Mantel-Haenszel Stratified Reltative Risk Confidence Interval

Calculates the confidence interval for the Mantel-Haenszel estimate of the common reltative risk across multiple 2x2 tables (strata)

Usage

ci_rel_risk_cmh_strata(x, by, strata, conf.level = 0.95, data = NULL)

Arguments

x: (binary/numeric/logical)
vector of a binary values, i.e. a logical vector, or numeric with values c(0, 1)
by: (string)
A character or factor vector with exactly two unique levels identifying the two groups to compare. Can also be a column name if a data frame provided in the data argument.
strata: (numeric)
A vector specifying the stratum for each observation. It needs to be the length of x or a multiple of x if multiple levels of strata are present. Can also be a column name (or vector of column names NOT quoted) if a data frame provided in the data argument.
conf.level: (scalar numeric)
a scalar in (0,1) indicating the confidence level. Default is 0.95
data: (data.frame)
Optional data frame containing the variables specified in x and by.

Value

An object containing the following components:

estimate: The Mantel-Haeszel estimated common risk difference
conf.low: Lower bound of the confidence interval
conf.high: Upper bound of the confidence interval
conf.level: The confidence level used
variance: Mantel-Haenszel variance estimate $Var(log(RR_MH))$
method: Description of the method used ("Mantel-Haenszel Common Relattive Risk Confidence Interval")

Details

The Mantel-Haenszel reltative risk difference is computed as:

$$RR_{MH} = \frac{\sum_{k} s_{xk}~n_{yk}/N_k}{\sum_{k} s_{yk}~n_{xk}/N_k}$$

The variance is:

$$\hat{\sigma}^2 = \hat{Var}(log(RR_{MH})) = \frac{\sum_{k}(n_{xk}~n_{yk}~(s_{xk}+s_{yk}) - s_{xk}~s_{yk}~N_k)/N_k^2} {(\sum_{k}s_{xk}~n_{yk}/N_k)(\sum_{k}s_{yk}~n_{xk}/N_k)}$$

The confidence interval is then $\left(RR_{MH}\times exp(-z_{1-\alpha/2} \sqrt{\hat{\sigma}^2}, RR_{MH}\times exp(z_{1-\alpha/2} \sqrt{\hat{\sigma}^2}\right)$.

References

Agresti, A. (2013). Categorical Data Analysis. 3rd Edition. John Wiley & Sons, Hoboken, NJ

Examples

# Generate binary samples with strata
responses <- expand(c(9, 3, 7, 2), c(10, 10, 10, 10))
arm <- rep(c("treat", "control"), 20)
strata <- rep(c("stratum1", "stratum2"), times = c(20, 20))

# Calculate common risk difference
ci_rel_risk_cmh_strata(x = responses, by = arm, strata = strata)
#> 
#> ── Mantel-Haenszel Common Relattive Risk Confidence Interval ───────────────────
#> • 12/20 - 9/20
#> • Estimate: 1.333
#> • Variance: 0.093
#> • 95% Confidence Interval:
#>   (0.7344, 2.4208)