ARD Incidence Rate — ard_incidence

Function takes a time at risk variable (time) and event count variable (count) and calculates the incidence rate in person-years.

Incidence rate is calculated as: Total number of events that occurred / Total person-time at risk

Usage

ard_incidence_rate(
  data,
  time,
  count = NULL,
  id = NULL,
  by = NULL,
  strata = NULL,
  n_person_time = 100,
  unit_label = "time",
  conf.level = 0.95,
  conf.type = c("normal", "normal-log", "exact", "byar")
)

Arguments

data

(data.frame)
a data frame.

time

(tidy-select)
column name of time at risk variable.

count

(tidy-select)
column name of variable indicating count of events that occurred. If NULL, each row in data is assumed to correspond to a single event occurrence.

id

(tidy-select)
column name used to identify unique subjects in data. If NULL, each row in data is assumed to correspond to a unique subject.

by, strata

(tidy-select)
columns to tabulate by/stratify by for summary statistic calculation. Arguments are similar, but with an important distinction:

by: results are calculated for all combinations of the columns specified, including unobserved combinations and unobserved factor levels.

strata: results are calculated for all observed combinations of the columns specified.

Arguments may be used in conjunction with one another.

n_person_time

(numeric)
amount of person-time to estimate incidence rate for. Defaults to 100.

unit_label

(string)
label for the unit of values in time and estimated person-time output (e.g. "years" for person-years, "days" for person-days, etc.). If the desired person-time estimate unit does not match the current time unit, values of time should be converted to the correct unit during pre-processing. Defaults to "time" (person-time).

conf.level

(numeric)
confidence level for the estimated incidence rate.

conf.type

(string)
confidence interval type for the estimated incidence rate.

One of: normal (default), normal-log, exact, or byar.

Value

an ARD data frame of class 'card'

Details

The formulas used to calculate the confidence interval for each CI type are as follows, where $x_i$ and $t_i$ represent the number of events and follow-up time for subject $i$, respectively.

byar: Byar's approximation of a Poisson CI. A continuity correction of 0.5 is included in the calculation.

$$CI = (\sum{x_i} + 0.5) (1 - 1 / (9 \times (\sum{x_i} + 0.5)) \pm Z_{1 - \alpha / 2} / (3 \sqrt{\sum{x_i} + 0.5}))^3 / \sum{t_i}$$
normal: Normal CI.

$$CI = \sum{x_i} / \sum{t_i} \pm Z_{1 - \alpha / 2} \sqrt{\sum{x_i}} / \sum{t_i}$$
normal-log: Normal-Log CI.

$$CI = \exp(\log(\sum{x_i} / \sum{t_i}) \pm Z_{1 - \alpha / 2} / \sqrt{\sum{x_i}})$$
exact: Exact CI for a Poisson mean.

$$CI_{lower} = \chi^2_{\alpha / 2, 2\sum{x_i} + 2} / {2 \sum{t_i}}$$ $$CI_{upper} = \chi^2_{1 - \alpha / 2, 2\sum{x_i} + 2} / {2 \sum{t_i}}$$

Examples

set.seed(1)
data <- data.frame(
  USUBJID = 1:100,
  TRTA = sample(LETTERS[1:3], 100, replace = TRUE),
  AETTE1 = abs(rnorm(100, mean = 0.5)),
  AETOT1 = sample(0:20, 100, replace = TRUE)
)

data |>
  ard_incidence_rate(time = AETTE1, count = AETOT1, id = USUBJID, by = TRTA, unit_label = "years")
#> # An ARD data frame: 27 × 10
#>    group1 group1_level variable context   stat_name stat_label stat      fmt_fun
#>    <chr>  <list>       <chr>    <chr>     <chr>     <chr>      <list>    <list> 
#>  1 TRTA   A            AETTE1   incidenc… estimate  Incidence… 976.3053  1      
#>  2 TRTA   A            AETTE1   incidenc… std.error Standard … 0.5783134 1      
#>  3 TRTA   A            AETTE1   incidenc… conf.low  CI Lower … 862.958   1      
#>  4 TRTA   A            AETTE1   incidenc… conf.high CI Upper … 1089.653  1      
#>  5 TRTA   A            AETTE1   incidenc… conf.type CI Type    normal    <fn>   
#>  6 TRTA   A            AETTE1   incidenc… conf.lev… CI Confid… 0.95      1      
#>  7 TRTA   A            AETTE1   incidenc… tot_pers… Person-Ye… 29.19169  1      
#>  8 TRTA   A            AETTE1   incidenc… n_events  Number of… 285       0      
#>  9 TRTA   A            AETTE1   incidenc… N         Number of… 33        0      
#> 10 TRTA   B            AETTE1   incidenc… estimate  Incidence… 1373.986  1      
#> # ℹ 17 more rows
#> # ℹ 2 more variables: warning <list>, error <list>