R/corrEvents.R
In phe2189/corrTests: What the Package Does (One Line, Title Case)
Defines functions
corrEvents
Documented in
corrEvents
#' Expected Number of Events Over Time With Staggered Entry For Overlapping Populations
#'
#' This function calculates the expected number of events under alternative hypothesis
#' at an analysis time, which is calculated from first subject in. The function
#' returns the expected number of events for each arm, based on the provided
#' enrollment distribution function and drop-off distribution if applicable.
#' If the total sample size is not provided, then only the corresponding probability of event
#' for each arm is provided. The expected number of events for each set of subjects is
#' calculated including in both A and B, in A not B, in B not A, and in A or B.
#'
#' @param T Analysis time calculated from first subject randomization date.
#' @param r Proportion of experimental subjects in both population A and B,
#' A not B, B not A. Default, 1/2 for 1:1 randomization stratified by A and B
#' @param h0 Hazard function of control arm for subjects in both population A and B,
#' A not B, B not A. h0(t) = log(2)/m0 means T~exponential distribution with
#' median m0. For study design without considering heterogeneous effect in
#' strata for control arm, then specify the same h0(t) function across strata.
#' @param S0 Survival function of control arm for subjects in both population A and B,
#' A not B, B not A. h0(t) = log(2)/m0 means T~exponential distribution with
#' median m0. For study design without considering heterogeneous effect in
#' strata for control arm, then specify the same S0(t) function across strata.
#' The density function f0(t) = h0(t) * S0(t).
#' @param h1 Hazard function of experimental arm for subjects in both population A and B,
#' A not B, B not A. For study design without considering heterogeneous effect in
#' strata for the experimental arm, then specify the same h1(t) function across strata.
#' @param S1 Survival function of experimental arm for subjects in both population A and B,
#' A not B, B not A. For study design without considering heterogeneous effect in
#' strata for the experimental arm, then specify the same h1(t) function across strata.
#' @param F.entry Distribution function of enrollment. For uniform enrollment,
#' F.entry(t) = (t/A) where A is the enrollment period, i.e., F.entry(t) = t/A for 0<=t<=A, and
#' F.entry(t) = 1 when t > A. For more general non-uniform enrollment with weight psi,
#' F.entry(t) = (t/A)^psi*I(0<=t<=A) + I(t>A). Default F.entry is uniform distribution function.
#' @param G.ltfu Distribution function of lost-to-follow-up censoring process. The observed
#' survival time is min(survival time, lost-to-follow-up time). For 3\% drop-off
#' every year as a constant rate, then G.ltfu = 1-exp(-0.03/12*t), i.e., drop-off~exp distribution.
#' Default G.ltfu = 0 (no lost-to-followup)
#' @param n Total sample size for two arms for subjects in both population A and B,
#' A not B, B not A. Default is NULL.
#'
#' @return An object with dataframes below.
#' \describe{
#' \item{p.event}{Probability of event for each arm (p.event0: control group; p.event1: experimental group)}
#' \item{n.events}{Expected number of events}
#' \itemize{
#' \item subgroup: Label of subgroups
#' \item n.events0: number of events for control group
#' \item n.events1: number of events for experimental group
#' \item n.events.total: total number of events for two groups
#' \item n0: number of subjects in control arm
#' \item n1: number of subjects in experimental arm
#' \item n.total: total number of subjects
#' \item maturity0: maturity in control arm, percent of events
#' \item maturity1: maturity in experimental arm, percent of events
#' \item maturity: maturity in both arms, percent of events
#' }
#' \item{param}{Parameters specified: T, r, and n}
#' \item{param.fun}{f0, f1, F.entry, G.ltfu}
#' }
#'
#' @examples
#' #PD-L1+ subgroup and overall population tests. Control arm has exponential
#' #distribution with median 12 months in all strata. Experimental arm has
#' #proportional hazards with a hazard ratio of 0.7 in all strata. The randomization
#' #is stratified by PD-L1+ status. 1:1 randomization. 300 subjects in PD-L1+ and
#' #450 total subjects in overall population. 3\% drop-off every year. Enrollment
#' #period is 18 months and weight 1.5. The expected number of events at 24 months is
#' #calculated as
#' corrEvents(T = 24, n = list(AandB = 300, AnotB=0, BnotA=450),
#' r = list(AandB=1/2, AnotB =0, BnotA = 1/2),
#' h0=list(AandB=function(t){log(2)/12}, AnotB=function(t){log(2)/12},
#' BnotA=function(t){log(2)/12}),
#' S0=list(AandB=function(t){exp(-log(2)/12*t)}, AnotB=function(t){exp(-log(2)/12*t)},
#' BnotA=function(t){exp(-log(2)/12*t)}),
#' h1=list(AandB=function(t){log(2)/12*0.70}, AnotB=function(t){log(2)/12*0.70},
#' BnotA=function(t){log(2)/12*0.70}),
#' S1=list(AandB=function(t){exp(-log(2)/12 * 0.7 * t)},AnotB=function(t){exp(-log(2)/12 * 0.7 * t)},
#' BnotA=function(t){exp(-log(2)/12 * 0.7 * t)}),
#' F.entry = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)},
#' G.ltfu = function(t){1-exp(-0.03/12*t)})
#'
#'
#' @export
#'
corrEvents = function(T = 24, n = list(AandB = 300, AnotB=0, BnotA=450),
r = list(AandB=1/2, AnotB =0, BnotA = 1/2),
h0=list(AandB=function(t){log(2)/12}, AnotB=function(t){log(2)/12},
BnotA=function(t){log(2)/12}),
S0=list(AandB=function(t){exp(-log(2)/12*t)}, AnotB=function(t){exp(-log(2)/12*t)},
BnotA=function(t){exp(-log(2)/12*t)}),
h1=list(AandB=function(t){log(2)/12*0.70}, AnotB=function(t){log(2)/12*0.70},
BnotA=function(t){log(2)/12*0.70}),
S1=list(AandB=function(t){exp(-log(2)/12 * 0.7 * t)},AnotB=function(t){exp(-log(2)/12 * 0.7 * t)},
BnotA=function(t){exp(-log(2)/12 * 0.7 * t)}),
F.entry = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)},
G.ltfu = function(t){0}){
f.e = function(h00=h0$AandB, h11=h1$AandB, S00=S0$AandB, S11=S1$AandB, nn=n$AandB, rr=r$AandB){
#Integrand of control arm and experimental arm for calculation of prob. of event
I0 = function(t){F.entry(T-t) * (1 - G.ltfu(t)) * h00(t) * S00(t)}
I1 = function(t){F.entry(T-t) * (1 - G.ltfu(t)) * h11(t) * S11(t)}
#prob. of event for control and experimental arm
p.event0 = integrate(I0, lower=0, upper=T)$value
p.event1 = integrate(I1, lower=0, upper=T)$value
p.event = data.frame(cbind(p.event0, p.event1))
#expected number of events
if(!is.null(nn)){
n.events0 = nn * F.entry(T) * (1-rr) * p.event0
n.events1 = nn * F.entry(T) * rr * p.event1
n.events.total = n.events0 + n.events1
}
n.events = data.frame(cbind(n.events0, n.events1, n.events.total))
ans = list()
ans$p.event = p.event; ans$n.events = n.events
return(ans)
}
##Trick the calculation: if no subjects in A not B; set h and S function as 0
z00 = function(t){0}
if(n$AnotB == 0){h0$AnotB=h1$AnotB=S0$AnotB=S1$AnotB=z00}
if(n$BnotA == 0){h0$BnotA=h1$BnotA=S0$BnotA=S1$BnotA=z00}
AandB = f.e(h00=h0$AandB, h11=h1$AandB, S00=S0$AandB, S11=S1$AandB, nn=n$AandB)
AnotB = f.e(h00=h0$AnotB, h11=h1$AnotB, S00=S0$AnotB, S11=S1$AnotB, nn=n$AnotB)
BnotA = f.e(h00=h0$BnotA, h11=h1$BnotA, S00=S0$BnotA, S11=S1$BnotA, nn=n$BnotA)
events = data.frame(rbind(AandB$n.events, AnotB$n.events, BnotA$n.events))
events[4,] = events[1,]+events[2,]
events[5,] = events[1,]+events[3,]
events[6,]= events[1,]+events[2,]+events[3,]
nA = n$AandB+n$AnotB
nB = n$AandB+n$BnotA
nAorB = n$AandB+n$AnotB+n$BnotA
rA = (n$AandB * r$AandB + n$AnotB*r$AnotB)/nA
rB = (n$AandB * r$AandB + n$AnotB*r$AnotB + n$BnotA*r$BnotA)/nB
rAorB = (n$AandB * r$AandB + n$BnotA*r$BnotA)/nAorB
n.total = c(n$AandB,n$AnotB,n$BnotA, nA,nB, nAorB)
n1 = n.total*c(r$AandB,r$AnotB,r$BnotA, rA,rB,rAorB)
n0 = n.total-n1
maturity0 = events$n.events0 / n0
maturity1 = events$n.events1 / n1
maturity = events$n.events.total / n.total
DCO = T
subgroup = c("AandB", "AnotB", "BnotA", "A", "B", "AorB")
out = data.frame(cbind(subgroup, DCO, events,n0, n1, n.total, maturity0, maturity1, maturity))
return(out)
}
phe2189/corrTests documentation built on Oct. 7, 2022, 11:13 a.m.
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Defines functions corrEvents
Documented in corrEvents
#' Expected Number of Events Over Time With Staggered Entry For Overlapping Populations
#'
#' This function calculates the expected number of events under alternative hypothesis
#' at an analysis time, which is calculated from first subject in. The function
#' returns the expected number of events for each arm, based on the provided
#' enrollment distribution function and drop-off distribution if applicable.
#' If the total sample size is not provided, then only the corresponding probability of event
#' for each arm is provided. The expected number of events for each set of subjects is
#' calculated including in both A and B, in A not B, in B not A, and in A or B.
#'
#' @param T Analysis time calculated from first subject randomization date.
#' @param r Proportion of experimental subjects in both population A and B,
#' A not B, B not A. Default, 1/2 for 1:1 randomization stratified by A and B
#' @param h0 Hazard function of control arm for subjects in both population A and B,
#' A not B, B not A. h0(t) = log(2)/m0 means T~exponential distribution with
#' median m0. For study design without considering heterogeneous effect in
#' strata for control arm, then specify the same h0(t) function across strata.
#' @param S0 Survival function of control arm for subjects in both population A and B,
#' A not B, B not A. h0(t) = log(2)/m0 means T~exponential distribution with
#' median m0. For study design without considering heterogeneous effect in
#' strata for control arm, then specify the same S0(t) function across strata.
#' The density function f0(t) = h0(t) * S0(t).
#' @param h1 Hazard function of experimental arm for subjects in both population A and B,
#' A not B, B not A. For study design without considering heterogeneous effect in
#' strata for the experimental arm, then specify the same h1(t) function across strata.
#' @param S1 Survival function of experimental arm for subjects in both population A and B,
#' A not B, B not A. For study design without considering heterogeneous effect in
#' strata for the experimental arm, then specify the same h1(t) function across strata.
#' @param F.entry Distribution function of enrollment. For uniform enrollment,
#' F.entry(t) = (t/A) where A is the enrollment period, i.e., F.entry(t) = t/A for 0<=t<=A, and
#' F.entry(t) = 1 when t > A. For more general non-uniform enrollment with weight psi,
#' F.entry(t) = (t/A)^psi*I(0<=t<=A) + I(t>A). Default F.entry is uniform distribution function.
#' @param G.ltfu Distribution function of lost-to-follow-up censoring process. The observed
#' survival time is min(survival time, lost-to-follow-up time). For 3\% drop-off
#' every year as a constant rate, then G.ltfu = 1-exp(-0.03/12*t), i.e., drop-off~exp distribution.
#' Default G.ltfu = 0 (no lost-to-followup)
#' @param n Total sample size for two arms for subjects in both population A and B,
#' A not B, B not A. Default is NULL.
#'
#' @return An object with dataframes below.
#' \describe{
#' \item{p.event}{Probability of event for each arm (p.event0: control group; p.event1: experimental group)}
#' \item{n.events}{Expected number of events}
#' \itemize{
#' \item subgroup: Label of subgroups
#' \item n.events0: number of events for control group
#' \item n.events1: number of events for experimental group
#' \item n.events.total: total number of events for two groups
#' \item n0: number of subjects in control arm
#' \item n1: number of subjects in experimental arm
#' \item n.total: total number of subjects
#' \item maturity0: maturity in control arm, percent of events
#' \item maturity1: maturity in experimental arm, percent of events
#' \item maturity: maturity in both arms, percent of events
#' }
#' \item{param}{Parameters specified: T, r, and n}
#' \item{param.fun}{f0, f1, F.entry, G.ltfu}
#' }
#'
#' @examples
#' #PD-L1+ subgroup and overall population tests. Control arm has exponential
#' #distribution with median 12 months in all strata. Experimental arm has
#' #proportional hazards with a hazard ratio of 0.7 in all strata. The randomization
#' #is stratified by PD-L1+ status. 1:1 randomization. 300 subjects in PD-L1+ and
#' #450 total subjects in overall population. 3\% drop-off every year. Enrollment
#' #period is 18 months and weight 1.5. The expected number of events at 24 months is
#' #calculated as
#' corrEvents(T = 24, n = list(AandB = 300, AnotB=0, BnotA=450),
#' r = list(AandB=1/2, AnotB =0, BnotA = 1/2),
#' h0=list(AandB=function(t){log(2)/12}, AnotB=function(t){log(2)/12},
#' BnotA=function(t){log(2)/12}),
#' S0=list(AandB=function(t){exp(-log(2)/12*t)}, AnotB=function(t){exp(-log(2)/12*t)},
#' BnotA=function(t){exp(-log(2)/12*t)}),
#' h1=list(AandB=function(t){log(2)/12*0.70}, AnotB=function(t){log(2)/12*0.70},
#' BnotA=function(t){log(2)/12*0.70}),
#' S1=list(AandB=function(t){exp(-log(2)/12 * 0.7 * t)},AnotB=function(t){exp(-log(2)/12 * 0.7 * t)},
#' BnotA=function(t){exp(-log(2)/12 * 0.7 * t)}),
#' F.entry = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)},
#' G.ltfu = function(t){1-exp(-0.03/12*t)})
#'
#'
#' @export
#'
corrEvents = function(T = 24, n = list(AandB = 300, AnotB=0, BnotA=450),
r = list(AandB=1/2, AnotB =0, BnotA = 1/2),
h0=list(AandB=function(t){log(2)/12}, AnotB=function(t){log(2)/12},
BnotA=function(t){log(2)/12}),
S0=list(AandB=function(t){exp(-log(2)/12*t)}, AnotB=function(t){exp(-log(2)/12*t)},
BnotA=function(t){exp(-log(2)/12*t)}),
h1=list(AandB=function(t){log(2)/12*0.70}, AnotB=function(t){log(2)/12*0.70},
BnotA=function(t){log(2)/12*0.70}),
S1=list(AandB=function(t){exp(-log(2)/12 * 0.7 * t)},AnotB=function(t){exp(-log(2)/12 * 0.7 * t)},
BnotA=function(t){exp(-log(2)/12 * 0.7 * t)}),
F.entry = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)},
G.ltfu = function(t){0}){
f.e = function(h00=h0$AandB, h11=h1$AandB, S00=S0$AandB, S11=S1$AandB, nn=n$AandB, rr=r$AandB){
#Integrand of control arm and experimental arm for calculation of prob. of event
I0 = function(t){F.entry(T-t) * (1 - G.ltfu(t)) * h00(t) * S00(t)}
I1 = function(t){F.entry(T-t) * (1 - G.ltfu(t)) * h11(t) * S11(t)}
#prob. of event for control and experimental arm
p.event0 = integrate(I0, lower=0, upper=T)$value
p.event1 = integrate(I1, lower=0, upper=T)$value
p.event = data.frame(cbind(p.event0, p.event1))
#expected number of events
if(!is.null(nn)){
n.events0 = nn * F.entry(T) * (1-rr) * p.event0
n.events1 = nn * F.entry(T) * rr * p.event1
n.events.total = n.events0 + n.events1
}
n.events = data.frame(cbind(n.events0, n.events1, n.events.total))
ans = list()
ans$p.event = p.event; ans$n.events = n.events
return(ans)
}
##Trick the calculation: if no subjects in A not B; set h and S function as 0
z00 = function(t){0}
if(n$AnotB == 0){h0$AnotB=h1$AnotB=S0$AnotB=S1$AnotB=z00}
if(n$BnotA == 0){h0$BnotA=h1$BnotA=S0$BnotA=S1$BnotA=z00}
AandB = f.e(h00=h0$AandB, h11=h1$AandB, S00=S0$AandB, S11=S1$AandB, nn=n$AandB)
AnotB = f.e(h00=h0$AnotB, h11=h1$AnotB, S00=S0$AnotB, S11=S1$AnotB, nn=n$AnotB)
BnotA = f.e(h00=h0$BnotA, h11=h1$BnotA, S00=S0$BnotA, S11=S1$BnotA, nn=n$BnotA)
events = data.frame(rbind(AandB$n.events, AnotB$n.events, BnotA$n.events))
events[4,] = events[1,]+events[2,]
events[5,] = events[1,]+events[3,]
events[6,]= events[1,]+events[2,]+events[3,]
nA = n$AandB+n$AnotB
nB = n$AandB+n$BnotA
nAorB = n$AandB+n$AnotB+n$BnotA
rA = (n$AandB * r$AandB + n$AnotB*r$AnotB)/nA
rB = (n$AandB * r$AandB + n$AnotB*r$AnotB + n$BnotA*r$BnotA)/nB
rAorB = (n$AandB * r$AandB + n$BnotA*r$BnotA)/nAorB
n.total = c(n$AandB,n$AnotB,n$BnotA, nA,nB, nAorB)
n1 = n.total*c(r$AandB,r$AnotB,r$BnotA, rA,rB,rAorB)
n0 = n.total-n1
maturity0 = events$n.events0 / n0
maturity1 = events$n.events1 / n1
maturity = events$n.events.total / n.total
DCO = T
subgroup = c("AandB", "AnotB", "BnotA", "A", "B", "AorB")
out = data.frame(cbind(subgroup, DCO, events,n0, n1, n.total, maturity0, maturity1, maturity))
return(out)
}
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