hrIPW

This function allows estimating the log hazard ratio associated with a binary exposure using a Cox PH model weighted by the propensity score. Propensity model is estimated using a simple logistic regression. Variance estimation takes into account the propensity score estimation step with the method proposed by Hajage et al. (2018) . Both the average treatment effect on the overall (ATE) or the treated (ATT) population can be estimated. For ATE, both unstabilized and stabilized weights can be used. Ties are handled throught the Breslow approximation.

Example

library(hrIPW)

## Using a simulated cohort
data(hrData, package = "hrIPW")
hrIPW(hrData, time = "time", status = "status", exposure = "Trt",
      variables = paste("X", 1:9, sep = ""), wtype = "ATE-stab")
#> $coefficient
#> [1] -0.01717167
#> 
#> $std
#> [1] 0.03282054
#> 
#> $ciinf
#> [1] -0.08149875
#> 
#> $cisup
#> [1] 0.04715541
#> 
#> $p.value
#> [1] 0.6008359

# Standard error could be compared with the (robust) Lin's standard error
# which does not take into account the propensity score estimation step:
modT <- glm(Trt ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9, data = hrData, family = "binomial")
probT <- predict(modT, type = "response")
hrData$w <- 1/ifelse(hrData$Trt == 1, probT, 1 - probT)
library(survival)
coxph(Surv(time, status) ~ Trt + cluster(id), data = hrData, method = "breslow", weights = w)
#> Call:
#> coxph(formula = Surv(time, status) ~ Trt + cluster(id), data = hrData, 
#>     weights = w, method = "breslow")
#> 
#>        coef exp(coef) se(coef) robust se     z    p
#> Trt -0.0174    0.9827   0.0142    0.0354 -0.49 0.62
#> 
#> Likelihood ratio test=1.52  on 1 df, p=0.2
#> n= 10000, number of events= 10000

# or with the bootstrap-based standard-error (see Austin 2016):
f.boot <- function(data, i, wtype) {
    df <- data[i, ]
    modT <- glm(Trt ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9, data = df, family = "binomial")
    probT <- predict(modT, type = "response")
    df$w <- 1/ifelse(df$Trt == 1, probT, 1 - probT)
    
    return(coxph(Surv(time, status) ~ Trt, data = df, weights = w)$coef)
}

library(boot); set.seed(1234)
#> 
#> Attaching package: 'boot'
#> The following object is masked from 'package:survival':
#> 
#>     aml
rcoefs <- boot(data = hrData, statistic = f.boot, R = 500)$t
sd(rcoefs)
#> [1] 0.03283661

## Using the DIVAT data base (package IPWsurvival, to be installed)
data(DIVAT, package = "IPWsurvival")
hrIPW(data = DIVAT, time = "times", status = "failures", exposure = "ecd",
      variables = c("age", "hla", "retransplant"), wtype = "ATE-unstab")
#> $coefficient
#> [1] 0.4661664
#> 
#> $std
#> [1] 0.2564084
#> 
#> $ciinf
#> [1] -0.03638477
#> 
#> $cisup
#> [1] 0.9687177
#> 
#> $p.value
#> [1] 0.0690546

# Standard error could be compared with the (robust) Lin's standard error
# which does not take into account the propensity score estimation step:
modT <- glm(ecd ~ age + hla + retransplant, data = DIVAT, family = "binomial")
probT <- predict(modT, type = "response")
DIVAT$w <- 1/ifelse(DIVAT$ecd == 1, probT, 1 - probT)
DIVAT$id <- 1:nrow(DIVAT)
coxph(Surv(times, failures) ~ ecd + cluster(id), data = DIVAT, method = "breslow", weights = w)
#> Call:
#> coxph(formula = Surv(times, failures) ~ ecd + cluster(id), data = DIVAT, 
#>     weights = w, method = "breslow")
#> 
#>       coef exp(coef) se(coef) robust se   z     p
#> ecd 0.4650    1.5920   0.0517    0.2579 1.8 0.071
#> 
#> Likelihood ratio test=83.28  on 1 df, p=<2e-16
#> n= 1837, number of events= 582

# or with the bootstrap-based estimation (see Austin 2016):
f.boot2 <- function(data, i, wtype) {
    df <- data[i, ]
    modT <- glm(ecd ~ age + hla + retransplant, data = df, family = "binomial")
    probT <- predict(modT, type = "response")
    df$w <- 1/ifelse(df$ecd == 1, probT, 1 - probT)
    
    return(coxph(Surv(times, failures) ~ ecd, data = df, weights = w)$coef)
}

set.seed(1234)
rcoefs2 <- boot(data = DIVAT, statistic = f.boot2, R = 500)$t
sd(rcoefs2)
#> [1] 0.2885173