Stratified Analysis of Survival Means and Rates

Zachary McCaw
Updated: 2021-01-18

Overview

Given stratified time to event data for two arms, this package calculates the mean and ratio of the marginal event rates, restricted mean survival times (RMSTs), and restricted mean times lost (RMTLs). The marginal means/rates are calculated as the stratum-size weighted-average of the per-stratum means/rates. Also see:

MargRates for comparing binary event rates.
CICs for comparing cumulative incidence curves.

Installation

devtools::install_github(repo = 'zrmacc/StratSurv')

Example

Data

Below, data are simulated from a two-arm trial with two strata. There are 100 patients in each arm, 50 per stratum. In stratum 1, treatment (arm == 1) reduces the event rate by half. In stratum 2, treatment has no effect.

library(StratSurv)
# Arm 1.
data1 <- GenData(
  n = c(50, 50),
  event_rates = c(1/36, 2/36),
  censor_rates = 1/20,
  tau = 36
)
data1$arm <- 1

# Arm 0.
data0 <- GenData(
  n = c(50, 50),
  event_rates = c(2/36, 2/36),
  censor_rates = 1/20,
  tau = 36
)
data0$arm <- 0

# Overall data set.
data <- rbind(data1, data0)
head(data)

## # A tibble: 6 x 4
##   strata    time status   arm
##    <int>   <dbl>  <dbl> <dbl>
## 1      1  7.82        1     1
## 2      1  2.02        1     1
## 3      1  9.85        0     1
## 4      1 11.6         0     1
## 5      1  0.0162      1     1
## 6      1  8.64        0     1

In these data, arm is the treatment arm, 0 for reference, 1 for treatment; time is the observation time in days; and status is the status indicator, 0 for censoring, 1 for recovery; and stratum is stratification factor, taking values 0, and 1. For analyzing other data sets, arm and status should likewise have 0/1 coding. stratum may be integer or factor valued.

Compare RMSTs and RMTLs

To compare RMSTs and RMTLs at $\tau = 18$ months:

rmst <- StratRMST(
  time = data$time,
  status = data$status,
  arm = data$arm,
  strata = data$strata,
  tau = 18
)
show(rmst)

## Marginal Statistics:
## # A tibble: 4 x 6
##     arm stat    est    se lower upper
##   <dbl> <chr> <dbl> <dbl> <dbl> <dbl>
## 1     0 RMST  10.9  0.689  9.58 12.3 
## 2     0 RMTL   7.07 0.689  5.72  8.42
## 3     1 RMST  13.2  0.721 11.7  14.6 
## 4     1 RMTL   4.84 0.721  3.43  6.25
## 
## 
## Contrasts:
## # A tibble: 4 x 6
##   stat  contrast    est  lower  upper      p
##   <chr> <chr>     <dbl>  <dbl>  <dbl>  <dbl>
## 1 RMST  A1-A0     2.23   0.273  4.18  0.0255
## 2 RMST  A1/A0     1.2    1.02   1.42  0.0264
## 3 RMTL  A1-A0    -2.23  -4.18  -0.273 0.0255
## 4 RMTL  A1/A0     0.685  0.483  0.971 0.0334

The output is on object of class stratSurv containing these slots:

@Stratified contains the per arm and stratum summary statistics.
@Marginal contains the per arm RMST and RMTL, marginalized across strata.
@Contrasts contains the difference and ratio of RMSTs and RMTLs.
@Weights contains the stratum sizes and weights.

By default, the weighting is proportional to stratum size. The weights may also be specified:

rmst <- StratRMST(
  time = data$time,
  status = data$status,
  arm = data$arm,
  strata = data$strata,
  tau = 18,
  weight = c(0.8, 0.2)
)
show(rmst)

## Marginal Statistics:
## # A tibble: 4 x 6
##     arm stat    est    se lower upper
##   <dbl> <chr> <dbl> <dbl> <dbl> <dbl>
## 1     0 RMST  11    0.844  9.31 12.6 
## 2     0 RMTL   7.03 0.844  5.38  8.69
## 3     1 RMST  13.7  0.828 12    15.3 
## 4     1 RMTL   4.34 0.828  2.71  5.96
## 
## 
## Contrasts:
## # A tibble: 4 x 6
##   stat  contrast    est  lower  upper      p
##   <chr> <chr>     <dbl>  <dbl>  <dbl>  <dbl>
## 1 RMST  A1-A0     2.7    0.381  5.02  0.0225
## 2 RMST  A1/A0     1.25   1.03   1.51  0.0247
## 3 RMTL  A1-A0    -2.7   -5.02  -0.381 0.0225
## 4 RMTL  A1/A0     0.616  0.396  0.959 0.0319

Compare Event Rates

To compare event rates at $\tau = 18$ months:

rates <- StratRate(
  time = data$time,
  status = data$status,
  arm = data$arm,
  strata = data$strata,
  tau = 18
)
show(rates)

## Marginal Statistics:
## # A tibble: 2 x 6
##     arm   tau  rate     se lower upper
##   <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0    18 0.238 0.0641 0.112 0.363
## 2     1    18 0.506 0.0656 0.377 0.634
## 
## 
## Contrasts:
## # A tibble: 3 x 7
##   strata stat    est     se  lower upper       p
##    <dbl> <chr> <dbl>  <dbl>  <dbl> <dbl>   <dbl>
## 1      1 rd    0.268 0.0917 0.0881 0.448 0.00349
## 2      1 rr    2.13  0.636  1.18   3.82  0.0117 
## 3      1 or    3.28  1.44   1.38   7.77  0.007

Here 'rd', 'rr', and 'or' are the rate difference, rate ratio, and rate odds ratio, respectively.