop.test
#>                         Estimate Std.Err   2.5%      97.5% P-value
#> factor(strata__)tcell=1  -0.5157  0.2631 -1.031 -5.483e-05 0.04998
#> ────────────────────────────────────────────────────────────
#> Null Hypothesis: 
#>   [factor(strata__)tcell=1] = 0 
#>  
#> chisq = 3.8423, df = 1, p-value = 0.04998
## score test equialent to Gray's test but variance estimated differently 
pmt$score.test
#>    Estimate Std.Err   2.5%   97.5% P-value
#> p1   -8.633   3.957 -16.39 -0.8764 0.02915
#> ────────────────────────────────────────────────────────────
#> Null Hypothesis: 
#>   [p1] = 0 
#>  
#> chisq = 4.7586, df = 1, p-value = 0.02915
 
### age-groups  
pmt <- test_marginalMean(Event(time,cause)~strata(age.f)+cluster(id),data=bmt,cause=1,
       death.code=1:2,death.code.prop=2,cens.code=0)
#> Warning: IC does not have mean zero (max |mean|/rms = 0.097). Using lava.options(check.ic = FALSE) disables the warning globally.
summary(pmt) 
#> coeffients:
#>                            p-value
#> time                       70.6322
#> Pepe-Mori                       NA
#> Ratio-AUC                   0.0060
#> Proportionality             0.0018
#> Proportionality-score-test  0.0002
#> 
 
## having a look at the cumulative incidences 
cifs <- cif(Event(time,cause)~strata(age.f)+cluster(id),data=bmt,cause=1)
plot(cifs) 

 
## recurrent events   
data(hfactioncpx12)
hf <- hfactioncpx12
pmt <- test_marginalMean(Event(entry,time,status)~strata(treatment)+cluster(id),data=hf,
       cause=1,death.code=2,cens.code=0)
#> Warning: IC does not have mean zero (max |mean|/rms = 0.051). Using lava.options(check.ic = FALSE) disables the warning globally.
summary(pmt) 
#> coeffients:
#>                            p-value
#> time                        3.9794
#> Pepe-Mori                   0.2918
#> Ratio-AUC                   0.2278
#> Proportionality             0.1641
#> Proportionality-score-test  0.1611
#>