# NOT RUN {
# -------------------------------------------------------------------------------
# Example 1: Usage on a single deterministic dataset in which the drug halves
# the hazard at all times (i.e., a proportional hazards situation)
# -------------------------------------------------------------------------------
oointnparticipants=100L
oointnparticipantsplacebo=oointnparticipants/2L
oointnparticipantsactive=oointnparticipants/2L
oodoublerateplacebo=0.250
oodoublerateactive=0.125
oovecinttreated=c(
base::rep(0L,length.out=oointnparticipantsplacebo),
base::rep(1L,length.out=oointnparticipantsactive)
)
oovecdoubletAabsolute=c( #the start time, i.e., when the subject enters the study.
base::seq(from=0.0,to=2.0,length.out=oointnparticipantsplacebo),
base::seq(from=0.0,to=2.0,length.out=oointnparticipantsactive)
)
#the duration of time from when the subject enters the study until the subject experiences the event
oovecdoubletAtoB=c(
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsplacebo),
rate=oodoublerateplacebo
),
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsactive),
rate=oodoublerateactive
)
)
oovecdoubletBabsolute=oovecdoubletAabsolute + oovecdoubletAtoB
#the analysis takes place at absolute time 6.0 months, and no other censoring (e.g., dropout) occurs
oovecdoubletCabsolute=6.0
oovecdoubletminBvsC=base::pmin(oovecdoubletBabsolute,oovecdoubletCabsolute)
oovecboolobservedB=(oovecdoubletBabsolute < oovecdoubletCabsolute)
oovecboolobservedC=(oovecdoubletCabsolute <= oovecdoubletBabsolute)
oodataframe=dplyr::tibble(id=1L:oointnparticipants,
treated=oovecinttreated,
Atime=oovecdoubletAabsolute,
Btime=oovecdoubletminBvsC,
Bobserved=oovecboolobservedB,
Ctime=oovecdoubletminBvsC,
Cobserved=oovecboolobservedC)
#standardized log-rank test statistic
oolistweightingfunctionsJustLogrank=base::list(
logrank=function(stminus){ base::return(1.0) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank
) #test statistic 2.92
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank
) #p-value 0.0017
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.92 > 1.96), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#standardized weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function,
#which places greater weight on later times
oolistweightingfunctionsJustFlemingHarrington01=base::list(
flemingharrington01=function(stminus){ base::return(1.0 - stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01
) #test statistic 2.83
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01
) #p-value 0.0023
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.83 > 1.96), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#standardized weighted log-rank test statistic with Fleming-Harrington 1-0 weighting function,
#which places greater weight on earlier times
oolistweightingfunctionsJustFlemingHarrington10=base::list(
flemingharrington10=function(stminus){ base::return(stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10
) #test statistic 2.71
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10
) #p-value 0.0033
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.71 > 1.96), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#the max-combo test statistic based on the first two of the above
oolistweightingfunctionsLogrankAndFlemingHarrington01=base::list(
logrank=function(stminus){ base::return(1.0) },
flemingharrington01=function(stminus){ base::return(1.0 - stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01
) #test statistic 2.92, i.e., just the maximum of 2.92 (from the log-rank test statistic) and 2.83
# (from the weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function)
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01
) #p-value 0.0028
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01,
oodoublealpha = 0.025
) #cutoff of 2.13 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.92 > 2.13), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#the max-combo test statistic based on the first three of the above
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10=base::list(
logrank=function(stminus){ base::return(1.0) },
flemingharrington01=function(stminus){ base::return(1.0 - stminus) },
flemingharrington10=function(stminus){ base::return(stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10
) #test statistic 2.92, i.e., just the maximum of 2.92 (from the log-rank test statistic), 2.83
# (from the weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function), and
# 2.71 (from the weighted log-rank test statistic with Fleming-Harrington 1-0 weighting function)
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10
) #p-value 0.0032
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10,
oodoublealpha = 0.025,
oointnmaxiter = 100L
) #cutoff of 2.19 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.92 > 2.19), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
# --------------------------------------------------------------------------------------------
# Example 2: Usage on a single deterministic dataset in which the drug delays
# the event by exactly one month for each subject (i.e., an early treatment effect situation)
# --------------------------------------------------------------------------------------------
oointnparticipants=100L
oointnparticipantsplacebo=oointnparticipants/2L
oointnparticipantsactive=oointnparticipants/2L
oodoublerateplacebo=0.250
oovecinttreated=c(
base::rep(0L,length.out=oointnparticipantsplacebo),
base::rep(1L,length.out=oointnparticipantsactive)
)
oovecdoubletAabsolute=c( #the start time, i.e., when the subject enters the study.
base::seq(from=0.0,to=2.0,length.out=oointnparticipantsplacebo),
base::seq(from=0.0,to=2.0,length.out=oointnparticipantsactive)
)
#the duration of time from when the subject enters the study until the subject experiences the event
oovecdoubletAtoB=c(
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsplacebo),
rate=oodoublerateplacebo
),
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsactive),
rate=oodoublerateplacebo
) + 1.0 #note the addition of 1.0 month time to event here for the active arm
)
oovecdoubletBabsolute=oovecdoubletAabsolute + oovecdoubletAtoB
#the analysis takes place at absolute time 6.0 months, and no other censoring (e.g., dropout) occurs
oovecdoubletCabsolute=6.0
oovecdoubletminBvsC=base::pmin(oovecdoubletBabsolute,oovecdoubletCabsolute)
oovecboolobservedB=(oovecdoubletBabsolute < oovecdoubletCabsolute)
oovecboolobservedC=(oovecdoubletCabsolute <= oovecdoubletBabsolute)
oodataframe=dplyr::tibble(id=1L:oointnparticipants,
treated=oovecinttreated,
Atime=oovecdoubletAabsolute,
Btime=oovecdoubletminBvsC,
Bobserved=oovecboolobservedB,
Ctime=oovecdoubletminBvsC,
Cobserved=oovecboolobservedC)
#standardized log-rank test statistic
oolistweightingfunctionsJustLogrank=base::list(
logrank=function(stminus){ base::return(1.0) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank
) #test statistic 1.66
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank
) #p-value 0.05
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic does not exceed the cutoff (since 1.66 < 1.96), so you fail to reject
#that the survival curves in the two arms are the same at the 0.025 level
#standardized weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function,
#which places greater weight on later times
oolistweightingfunctionsJustFlemingHarrington01=base::list(
flemingharrington01=function(stminus){ base::return(1.0 - stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01
) #test statistic 0.53
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01
) #p-value 0.30
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic does not exceed the cutoff (since 0.53 < 1.96), so you fail to reject
#that the survival curves in the two arms are the same at the 0.025 level
#standardized weighted log-rank test statistic with Fleming-Harrington 1-0 weighting function,
#which places greater weight on earlier times
oolistweightingfunctionsJustFlemingHarrington10=base::list(
flemingharrington10=function(stminus){ base::return(stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10
) #test statistic 2.07
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10
) #p-value 0.02
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.07 > 1.96), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#the max-combo test statistic based on the first two of the above
oolistweightingfunctionsLogrankAndFlemingHarrington01=base::list(
logrank=function(stminus){ base::return(1.0) },
flemingharrington01=function(stminus){ base::return(1.0 - stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01
) #test statistic 1.66, i.e., just the maximum of 1.66 (from the log-rank test statistic) and 0.53
# (from the weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function)
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01
) #p-value 0.07
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01,
oodoublealpha = 0.025
) #cutoff of 2.13 for the max-combo test statistic
#the max-combo test statistic does not exceed the cutoff (since 1.66 < 2.13), so you fail to reject
#that the survival curves in the two arms are the same at the 0.025 level
#the max-combo test statistic based on the first three of the above
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10=base::list(
logrank=function(stminus){ base::return(1.0) },
flemingharrington01=function(stminus){ base::return(1.0 - stminus) },
flemingharrington10=function(stminus){ base::return(stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10
) #test statistic 2.07, i.e., just the maximum of 1.66 (from the log-rank test statistic), 0.53
# (from the weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function), and
# 2.07 (from the weighted log-rank test statistic with Fleming-Harrington 1-0 weighting function)
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10
) #p-value 0.03
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10,
oodoublealpha = 0.025,
oointnmaxiter = 100L
) #cutoff of 2.20 for the max-combo test statistic
#the max-combo test statistic does not exceed the cutoff (since 2.06 < 2.20), so you fail to reject
#that the survival curves in the two arms are the same at the 0.025 level
# -------------------------------------------------------------------------------------------------
# Example 3: Usage on a single deterministic dataset in which subjects in the placebo arm all have
# the event after being on the study for 1.2 months (i.e., a delayed treatment effect situation)
# -------------------------------------------------------------------------------------------------
oointnparticipants=100L
oointnparticipantsplacebo=oointnparticipants/2L
oointnparticipantsactive=oointnparticipants/2L
oodoublerateactive=0.250
oovecinttreated=c(
base::rep(0L,length.out=oointnparticipantsplacebo),
base::rep(1L,length.out=oointnparticipantsactive)
)
oovecdoubletAabsolute=c( #the start time, i.e., when the subject enters the study.
base::seq(from=0.0,to=2.0,length.out=oointnparticipantsplacebo),
base::seq(from=0.0,to=2.0,length.out=oointnparticipantsactive)
)
#the duration of time from when the subject enters the study until the subject experiences the event
oovecdoubletAtoB=c(
base::ifelse(
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsplacebo),
rate=oodoublerateactive
) <= 1.2,
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsplacebo),
rate=oodoublerateactive
),
1.2
),
stats::qexp(
base::seq(from=0.0,to=0.98,length.out=oointnparticipantsactive),
rate=oodoublerateactive
)
)
oovecdoubletBabsolute=oovecdoubletAabsolute + oovecdoubletAtoB
#the analysis takes place at absolute time 6.0 months, and no other censoring (e.g., dropout) occurs
oovecdoubletCabsolute=6.0
oovecdoubletminBvsC=base::pmin(oovecdoubletBabsolute,oovecdoubletCabsolute)
oovecboolobservedB=(oovecdoubletBabsolute < oovecdoubletCabsolute)
oovecboolobservedC=(oovecdoubletCabsolute <= oovecdoubletBabsolute)
oodataframe=dplyr::tibble(id=1L:oointnparticipants,
treated=oovecinttreated,
Atime=oovecdoubletAabsolute,
Btime=oovecdoubletminBvsC,
Bobserved=oovecboolobservedB,
Ctime=oovecdoubletminBvsC,
Cobserved=oovecboolobservedC)
#standardized log-rank test statistic
oolistweightingfunctionsJustLogrank=base::list(
logrank=function(stminus){ base::return(1.0) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank
) #test statistic 1.55
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank
) #p-value 0.06
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustLogrank,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic does not exceed the cutoff (since 1.55 < 1.96), so you fail to reject
#that the survival curves in the two arms are the same at the 0.025 level
#standardized weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function,
#which places greater weight on later times
oolistweightingfunctionsJustFlemingHarrington01=base::list(
flemingharrington01=function(stminus){ base::return(1.0 - stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01
) #test statistic 2.28
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01
) #p-value 0.01
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington01,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.28 > 1.96), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#standardized weighted log-rank test statistic with Fleming-Harrington 1-0 weighting function,
#which places greater weight on earlier times
oolistweightingfunctionsJustFlemingHarrington10=base::list(
flemingharrington10=function(stminus){ base::return(stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10
) #test statistic 1.35
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10
) #p-value 0.09
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsJustFlemingHarrington10,
oodoublealpha = 0.025
) #cutoff of 1.96 for the max-combo test statistic
#the max-combo test statistic does not exceed the cutoff (since 1.35 < 1.96), so you fail to reject
#that the survival curves in the two arms are the same at the 0.025 level
#the max-combo test statistic based on the first two of the above
oolistweightingfunctionsLogrankAndFlemingHarrington01=base::list(
logrank=function(stminus){ base::return(1.0) },
flemingharrington01=function(stminus){ base::return(1.0 - stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01
) #test statistic 2.28, i.e., just the maximum of 1.55 (from the log-rank test statistic) and 2.28
# (from the weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function)
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01
) #p-value 0.02
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus = oolistweightingfunctionsLogrankAndFlemingHarrington01,
oodoublealpha = 0.025
) #cutoff of 2.13 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.28 > 2.13), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
#the max-combo test statistic based on the first three of the above
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10=base::list(
logrank=function(stminus){ base::return(1.0) },
flemingharrington01=function(stminus){ base::return(1.0 - stminus) },
flemingharrington10=function(stminus){ base::return(stminus) }
)
maxcombo::oogetdoublemaxcomboteststatistic(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10
) #test statistic 2.28, i.e., just the maximum of 1.55 (from the log-rank test statistic), 2.28
# (from the weighted log-rank test statistic with Fleming-Harrington 0-1 weighting function), and
# 1.35 (from the weighted log-rank test statistic with Fleming-Harrington 1-0 weighting function)
maxcombo::oogetdoublemaxcombotestpvalue(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10
) #p-value 0.02
maxcombo::oogetdoublemaxcombocutoff(
oodataframe = oodataframe,
oolistfunctionweightasafunctionofstminus =
oolistweightingfunctionsLogrankAndFlemingHarrington01AndFlemingHarrington10,
oodoublealpha = 0.025,
oointnmaxiter = 200L
) #cutoff of 2.15 for the max-combo test statistic
#the max-combo test statistic exceeds the cutoff (since 2.28 > 2.15), so you can declare that
#the survival curves in the two arms are statistically significantly different at the 0.025 level
# }
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