Validation

In BSW: Fitting a Log-Binomial Model using the Bekhit-Schöpe-Wagenpfeil (BSW) Algorithm

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Test Suite

The following fictitious example of a prospective cohort study will be used to validate the correct estimation of the BSW package in R.

||Exposed|Non-Exposed| |:--:|:--:|:--:| |Cases|200|50| |Non-Cases|50|200|

library(testthat)
library(BSW)
df <- data.frame(y = rep(c(0, 1), each = 250), 
                 x = rep(c(0, 1, 0, 1), times = c(200, 50, 50, 200))
                 )
RR <- (200 * 250) / (50 * 250)
SE <- sqrt((1/200 + 1/50) - (1/250 + 1/250))
fit <- bsw(y ~ x, df)
out <- summary(fit)

The relative risk for exposed individuals compared to non-exposed individuals can be calculated from

$RR = \displaystyle\frac{200 * 250}{50*250} = 4$.

test_that(desc = "Estimated relative risk is equal to 4",
          code = {
                  expect_equal(object = unname(exp(coef(fit)[2])),
                               expected = RR)
            }
          )

The standard error of the natural logarithm of the relative risk can be calculated from

$SE(ln(RR)) = \displaystyle\sqrt{\Big(\frac{1}{200} + \frac{1}{50}\Big) - \Big(\frac{1}{250}+\frac{1}{250}\Big)} = 0.130384$.

test_that(desc = "Estimated standard error is equal to 0.1303840",
          code = {
                  expect_equal(object = unname(out$std.err[2]), 
                               expected = SE)
            }
          )

The z-value can be calculated from

$z = \displaystyle\frac{1.386294}{0.130384} = 10.63239$.

test_that(desc = "Estimated z-value is equal to 10.63239",
          code = {
                  expect_equal(object = unname(out$z.value[2]), 
                               expected = log(RR) / SE)
            }
          )

The 95% confidence interval limits can be calculated from

$exp(1.386294 \pm 1.959964 * 0.1303840) = [3.097968; 5.164676]$.

test_that(desc = "Estimated 95% confidence interval limits are equal to 3.097968 and 5.164676",
          code = {
                  expect_equal(object = unname(exp(confint(fit)[2,])), 
                               expected = exp(log(RR) + SE * qnorm(c(0.025, 0.975))))
            }
          )

BSW documentation built on March 22, 2021, 5:07 p.m.