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Weighted Cox Model with Rho-Gamma Weights

Source: R/weightedCox.R
cox_rhogamma.Rd

Fits a weighted Cox proportional hazards model using flexible time-dependent weights (e.g., Fleming-Harrington, Magirr-Burman). Supports resampling-based inference for variance estimation and bias correction.

Usage

cox_rhogamma(
  dfcount,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0.5),
  draws = 0,
  alpha = 0.05,
  verbose = FALSE,
  lr.digits = 4
)

Arguments

dfcount

List; output from df_counting containing counting process data including time, delta, z, w_hat, survP_all, survG_all, etc.

scheme

Character; weighting scheme. See wt.rg.S for options. Default: "fh".

scheme_params

List; parameters for the selected scheme. Default: list(rho = 0, gamma = 0.5). Required parameters depend on scheme:

  • "fh": rho, gamma

  • "MB": mb_tstar

  • "custom_time": t.tau, w0.tau, w1.tau

draws

Integer; number of resampling draws for variance estimation and bias correction. If 0, only asymptotic inference is performed. Default: 0.

alpha

Numeric; significance level for confidence intervals. Default: 0.05.

verbose

Logical; whether to print detailed output. Default: FALSE.

lr.digits

Integer; number of decimal places for formatted output. Default: 4.

Value

A list containing:

fit

List with fitted model components:

  • bhat: Estimated log hazard ratio

  • sig_bhat_asy: Asymptotic standard error

  • u.zero: Score statistic at beta=0 (log-rank)

  • z.score: Standardized score statistic

  • sig2_score: Variance of score statistic

  • wt_rg: Vector of time-dependent weights

  • bhat_debiased: Bias-corrected estimate (if draws > 0)

  • sig_bhat_star: Resampling-based standard error (if draws > 0)

hr_ci_asy

Data frame with asymptotic HR and CI

hr_ci_star

Data frame with resampling-based HR and CI (if draws > 0)

cox_text_asy

Formatted string with HR and asymptotic CI

cox_text_star

Formatted string with HR and resampling CI (if draws > 0)

z.score_debiased

Bias-corrected score statistic (if draws > 0)

zlogrank_text

Formatted log-rank test result

Details

This function solves the weighted Cox partial likelihood score equation: U(beta) = sum_i w_i K_i (dN_0/Y_0 - dN_1/Y_1) = 0

where K_i are time-dependent weights and Y_j, dN_j are risk sets and event counts for group j.

When draws > 0, the function performs resampling to:

  • Estimate finite-sample variance (more accurate than asymptotic)

  • Compute bias correction for \(\hat{\beta}\)

  • Provide improved confidence intervals for small samples

The score test at \(\beta=0\) corresponds to the weighted log-rank test.

Note

The treatment variable in dfcount must be coded as 0=control, 1=experimental.

References

Magirr, D. and Burman, C. F. (2019). Modestly weighted logrank tests. Statistics in Medicine, 38(20), 3782-3790.

See also

df_counting for preprocessing wt.rg.S for weighting schemes cox_score_rhogamma for score function

Other survival_analysis: KM_diff(), df_counting(), wt.rg.S()

Other weighted_tests: df_counting(), wt.rg.S()

Examples

# First get counting process data
library(survival)
str(veteran)
#> 'data.frame':	137 obs. of  8 variables:
#>  $ trt     : num  1 1 1 1 1 1 1 1 1 1 ...
#>  $ celltype: Factor w/ 4 levels "squamous","smallcell",..: 1 1 1 1 1 1 1 1 1 1 ...
#>  $ time    : num  72 411 228 126 118 10 82 110 314 100 ...
#>  $ status  : num  1 1 1 1 1 1 1 1 1 0 ...
#>  $ karno   : num  60 70 60 60 70 20 40 80 50 70 ...
#>  $ diagtime: num  7 5 3 9 11 5 10 29 18 6 ...
#>  $ age     : num  69 64 38 63 65 49 69 68 43 70 ...
#>  $ prior   : num  0 10 0 10 10 0 10 0 0 0 ...
veteran$treat <- as.numeric(veteran$trt) - 1

dfcount <- df_counting(
  df = veteran,
  tte.name = "time",
  event.name = "status",
  treat.name = "treat"
)

# Fit weighted Cox model with FH(0,0.5) weights
fit <- cox_rhogamma(
  dfcount = dfcount,
  scheme = "fh",
  scheme_params = list(rho = 0, gamma = 0.5),
  draws = 1000,
  verbose = TRUE
)
#> z-statistic:  logrank (1-sided) p = 0.3167 
#> Hazard Ratio (HR): 0.912
#> 95% CI: [0.624, 1.332]
#> Hazard Ratio (HR): 0.914
#> 95% CI: [0.626, 1.335]

print(fit$cox_text_star)  # Resampling-based CI
#> [1] "HR = 0.912 (0.6261, 1.3351)"
print(fit$zlogrank_text)  # Weighted log-rank test
#> [1] "logrank (1-sided) p = 0.3167"

# Compare asymptotic and resampling CIs
print(fit$hr_ci_asy)
#>          beta  sig_bhat        hr     lower    upper
#> 1 -0.09211436 0.1932503 0.9120009 0.6244538 1.331957
print(fit$hr_ci_star)
#>          beta  sig_bhat        hr     lower    upper
#> 1 -0.08962629 0.1931806 0.9142728 0.6260949 1.335093