wlr.asym: Asymptotic Distribution of Weighted Log-rank Statistic

In phe9480/rgs: What the Package Does (One Line, Title Case)

Description

This function calculates the asymptotic distribution (mean and variance) at a DCO.

Usage

wlr.asym(
  DCO = 24,
  r = 1,
  n = 450,
  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) },
  cuts = c(6),
  rho = 0,
  gamma = 0,
  tau = NULL,
  s.tau = 0,
  f.ws = NULL,
  Lambda = function(t) {     (t/18) * as.numeric(t <= 18) + as.numeric(t > 18) },
  G0 = function(t) {     0 },
  G1 = function(t) {     0 }
)

Arguments

r	Proportion of subjects in experimental arm. For 1:1 randomization, r = 1/2.
n	Total sample size for two arms.
h0	Hazard function of control arm, eg, h0(t) = log(2)/m0 for the exponential distribution with median m0.
S0	Survival function of control arm.
h1	Hazard function of experimental arm.
S1	Survival function of experimental arm.
cuts	Piece wise interval cut points of the curresponding survival functions. For delayed effect model with 6 months of delay, cuts = 6. Incorrect specification of cuts may lead to numerical integration issues.
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.
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.
T	Analysis time, calculated from first subject in.
method	Non-centrality parameter options: "SIGWA", "Schoenfeld", "YL 2020", "LM 2019". Default "SIGWA". "YL 2020" is based on Yung and Liu (2020) and "LM 2019" is based on Luo et al (2019).

Value

A dataframe with variables including

• mu: Mean of the weighted logrank test statistic Z = U/sqrt(V). E(Z) = mu = sqrt(n)*delta/sigma

• mu_SF: Mean of the weighted logrank test statistic Z using Schoenfeld method. E(Z) = mu_SF = sqrt(n)*eta/sigma

• delta: Mean of U/n. E(U/n)=delta = r0 * delta0 + r1 * delta1

• delta0: Mean of U0/n0 for control arm. E(U0/n0) = delta0

• delta1: Mean of U1/n1 for experimental arm E(U1/n1) = delta1

• eta: Mean of U/n in weighted logrank test in Schoenfeld method. E(U/n)=eta

• sigma2: Estimate of V/n –> sigma2 for n large. Also, under H0, var(n^(-1/2)U) = sigma2 Under H1, var(n^(-1/2)U) = sigma2 + O(n^(-1/2)). So sigma2 is also an estimate of var(n^(-1/2)U)

• sigma2_b: Var(n^(-1/2)U) using Yung and Liu (2020)'s method Z ~ N(mu, sigma2_b/sigma2)

• sigma2_s: Var(n^(-1/2)U) using Luo et al (2019)'s method Z ~ N(mu, sigma2_s/sigma2)

• sigma2_h: Var(n^(-1/2)U) using He et al (2022)'s method Z ~ N(mu, sigma2_h/sigma2)

• R: Location Factor. Under H1, mu = sqrt(n)*R. For a fixed sample size n, R represents the magnitude of followup.

• var_YL: var_YL = sigma2_b/sigma2

• var_LM: var_LM = sigma2_s/sigma2

• var_HK: var_HK = sigma2_h/sigma2

• pow_YL: Power for a test with rejection bound 1.96: P(Z > 1.96)=PHI((mu-1.96)*sigma/sigma_x). 2.5% alpha with only 1 analysis.

• pow_LM: See pow_YL

• pow_HK: See pow_YL

• pow_SF: Power of Schoenfeld method: PHI(mu_SF-1.96)

• pow_mu: Power of mu method with simpler approximation: PHI(mu-1.96)

Another dataframe including variables: method, mean, var, pow

Examples

#Example: Assume HR 0.65 after 6 months of delayed effect. Control arm follows
exponential distribution with median 12 months.

HR = 0.4; delay = 6; lam0 = log(2) / 12; 
h0 = function(t){lam0}; S0 = function(t){exp(-lam0 * t)}
h1.D6 = function(t){lam0*as.numeric(t < delay)+HR*lam0*as.numeric(t >= delay)}
c = exp(-delay*lam0*(1-HR)); 
S1.D6 = function(t){exp(-lam0*t)*as.numeric(t<delay) + c*exp(-HR*lam0*t)*as.numeric(t>=delay)}
f.logHR.D6 = function(t){log(as.numeric(t<6) + as.numeric(t>= 6)*HR)}
Lambda = function(t){(t/18)^1.5*as.numeric(t <= 18) + as.numeric(t > 18)}
G0.ltfu = G1.ltfu = function(t){0}

wlr.mu(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, f.logHR = f.logHR.D6,
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     F.entry = Lambda)
wlr.asym(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, 
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     Lambda = Lambda, cuts=c(6))
wlr.asym(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, 
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     Lambda = Lambda, cuts=c(6))
wlr.asym(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, 
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     Lambda = Lambda, cuts=c(6))
wlr.mu.schoenfeld(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, f.logHR = f.logHR.D6,
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     F.entry = Lambda)
     
wlr.asym(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, 
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     Lambda = Lambda, cuts=c(6))
wlr.asym(DCO = 24, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, 
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     Lambda = Lambda, cuts=c(6))
wlr.asym(DCO = 30, r = 1, n = 450, h0 = h0, S0=S0,
     h1 = h1.D6, S1=S1.D6, 
     rho = 0, gamma = 0, tau = NULL, s.tau = 0, f.ws = NULL,
     Lambda = Lambda, cuts=NULL)
     

phe9480/rgs documentation built on March 1, 2022, 12:26 a.m.