grprr

Rates and proportions by group: ratios and differences

R

grprr(
  x,
  n = NULL,
  grp = NULL,
  ref = NULL,
  type = "rate",
  per = 1,
  level = 0.95
)

The rate (events over exposure) or the proportion (events over trials) of each group, and its ratio to and difference from a reference group, with approximate and exact intervals. Rows that share a group are pooled: give one row per group, or one per case (0/1 outcomes with n = 1, the default for proportions), or anything between.

Parameters

x

The events: numbers from 0; or a clpre list from clprep().

n

The exposure (person-time, population) of each row for rates, or the trials for proportions: positive numbers; NULL for one trial per row (proportions only).

grp

NULL (each row is a group, named by the names of x) or the group of each row: labels.

ref

The reference group: a label or a position; the first group by default.

type

"rate" (events over exposure) or "prop" (a proportion).

per

The rates and differences are given per per units of n (1e5 for rates per 100,000, 100 for percentages): one positive number.

level

The confidence level of the intervals: one number strictly between 0 and 1.

Returns

An object of class grprr, a list: rates, a data frame with one row per group (group, x, n, rate, lo, hi the approximate interval, elo, ehi the exact one, rep); cmp, one row per group but the reference (group, ratio, lo, hi, elo, ehi, diff, dlo, dhi); ref, type, per and level.

Notes

For a rate x / n the approximate interval is rate * exp(-+z / sqrt(x)) and the exact one the Poisson interval through the gamma quantiles, as stats::poisson.test(); the ratio’s approximate interval is log-normal with variance 1 / x + 1 / x0, its exact interval the one conditional on the total count (the Clopper-Pearson interval of x / (x + x0), as the two-sample stats::poisson.test()), and the difference’s is Wald. For a proportion the intervals are Wilson’s score interval and the exact Clopper-Pearson one (stats::binom.test()); the ratio’s is log-normal (Katz et al.), with no exact interval (NA), and the difference’s is Newcombe’s hybrid score interval. With a zero count the log-normal intervals are NA: no continuity correction is made.

rep is a group’s share of the events over its share of the exposure (or the trials): over 1 when the group is over-represented among the events, as in a comparison of who is placed in segregation with who is in custody.

References

Katz, D., Baptista, J., Azen, S. P. and Pike, M. C. (1978). Obtaining confidence intervals for the risk ratio in cohort studies. Biometrics, 34(3), 469-474. doi:10.2307/2530610

Newcombe, R. G. (1998). Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine, 17(8), 873-890. doi:10.1002/(SICI)1097-0258(19980430)17:8<873::AID-SIM779>3.0.CO;2-I

Examples

# use-of-force incidents per 1,000 contacts by perceived race
grprr(c(white = 120, black = 95, other = 30),
      c(white = 60000, black = 21000, other = 15000), per = 1000)
# proportions from one row per case
grprr(c(1, 0, 0, 1, 1, 0, 1, 1), grp = c(1, 1, 1, 1, 2, 2, 2, 2),
      type = "prop")

Generated from the R help page: grprr in the R reference.