Optimal Surrogate Survival: Quantifying the Feasibility of Shortening Clinical Trial Duration Using Surrogate Markers

The goal of Optimal Surrogate Survival (OSsurvival) is to nonparametrically estimate the proportion of treatment on the primary outcome explained by a surrogate (PTE) of an optimally transformation of surrogate marker measured at an earlier time. The primary outcome measured at a later time may be subject to censoring.

Installation

The development version of this package can be installed from GitHub with:

library(devtools)
devtools::install_github("celehs/OSsurvival")

Example

This is a basic example which shows you how to solve a common problem:

library(OSsurvival)
# load the data
data("sysdata")

# time at which the surrogate is measured
t.0 = data.example$t.0

# time at which the primary outcome is measured
t = data.example$t

# observed survival time
xob = data.example$data$xob

# surrogate information at t.0
s.ob = data.example$data$s.ob

# event indicator
deltaob = data.example$data$deltaob

# treatment indicator
aob = data.example$data$aob

# main estimation function
# varind: whether to estimate variance; re:number of replications for resampling
out = pte.survival(xob, s.ob, deltaob, aob, t, t.0, varind=0, re=100)

# estimated PTE
out$pte.est
#> [1] 0.8413843

# estimated g1
out$g1.est
#> [1] -0.0180641

# estimated g2(s) at equally spaced s point
plot(out$sgrid, out$gs.est, type="l", xlab = "Surrogate Marker", ylab = "Optimal Transformation")

The PTE result indicates that this is a moderate to high surrogate marker in this setting.

Some background

The observable data for analysis consist of n sets of independent and identically distributed random vectors {D_i = (X_i, δ_i, S_iI(X_i ≥ t₀), A_i), i = 1, ..., n}, where T_i = T_i⁽¹⁾A_i + T_i⁽⁰⁾(1 − A_i), C_i = C_i⁽¹⁾A_i + C_i⁽⁰⁾(1 − A_i), X_i = min(T_i, C_i), the primary outcome Y_i = I(X_i > t), the surrogate S_i = S_i⁽¹⁾A_i + S_i⁽⁰⁾(1 − A_i) is only observed for those with X_i > t₀.

The function outputs estimates (and standard error estimates if indicated) of PTE = Δ_gopt(S)/Δ, the proportion of treatment effect explained quantity based on the ratio between the treatment effect on the optimal transformation of the potential surrogate marker and the treatment effect on the primary outcome, where Δ is the treatment effect on the primary outcome Y; Δ_gopt(S) is the treatment effect on the optimal transformation of the surrogate g_opt(S) = I(T ≤ t₀) g_1, opt + I(T > t₀) g_2, opt ≈ I(T > t₀) g_2, opt.

Citation

Wang X, Cai T, Tian L, Bourgeois F, Parast L. Quantifying the Feasibility of Shortening Clinical Trial Duration Using Surrogate Markers. Under revision.