Bias and tipping points • ggextreme

Every observational estimate invites the same question: how strong would unmeasured confounding have to be to change the conclusion? ggsensitivity() answers it for every combination of strengths at once, and marks where the answer changes.

library(ggextreme)

A first explorer

Suppose an analysis gives a risk ratio of 1.80 (1.40 to 2.31), that a risk ratio of 1.25 is the smallest that would matter clinically, and that the two strongest measured confounders, age and smoking, were associated with the exposure and the outcome as below:

bench <- data.frame(label = c("Age", "Smoking"),
                    exposure = c(1.6, 2.3), outcome = c(1.9, 1.5))
s <- ggsensitivity(1.8, 1.4, 2.31, important = 1.25, benchmarks = bench,
                   title = "How strong would confounding have to be?")
s

Each point of the surface is an unmeasured confounder with a risk ratio with the exposure on one axis and with the outcome on the other. The shading says what would survive it: a clinically important effect with an interval clear of 1, an interval clear of 1, an estimate on the same side of 1, or nothing. Click the surface, or use the sliders, to choose a confounder; the row “Under the chosen confounder” and the sentence under the plot follow.

s$evalues
#>             target   evalue
#> 1         estimate 3.000000
#> 2 confidence limit 2.148331
s$benchmarks
#>     label exposure outcome     bias estimate    lower    upper
#> 1     Age      1.6     1.9 1.216000 1.480263 1.151316 1.899671
#> 2 Smoking      2.3     1.5 1.232143 1.460870 1.136232 1.874783

The E-value is the strength, on both axes at once, that could just explain the estimate away; the second E-value does the same for the confidence limit. A confounder as strong as the benchmarks would leave the estimate clear of 1, which is some reassurance, not proof: an unmeasured confounder need not resemble the measured ones.

The method

The adjustment divides the estimate by the bounding factor of Ding and VanderWeele, which is the most bias a confounder of given strengths could produce, so every adjusted value is a worst case. A protective estimate is handled by symmetry. An odds ratio or hazard ratio for a common outcome is first converted to an approximate risk ratio; set rare = TRUE when the outcome is rare.

ggsensitivity(0.62, 0.48, 0.80, measure = "HR", important = 0.8)