sir_ratio {popEpi}

Confidence intervals for the ratio of two SIRs/SMRs

Description

Calculate ratio of two SIRs/SMRs and the confidence intervals of the ratio.

Usage

sir_ratio(
  x,
  y,
  digits = 3,
  alternative = "two.sided",
  conf.level = 0.95,
  type = "exact"
)

Arguments

x

a sir-object or a vector of two; observed and expected cases.

y

a sir-object or a vector of two; observed and expected cases.

digits

number of digits in the output

alternative

The null-hypothesis test: (default:) two.sided, less, greater

conf.level

the type-I error in confidence intervals, default 0.95 for 95% CI.

type

How the binomial confidence intervals are calculated (default:) exact or asymptotic.

Details

Function works with pooled sir-objects i.e. the print argument in sir is ignored. Also x and y can be a vector of two where first index is the observed cases and second is expected cases (see examples). Note that the ratio of two SIR's is only applicable when the age distributions are similar in both populations.

Formula

The observed number of first sir O1 is considered as a Binomial variable with sample size of O1+O2. The confidence intervals for Binomial proportion A is solved using exact or asymptotic method. Now the CI for ratio O1/O2 is B = A/(1 - A). And further the CI for SIR/SMR is B*E2/E1. (Ederer and Mantel)

Value

A vector length of three: sir_ratio, and lower and upper confidence intervals.

Note

Parameter alternative is always two.sided when parameter type is set to asymptotic.

Author(s)

Matti Rantanen

References

Statistics with Confidence: Confidence Intervals and Statistical Guidelines, Douglas Altman, 2000. ISBN: 978-0-727-91375-3

See Also

sir A SIR calculation vignette

Other sir functions: lines.sirspline(), plot.sirspline(), sir(), sir_exp(), sirspline()

Examples

## Ratio for sir-object and the same values given manually:


## create example dataset
dt1 <- data.frame(obs = rep(c(5,7), 10),
                  pyrs = rep(c(250,300,350,400), 5),
                  var = 1:20)
Ref <- data.frame(obs = rep(c(50,70,80,100), 5),
                 pyrs = rep(c(2500,3000,3500,4000), 5),
                 var = 1:20)
## sir using the function
s1 <- sir(coh.data = dt1, coh.obs = obs, coh.pyrs = pyrs, 
          ref.data = Ref, ref.obs = obs, ref.pyrs = pyrs,
          adjust = var)

## Ratio is simply 1:
sir_ratio(s1, c(120, 150))