Sample size or precision for risk ratio

Source: R/differences.R

prec_riskratio returns the risk ratio and the sample size or the precision for the provided proportions.

prec_riskratio(
  p1,
  p2,
  n1 = NULL,
  r = 1,
  conf.width = NULL,
  conf.level = 0.95,
  method = c("koopman", "katz"),
  ...
)

Arguments

p1

risk among exposed.

p2

risk among unexposed.

n1

number of patients in exposed group.

r

allocation ratio (relative size of unexposed and exposed cohort (n2 / n1)).

conf.width

precision (the full width of the confidence interval).

conf.level

confidence level.

method

Exactly one of koopman (default), katz. Methods can be abbreviated.

...

other arguments to uniroot (e.g. tol).

Details

Exactly one of the parameters n1 or conf.width must be passed as NULL, and that parameter is determined from the other.

Koopman (koopman) provides an asymptotic score confidence interval that is always consistent with Pearsons chi-squared test. It is the recommended interval (Fagerland et al.).

Katz (katz) use a logarithmic transformation to calculate the confidence interval. The CI cannot be computed if one of the proportions is zero. If both proportions are 1, the estimate of the standard error becomes zero, resulting in a CI of [1, 1].

uniroot is used to solve n for the katz, and koopman method.

References

Fagerland MW, Lydersen S, and Laake P (2015). Recommended confidence intervals for two independent binomial proportions, Statistical methods in medical research 24(2):224-254.

Katz D, Baptista J, Azen SP, and Pike MC (1978) Obtaining Confidence Intervals for the Risk Ratio in Cohort Studies, Biometrics 34:469-474.

Koopman PAR (1984) Confidence Intervals for the Ratio of Two Binomial Proportions, Biometrics 40:513-517.

Examples

# Validate function with example in Fagerland et al. (2015), Table 5.
prec_riskratio(p1 = 7/34, p2 = 1/34, n1 = 34, r = 1, met = "katz")
#> 
#>      precision for a relative risk with katz confidence interval 
#> 
#>          p1         p2 n1 n2 ntot r rr       lwr      upr conf.width conf.level
#> 1 0.2058824 0.02941176 34 34   68 1  7 0.9096055 53.86951    52.9599       0.95
# 7 (0.91 to 54)
prec_riskratio(p1 = 7/34, p2 = 1/34, n1 = 34, r = 1, met = "koopman")
#> 
#>      precision for a relative risk with koopman confidence interval 
#> 
#>          p1         p2 n1 n2 ntot r rr      lwr      upr conf.width conf.level
#> 1 0.2058824 0.02941176 34 34   68 1  7 1.220853 42.57571   41.35486       0.95
# 7 (1.21 to 43)

# Validate the Koopman method with example in Koopman (1984)
prec_riskratio(p1 = 36/40, p2 = 16/80, n1 = 40, r = 2, met = "koopman")
#> 
#>      precision for a relative risk with koopman confidence interval 
#> 
#>    p1  p2 n1 n2 ntot r  rr      lwr      upr conf.width conf.level
#> 1 0.9 0.2 40 80  120 2 4.5 2.939572 7.152241   4.212668       0.95
# 4.5 (2.94 to 7.15)