wlr.power.maxcombo: Power Calculation for Group Sequential Design Using A...
In phe9480/rgs: What the Package Does (One Line, Title Case)

Description Usage Arguments Value Examples

Power Calculation for Group Sequential Design Using A Max-combo Test

wlr.power.maxcombo(
  n = 600,
  r = 1,
  DCO = c(24, 36),
  alpha = c(0.02, 0.03)/2,
  h0 = function(t) {     log(2)/12 },
  S0 = function(t) {     exp(-log(2)/12 * t) },
  h1 = function(t) {     log(2)/12 * 0.7 },
  S1 = function(t) {     exp(-log(2)/12 * 0.7 * t) },
  f.ws = list(IA1 = list(function(s) {     1 }), FA = list(function(s) {     1 },
    function(s) {     s * (1 - s) })),
  cuts = NULL,
  Lambda = function(t) {     (t/18)^1.5 * as.numeric(t <= 18) + as.numeric(t > 18) },
  G0 = function(t) {     0 },
  G1 = function(t) {     0 },
  mu.method = "Schoenfeld",
  cov.method = "H0"
)

`n`	Total sample size for two arms.
`r`	Randomization ratio of experimental arm : control arm as r:1. When r = 1, it is equal allocation. Default r = 1.
`DCO`	Analysis time, calculated from first subject in.
`alpha`	Allocated one-sided alpha levels. sum(alpha) is the total type I error. If alpha spending function a(t) is used for information time c(t1, ..., tK), then alpha1 = a(t1), alpha2 = a(t2)-a(t1), ..., alphaK = a(tK)-a(t_K-1), and the total alpha for all analyses is a(tK).
`h0`	Hazard function of control arm. h0(t) = log(2)/m0 means T~exponential distribution with median m0.
`S0`	Survival function of control arm. In general, S0(t) = exp(- integral of h0(u) for u from 0 to t). but providing S0(t) can improves computational efficiency and usually the survival function is known in study design. The density function f0(t) = h0(t) * S0(t).
`h1`	Hazard function of experimental arm. h1(t) = log(2)/m1 means T~exponential distribution with median m0.
`S1`	Survival function of experimental arm. In general, S1(t) = exp(- integral of h1(u) for u from 0 to t). but providing S1(t) can improves computational efficiency and usually the survival function is known in study design. The density function f1(t) = h1(t) * S1(t).
`f.ws`	Self-defined weight function of survival rate, eg, f.ws = function(s)1/max(s, 0.25) When f.ws is specified, sFH parameter will be ignored.
`cuts`	A vector of cut points to define piecewise distributions. If cuts is not specified or incorrectly specified, it might occasionally have numerical integration issue.
`Lambda`	Cumulative distribution function of enrollment.
`G0`	Cumulative distribution function of drop-off for control arm, eg, G.ltfu=function(t)1-exp(-0.03/12*t) is the distribution function for 3 percent drop-off in 12 months of followup.
`G1`	Cumulative distribution function of drop-off for experimental arm, eg, G.ltfu=function(t)1-exp(-0.03/12*t) is the distribution function for 3 percent drop-off in 12 months of followup.
`mu.method`	Method for mean of weighted logrank test Z statistic. "Schoenfeld" or "H1"
`cov.method`	Method for covariance matrix calculation in power calculation: "H0", "H1", "H1.LA" for null hypothesis H0, H1, H1 under local alternative
`b`	Rejection boundary in normalized Z. If b is NULL, then the boundaries will be calculated based on alpha at each analysis time T. Default b = NULL. If b is provided, then alpha is ignored. Default NULL.
`rho`	Parameter for Fleming-Harrington (rho, gamma) weighted log-rank test.
`gamma`	Parameter for Fleming-Harrington (rho, gamma) weighted log-rank test. For log-rank test, set rho = gamma = 0.
`tau`	Cut point 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`	Survival rate cut S(tau) at t = tau1; default 0.5, ie. cut at median. s.tau = 0 reduces to regular Fleming-Harrington test(rho, gamma)

An object with dataframes below.

n: Total number of subjects for two arms
DCO: Expected analysis time
targetEvents: Expected number of events
power: Power of the max-combo test at each analysis
overall.power Overall power of the study
incr.power Incremental power for each analysis. The sum of all incremental powers is the overall power.
medians: Median of each treatment group
b: Expected rejection boundary in z value
Expected_HR: Expected HR

Omega0: Covariance matrix under H0; Omega1: Covariance matrix for power calculation request in cov.method.

#Distributions for both arms
m0 = 12; #median OS for control arm
lambda0 = log(2) / m0
h0 = function(t){lambda0}; 
S0 = function(t){exp(-lambda0 * t)}
HRd = 0.60 #hazard ratio after delay

h.D3=function(t){lambda0*as.numeric(t<3)+HRd*lambda0*as.numeric(t>=3)}
c3 = exp(-3*lambda0*(1-HRd)); 
S.D3 = function(t){S0(t)*as.numeric(t<3)+c3*exp(-HRd*lambda0*t)*as.numeric(t>=3)}

#Define weight functions for weighted log-rank tests
lr = function(s){1}
fh01 = function(s){(1-s)}
fh11 = function(s){s*(1-s)}

#Enrollment
Lambda = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)};
G0 = function(t){0}; G1 = function(t){0}; 

#Schoenfeld method with power based on covariance matrix under H0
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(fh01)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "Schoenfeld", cov.method = "H0")
  
#Schoenfeld method with power based on covariance matrix under H1
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(fh01)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "Schoenfeld", cov.method = "H1")
  
#Schoenfeld method with power based on covariance matrix under H1 in Local Alternative (simplified)
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(fh01)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "Schoenfeld", cov.method = "H1.LA")   
     
#Mean(Z) under H1 with power based on covariance matrix under H0
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(fh01)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "H1", cov.method = "H0")
  
#Mean(Z) under H1 with power based on covariance matrix under H1
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(fh01)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "H1", cov.method = "H1")
  
#Mean(Z) under H1 with power based on covariance matrix under H1 in Local Alternative (simplified)
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(fh01)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "H1", cov.method = "H1.LA")   

#max-combo(logrank, FH11) at FA   
#Mean(Z) under H1 with power based on covariance matrix under H1 in Local Alternative (simplified)
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(lr, fh11)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "H1", cov.method = "H1.LA")   
  
#max-combo(logrank, FH11) at FA   
#Mean(Z) under H1 with power based on covariance matrix under H1
wlr.power.maxcombo(DCO = c(24, 36),  
  alpha=c(0.01, 0.04)/2, 
  r = 1, n = 500, 
  h0 = h0, S0=S0,h1 = h.D3, S1= S.D3, 
  f.ws = list(IA1 = list(lr), FA=list(lr, fh11)), 
  Lambda=Lambda, G0=G0, G1=G1,
  mu.method = "H1", cov.method = "H1")