Lu-Tsiatis More Efficient Log-Rank for Randomized Studies with Baseline Covariates

Efficient implementation of the Lu-Tsiatis improvement using baseline covariates, extended to competing risks and recurrent events. The results are almost equivalent to the speffSurv function of the speff2trial package in the survival case. A dynamic censoring augmentation regression is also computed to gain additional efficiency from the censoring augmentation. The function handles two-stage randomizations and recurrent events (start,stop) with cluster structure.

Usage

phreg_rct(
  formula,
  data,
  cause = 1,
  cens.code = 0,
  typesR = c("R0", "R1", "R01"),
  typesC = c("C", "dynC"),
  weights = NULL,
  augmentR0 = NULL,
  augmentR1 = NULL,
  augmentC = NULL,
  treat.model = ~+1,
  RCT = TRUE,
  treat.var = NULL,
  km = TRUE,
  level = 0.95,
  cens.model = NULL,
  estpr = 1,
  pi0 = 0.5,
  base.augment = FALSE,
  return.augmentR0 = FALSE,
  mlogit = FALSE,
  ...
)

Arguments

formula: Formula with Surv or Event outcome (see coxph) and treatment variable (randomization 0/1). The treatment variable must be the first covariate on the right-hand side.
data: Data frame containing all variables referenced in the formula.
cause: Numeric code for the event of interest in competing risks or recurrent events.
cens.code: Numeric code for censoring in competing risks or recurrent events.
typesR: Character vector specifying augmentation types for randomization (options: "R0" for baseline, "R1" for post-baseline, "R01" for both).
typesC: Character vector specifying augmentation types for censoring (options: "C" for static, "dynC" for dynamic).
weights: Weights to be used for phreg.
augmentR0: Formula for the first randomization augmentation (e.g., ~age+sex).
augmentR1: Formula for the second randomization augmentation (e.g., ~age+sex).
augmentC: Formula for the censoring augmentation (e.g., ~age+sex).
treat.model: Propensity score model formula (default is ~+1, assuming RCT).
RCT: Logical; if FALSE, uses propensity score adjustment for marginal model.
treat.var: Variable indicating treatment times in two-stage randomization.
km: Logical; use Kaplan-Meier for censoring weights (stratified on treatment).
level: Confidence level for intervals (default 0.95).
cens.model: Censoring model formula (default is ~strata(treatment)).
estpr: Numeric code (1/0); estimate propensity scores or not (default TRUE).
pi0: Fixed propensity scores for randomizations (if not estimating).
base.augment: Logical; covariate augment baselines (only for R0 augmentation).
return.augmentR0: Logical; return augmentation data.
mlogit: Logical; use multinomial logistic regression for propensity scores.
...: Additional arguments passed to phreg function.

Value

An object of class "phreg_rct" containing:

coefs: Coefficient estimates for the treatment effect.
iid: Influence function (IID) decomposition for variance estimation.
AugR0, AugR1, AugCdyn, AugClt: Augmentation terms for different strategies.
cumhaz: Cumulative hazards.
var: Variance-covariance matrix.
se: Standard errors.
call: Original function call.
formula: Formula used.
data: The data used (if requested).

The object includes results for different augmentation combinations (R0, R1, R01, C, dynC).

Details

The method improves the efficiency of the log-rank test by utilizing auxiliary baseline covariates to reduce variance, particularly useful in randomized clinical trials (RCTs) where covariate adjustment can increase power.

References

Lu, T. and Tsiatis, A. A. (2008), Improving the efficiency of the log-rank test using auxiliary covariates, Biometrika, 95, 679–694.

Scheike, T. H., Nerstroem, C. and Martinussen, T. (2026), Randomized clinical trials and the proportional hazards model for recurrent events, TEST.

Author

Thomas Scheike

Examples

## Lu, Tsiatis simulation
data <- mets:::simLT(0.7,100)
dfactor(data) <- Z.f~Z

out <- phreg_rct(Surv(time,status)~Z.f,data=data,augmentR0=~X,augmentC=~factor(Z):X)
summary(out)
#>                Estimate   Std.Err        2.5%     97.5%    P-value
#> Marginal-Z.f1 0.6721162 0.2763128  0.13055314 1.2136793 0.01499718
#> R0_C:Z.f1     0.4990308 0.2230568  0.06184748 0.9362141 0.02527090
#> R0_dynC:Z.f1  0.3950996 0.2172938 -0.03078852 0.8209876 0.06902238
#> attr(,"class")
#> [1] "summary.phreg_rct"