wlr.maxcombo: Max-combo Test (Stratified) At A Single Time Point
In phe9480/rgs: What the Package Does (One Line, Title Case)

Description Usage Arguments Details Value Examples

Max-combo is a class of multiple combination tests. This function considers the maximum of multiple weighted log-rank tests, i.e. z_maxcombo = max(z1, z2, ..., zk), where zi is the weighted log-rank test statistic with weight function wi. This function calculates the p-value and associated statistics when performing the max-combo test. The weight function wi can be the flexible Stabilized Fleming-Harrington class sFH(rho, gamma, tau, s.tau), or any user-defined weight function.

wlr.maxcombo(
  time = c(5, 7, 10, 12, 12, 15, 20, 20),
  event = c(1, 0, 0, 1, 1, 0, 1, 1),
  group = c(0, 1, 0, 1, 0, 1, 0, 1),
  strata1 = NULL,
  strata2 = NULL,
  strata3 = NULL,
  rho = c(0, 0, 0),
  gamma = c(0, 0.5, 1),
  tau = NULL,
  s.tau = c(0, 0, 0.5),
  f.ws = list(lr = function(s) {     return(1) }, fh005 = function(s) {     sqrt(1 - s)
    }, sfh01 = function(s) {     1 - apply(cbind(s, 0.5), MARGIN = 1, FUN = max) }),
  side = c("two.sided", "one.sided")
)

`time`	Survival time
`event`	Event indicator; 1 = event, 0 = censor
`group`	Treatment group; 1 = experimental group, 0 = control
`strata1`	Stratification variable 1
`strata2`	Stratification variable 2
`strata3`	Stratification variable 3
`rho`	A vector of rho parameters for Fleming-Harrington (rho, gamma) weighted log-rank tests.
`gamma`	A vector of gamma parameters for Fleming-Harrington (rho, gamma) weighted log-rank tests. For log-rank test, set rho = gamma = 0.
`tau`	A vector of cut points for stabilized FH test, sFH(rho, gamma, tau); with weight function defined as w(t) = s_tilda^rho*(1-s_tilda)^gamma, where s_tilda = max(s(t), s.tau) or max(s(t), s(tau)) if s.tau = NULL tau = Inf reduces to regular Fleming-Harrington test(rho, gamma)
`s.tau`	A vector of survival rate cuts S(tau) at t = tau; default 0.5, ie. cut at median. s.tau = 0 reduces to regular Fleming-Harrington test(rho, gamma)
`f.ws`	Self-defined weight functions of survival rate. For example, f.ws=list( lr = function(s)return(1), fh005=function(s)sqrt(1-s), sfh01=function(s)1-apply(cbind(s, 0.5),MARGIN=1,FUN=max) ) defines 3 weighted log-rank tests: log-rank, FH(0, 0.5), and sFH(0, 1, s.tau=0.5) When f.ws is specified, the weight function takes it as priority. Note: The actual math formula for weighting function is based on the left of each event time t, i.e., w(t) = f.ws(s(t-)). For FH(rho, gamma) test, when gamma = 0, then the first event time has weight 1; when gamma > 0, the first event weight is 0. This can ensure consistency with FH(0,0) = logrank; and FH(1,0) = generalized Wilcoxon.
`side`	Type of test. one.sided or two.sided. default = two.sided

Refer to Karrinson (2016) for the method of max-combo when it is defined based on FH(0, 0), FH(1, 0), FH(0, 1) and FH(1, 1). However, this function extends the concept to include any type of weighted log-rank tests. The kth weighted log-rank test has parameters of (rho_k, gamma_k, tau_k, s.tau_k) defined in the stabilized Fleming-Harrington class (He et al 2021) or user-defined weight function f.ws_k, for k = 1, ..., K. For the stabilized Fleming-Harrington class, specify either tau or s.tau, which are thresholds in survival time and survival rate, respectively. In addition, the weight function is estimated within each strata. One-sided test is more appropriate in maxcombo test.

data: dataframe including the following variables:

time: Survival time
event: Event indicator; 0 = censor; 1 = event
group: Group indicator; 0 = control; 1 = experimental treatment
strata1; Strata 1
strata2; Strata 2
strata3; Strata 3

corr: Correlation matrix of weighted log-rank tests
test.results: dataframe including the following variables:

rho: Stabilized Fleming-Harrington test parameter
gamma: Stabilized Fleming-Harrington test parameter
tau: Stabilized Fleming-Harrington test parameter if provided
s.tau: Stabilized Fleming-Harrington test parameter if provided
test.side: 1 or 2
z: Normalized weighted log-rank z statistics
z.max: maximum of weighted log-rank test statistics(1-sided test)
abs.z.max maximum of absolute values of weighted log-rank test statistics (2-sided tests)
p: P value

wt: Weight function(s) used in the calculation

#Example (1) Stratified max-combo test including 3 weighted log-rank test statistics:
#log-rank, FH(0, 0.5), and sFH(0, 1, tau=0.5).
time=rexp(100); event=sample(c(0,1), 100, replace = TRUE); 
group=c(rep(0, 50), rep(1, 50)); 
strata1=sample(c(1,2), 100, replace = TRUE)
strata2=sample(c(1,2), 100, replace = TRUE) 
strata3=sample(c(3,4), 100, replace = TRUE)
rho = c(0,0,0); gamma=c(0,0.5,1); tau = NULL; s.tau=c(0, 0, 0.5);
f.ws=list(
         lr = function(s){return(1)}, 
         fh005=function(s){sqrt(1-s)},
         sfh01=function(s){1-apply(cbind(s, 0.5),MARGIN=1,FUN=max)}
         )
side = c("one.sided")

wlr.maxcombo(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=rho, gamma=gamma, 
tau = tau, s.tau=s.tau, f.ws=f.ws, side = side)

#Equivalent to 
wlr.maxcombo(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=rho, gamma=gamma, 
tau = tau, s.tau=s.tau, f.ws=NULL, side = side)

#Example (2) If there is only 1 weighted log-rank test, max-combo reduces to weighted log-rank test
#FH01 test
wlr.maxcombo(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=0, gamma=1, 
tau = NULL, s.tau=0, f.ws=NULL, side = side)

#equivalent to
wlr(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=0, gamma=1, 
tau = NULL, s.tau=0, f.ws=NULL, side = side)

#Example (3) maxcombo of (logrank, FH01, FH11)
wlr.maxcombo(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=c(0,0,1), gamma=c(0,1,1), 
tau = NULL, s.tau=c(0,0,0), f.ws=NULL, side = side)

#Example (4) maxcombo of (logrank, FH01)
wlr.maxcombo(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=c(0,0), gamma=c(0,1), 
tau = NULL, s.tau=c(0,0), f.ws=NULL, side = side)

#Example (5) maxcombo of (logrank, modestly logrank)
wlr.maxcombo(time=time, event=event, group=group, strata1=strata1, 
strata2=strata2, strata3=strata3, rho=NULL, gamma=NULL, 
tau = NULL, s.tau=NULL, f.ws=list(
lr = function(s){1},
mlr = function(s){1/apply(cbind(s, 0.5),MARGIN=1,FUN=max)}), side = side)