Exposure Adjusted Event Rate

This vignette explains how to calculate exposure-adjusted event rates (EAERs) and demonstrates the corresponding workflow in metalite.ae.

EAER formula explanation

EAER formula

$$\begin{aligned} EAER_j (\text{EAER for } Trt_j) &= \frac{\text{total number of events for } Trt_j}{\text{total person-days for } Trt_j/(\text{exp factor})} \\ &= \frac{\text{total number of events for } Trt_j \times \text{exp factor}}{\text{total person-days for } Trt_j} \end{aligned}$$

The exposure factor depends on the requested adjustment unit. For example, an adjustment unit of 100 person-months gives:

$$\begin{aligned} EAER_j (\text{100 person-months}) &= \frac{\text{total number of events for } Trt_j \times \text{exp factor} (=100\times30.4367)}{\text{total person-days for } Trt_j} \\ &= \frac{\text{total number of events for } Trt_j \times 3043.67}{\text{total person-days for } Trt_j} \end{aligned}$$

EAER for different types of AEs

The following examples define EAERs for three AE categories and three treatment groups: placebo (PBO), low dose (LD), and high dose (HD).

Any AE

$$EAER_{PBO} (\text{100 person-months}) =\frac{\text{total number of AEs for PBO} \times 3043.67}{\text{total person-days for PBO}}$$

$$EAER_{LD} (\text{100 person-months}) =\frac{\text{total number of AEs for Low Dose} \times 3043.67}{\text{total person-days for Low Dose}}$$

$$EAER_{HD} (\text{100 person-months}) =\frac{\text{total number of AEs for High Dose} \times 3043.67}{\text{total person-days for High Dose}}$$

Serious AEs

$$EAER_{PBO} (\text{100 person-months}) =\frac{\text{total number of SAEs for PBO} \times 3043.67}{\text{total person-days for PBO}}$$

$$EAER_{LD} (\text{100 person-months}) =\frac{\text{total number of SAEs for Low Dose} \times 3043.67}{\text{total person-days for Low Dose}}$$

$$EAER_{HD} (\text{100 person-months}) =\frac{\text{total number of SAEs for High Dose} \times 3043.67}{\text{total person-days for High Dose}}$$

Drug-related AEs

$$EAER_{PBO} (\text{100 person-months}) =\frac{\text{total number of Drug-Related AEs for PBO} \times 3043.67}{\text{total person-days for PBO}}$$

$$EAER_{LD} (\text{100 person-months}) =\frac{\text{total number of Drug-Related AEs for Low Dose} \times 3043.67}{\text{total person-days for Low Dose}}$$

$$EAER_{HD} (\text{100 person-months}) =\frac{\text{total number of Drug-Related AEs for High Dose} \times 3043.67}{\text{total person-days for High Dose}}$$

Calculate EAERs

The following workflow prepares the analysis data and metadata, calculates the AE summary results with prepare_ae_summary(), and adds EAERs with extend_ae_summary_eaer(). Specify the treatment-duration variable with duration_var and the exposure unit with adj_unit.

library(metalite.ae)

adsl <- forestly::forestly_adsl
adae <- forestly::forestly_adae

adsl$TRT01A <- factor(
  adsl$TRT01A,
  levels = c("Xanomeline Low Dose", "Placebo"),
  labels = c("Low Dose", "Placebo")
)
adae$TRTA <- factor(
  adae$TRTA,
  levels = c("Xanomeline Low Dose", "Placebo"),
  labels = c("Low Dose", "Placebo")
)

analysis_plan <- metalite::plan(
  analysis = "ae_summary",
  population = "apat",
  observation = "wk12",
  parameter = "any;rel;ser"
)

meta <- metalite::meta_adam(observation = adae, population = adsl) |>
  metalite::define_plan(analysis_plan) |>
  metalite::define_population(
    name = "apat",
    var = c(
      "USUBJID", "SAFFL", "TRT01A", "TRTDUR",
      "SITEID", "SEX", "RACE", "AGE"
    ),
    group = "TRT01A",
    subset = SAFFL == "Y",
    label = "All Participants as Treated"
  ) |>
  metalite::define_observation(
    name = "wk12",
    var = c(
      "USUBJID", "SAFFL", "TRTA", "AEDECOD", "AEBODSYS", "AEREL",
      "AESER", "AEOUT", "AEACN", "AESDTH", "ASTDT", "AENDT"
    ),
    group = "TRTA",
    subset = SAFFL == "Y",
    label = "Weeks 0 to 12"
  ) |>
  metalite::define_parameter(
    name = "any",
    term1 = "",
    term2 = "",
    var = "AEDECOD",
    soc = "AEBODSYS",
    label = "All AEs"
  ) |>
  metalite::define_parameter(
    name = "rel",
    term1 = "Drug-Related",
    term2 = "",
    subset = AEREL %in% c("POSSIBLE", "PROBABLE"),
    var = "AEDECOD",
    soc = "AEBODSYS",
    label = "Drug-related AEs"
  ) |>
  metalite::define_parameter(
    name = "ser",
    term1 = "Serious",
    term2 = "",
    subset = AESER == "Y",
    var = "AEDECOD",
    soc = "AEBODSYS",
    label = "Serious AEs"
  ) |>
  metalite::define_analysis(
    name = "ae_summary",
    title = "Adverse Event Summary"
  ) |>
  metalite::meta_build()

x <- meta |>
  prepare_ae_summary(
    population = "apat",
    observation = "wk12",
    parameter = "any;rel;ser",
  ) |>
  extend_ae_summary_eaer(
    duration_var = "TRTDUR",
    adj_unit = "month"
  )

x

## List of 17
##  $ meta           :List of 7
##  $ population     : chr "apat"
##  $ observation    : chr "wk12"
##  $ parameter      : chr "any;rel;ser"
##  $ n              :'data.frame': 5 obs. of  3 variables:
##  $ order          : num [1:5] 1 100 200 300 400
##  $ group          : chr [1:3] "Low Dose" "Placebo" "Total"
##  $ reference_group: num 2
##  $ prop           :'data.frame': 5 obs. of  3 variables:
##  $ diff           :'data.frame': 5 obs. of  1 variable:
##  $ n_pop          :'data.frame': 1 obs. of  3 variables:
##  $ name           : chr [1:5] "Participants in population" "with one or more adverse events" "with no adverse events" "with drug-related{^a} adverse events" ...
##  $ prepare_call   : language prepare_ae_summary(meta = meta, population = "apat", observation = "wk12",      parameter = "any;rel;ser", )
##  $ total_exp      :'data.frame': 1 obs. of  3 variables:
##  $ event_num      :'data.frame': 3 obs. of  3 variables:
##  $ eaer           :'data.frame': 3 obs. of  3 variables:
##  $ adj_unit       : chr "month"

The calculated rates are stored in x$eaer:

x$eaer

##      Low Dose  Placebo       Total
## 1 159.1724513 71.46214 105.9769666
## 2 106.8467949 31.57630  61.1959386
## 3   0.3659137  0.00000   0.1439904