Effect size and standard error from confidence interval

Usage

ci2ms(ci, logscale = TRUE, alpha = 0.05)

Arguments

ci: confidence interval (CI). The delimiter between lower and upper limit is either a hyphen (-) or en dash (–).
logscale: a flag indicating the confidence interval is based on a log-scale.
alpha: Type 1 error.

Value

Based on CI, the function provides a list containing estimates

m effect size (log(OR))
s standard error
direction a decrease/increase (-/+) sign such that sign(m)=-1, 0, 1, is labelled "-", "0", "+", respectively as in PhenoScanner.

Details

Effect size is a measure of strength of the relationship between two variables in a population or parameter estimate of that population. Without loss of generality, denote m and s to be the mean and standard deviation of a sample from $N(\mu,\sigma^2)$). Let $z \sim N(0,1)$ with cutoff point $z_\alpha$, confidence limits L, U in a CI are defined as follows, $$ \begin{aligned} L & = m - z_\alpha s \cr U & = m + z_\alpha s \end{aligned} $$ $\Rightarrow$ $U + L = 2 m$, $U - L=2 z_\alpha s$. Consequently, $$ \begin{aligned} m & = \frac{U + L}{2} \cr s & = \frac{U - L}{2 z_\alpha} \end{aligned} $$ Effect size in epidemiological studies on a binary outcome is typically reported as odds ratio from a logistic regression or hazard ratio from a Cox regression, $L\equiv\log(L)$, $U\equiv\log(U)$.

Examples

# rs3784099 and breast cancer recurrence/mortality
ms <- ci2ms("1.28-1.72")
print(ms)
#> $m
#> [1] 0.3945922
#> 
#> $s
#> [1] 0.07537491
#> 
#> $direction
#> [1] "+"
#> 
# Vector input
ci2 <- c("1.28-1.72","1.25-1.64")
ms2 <- ci2ms(ci2)
print(ms2)
#> $m
#> [1] 0.3945922 0.3589199
#> 
#> $s
#> [1] 0.07537491 0.06927492
#> 
#> $direction
#> [1] "+" "+"
#>