corrTime: Correlation Between Two Logrank Test Statistics Over Time...

In phe2189/corrTests: What the Package Does (One Line, Title Case)

Correlation Between Two Logrank Test Statistics Over Time With Staggered Entry

Description

This function calculates the correlation of two logrank test statistics on overlapping populations A and B over time calculated from first subject in.

Usage

corrTime(
  T = 24,
  n = list(AandB = 300, AnotB = 0, BnotA = 450),
  r = list(AandB = 1/2, AnotB = 0, BnotA = 1/2),
  rA = 1/2,
  rB = 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 * 0.7 }, AnotB = function(t) {    
    log(2)/12 * 0.7 }, BnotA = function(t) {     log(2)/12 * 0.7 }),
  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 },
  strat.ana = "Y"
)

Arguments

T	Analysis time calculated from first subject randomization date.
n	Total sample size for two arms for subjects in both population A and B, A not B, B not A. Default is NULL.
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
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.
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).
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.
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.
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.
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\ 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)
strat.ana	Stratified Analysis by A and B "Y" or "N". Default "Y"

Value

An object with dataframes below.

n.events

Expected number of events

• n.events0: number of events for control group

• n.events1: number of events for experimental group

• n.events.total: total number of events for two groups

• subgroup Label of subgroups

corr

Correlation of the two test statistics for populations A and B at time T

Examples

################################
# Example 1: PD-L1+ subgroup 
# and overall population tests.
################################
#Control arm has exponential
#distribution with median 12 months in all strata. 
#1:1 randomization stratified by PD-L1+ status. 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.

#################
# h(t) and S(t)
#################

h0 = function(t){log(2)/12}
S0 = function(t){exp(-log(2)/12 * t)}
h0.5 = function(t){log(2)/12*0.5}
h0.65 = function(t){log(2)/12*0.65}
h0.8 = function(t){log(2)/12*0.8}
S0.5 = function(t){exp(-log(2)/12 * 0.5 * t)}
S0.65 = function(t){exp(-log(2)/12 * 0.65 * t)}
S0.8 = function(t){exp(-log(2)/12 * 0.8 * t)}

#Entry distribution: enrollment period 18 mo, acceleration weight 1.5.
Fe = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)}

#Drop-off distribution: 3\% drop-off every year.
G = function(t){1-exp(-0.03/12*t)}

#Plot correlation over time after enrollment complete
t = seq(18, 50, 1) #Analysis time, must be greater than enrollment period 18.
omega = matrix(NA, nrow=6, ncol=length(t))

for (i in 1:length(t)){
  #(1) Homogeneous regardless of PD-L1 status: HR = 0.65
  omega[1,i]=corrTime(T = t[i], n = list(AandB = 300, AnotB=0, BnotA=450), 
      r = list(AandB=1/2, AnotB =0, BnotA = 1/2, A=1/2, B=1/2), 
      h0=list(AandB=h0, AnotB=h0, BnotA=h0), 
      S0=list(AandB=S0, AnotB=S0, BnotA=S0),
      h1=list(AandB=h0.65, AnotB=NULL, BnotA=h0.65), 
      S1=list(AandB=S0.65, AnotB=NULL, BnotA=S0.65),
      F.entry = Fe, G.ltfu = G, strat.ana="Y")$corr
      
  omega[2,i]=corrTime(T = t[i], n = list(AandB = 300, AnotB=0, BnotA=450), 
      r = list(AandB=1/2, AnotB =0, BnotA = 1/2, A=1/2, B=1/2), 
      h0=list(AandB=h0, AnotB=h0, BnotA=h0), 
      S0=list(AandB=S0, AnotB=S0, BnotA=S0),
      h1=list(AandB=h0.65, AnotB=NULL, BnotA=h0.65), 
      S1=list(AandB=S0.65, AnotB=NULL, BnotA=S0.65),
      F.entry = Fe, G.ltfu = G, strat.ana="N")$corr
      
  #(2) Stronger effect in PD-L1+: HR = 0.65; PD-L1-: HR = 0.85
  omega[3,i]=corrTime(T = t[i], n = list(AandB = 300, AnotB=0, BnotA=450), 
      r = list(AandB=1/2, AnotB =0, BnotA = 1/2, A=1/2, B=1/2), 
      h0=list(AandB=h0, AnotB=h0, BnotA=h0), 
      S0=list(AandB=S0, AnotB=S0, BnotA=S0),
      h1=list(AandB=h0.65, AnotB=NULL, BnotA=h0.8), 
      S1=list(AandB=S0.65, AnotB=NULL, BnotA=S0.8),
      F.entry = Fe, G.ltfu = G, strat.ana="Y")$corr
      
  omega[4,i]=corrTime(T = t[i], n = list(AandB = 300, AnotB=0, BnotA=450), 
      r = list(AandB=1/2, AnotB =0, BnotA = 1/2, A=1/2, B=1/2), 
      h0=list(AandB=h0, AnotB=h0, BnotA=h0), 
      S0=list(AandB=S0, AnotB=S0, BnotA=S0),
      h1=list(AandB=h0.65, AnotB=NULL, BnotA=h0.8), 
      S1=list(AandB=S0.65, AnotB=NULL, BnotA=S0.8),
      F.entry = Fe, G.ltfu = G, strat.ana="N")$corr
      
  #(3) Weaker effect in PD-L1+: HR = 0.85; PD-L1-: HR = 0.65
  omega[5,i]=corrTime(T = t[i], n = list(AandB = 300, AnotB=0, BnotA=450), 
      r = list(AandB=1/2, AnotB =0, BnotA = 1/2, A=1/2, B=1/2), 
      h0=list(AandB=h0, AnotB=h0, BnotA=h0), 
      S0=list(AandB=S0, AnotB=S0, BnotA=S0),
      h1=list(AandB=h0.65, AnotB=NULL, BnotA=h0.5), 
      S1=list(AandB=S0.65, AnotB=NULL, BnotA=S0.5),
      F.entry = Fe, G.ltfu = G, strat.ana="Y")$corr
      
  omega[6,i]=corrTime(T = t[i], n = list(AandB = 300, AnotB=0, BnotA=450), 
      r = list(AandB=1/2, AnotB =0, BnotA = 1/2, A=1/2, B=1/2), 
      h0=list(AandB=h0, AnotB=h0, BnotA=h0), 
      S0=list(AandB=S0, AnotB=S0, BnotA=S0),
      h1=list(AandB=h0.65, AnotB=NULL, BnotA=h0.5), 
      S1=list(AandB=S0.65, AnotB=NULL, BnotA=S0.5),
      F.entry = Fe, G.ltfu = G, strat.ana="N")$corr
}

#Plot the correlations vs time
plot(t, omega[1,], type="n", ylim=range(omega),
xlab="Analysis Time", ylab="Correlation")
lines(t, omega[1,], lty=1, col=1, lwd=2)
lines(t, omega[2,], lty=2, col=2, lwd=2)
lines(t, omega[3,], lty=1, col=3, lwd=2)
lines(t, omega[4,], lty=2, col=3, lwd=2)
lines(t, omega[5,], lty=1, col=4, lwd=2)
lines(t, omega[6,], lty=2, col=4, lwd=2)
legend(18,0.642, c("PD-L1+/- HR 0.65/0.65: S", 
"PD-L1+/- HR 0.65/0.65: U", "PD-L1+/- HR 0.65/0.8: S"),
lwd=rep(2,3), col=c(1,2,3), lty=c(1,2,1), bty="n", cex=0.6) 

legend(18,0.632, c("PD-L1+/- HR 0.65/0.8: U","PD-L1+/- HR 0.65/0.5: S","PD-L1+/- HR 0.65/0.5: U"),
lwd=rep(2,3), col=c(3,4,4), lty=c(2,1,2), bty="n", cex=0.6) 

phe2189/corrTests documentation built on Oct. 7, 2022, 11:13 a.m.