Compute selection bias E-value for a hazard ratio and its confidence interval limits

Returns a data frame containing point estimates, the lower confidence limit, and the upper confidence limit on the risk ratio scale (through an approximate conversion if needed when outcome is common) as well as E-values for the point estimate and the confidence interval limit closer to the null.

selection_evalue(
  est,
  lo = NA,
  hi = NA,
  true = 1,
  sel_pop = FALSE,
  S_eq_U = FALSE,
  risk_inc = FALSE,
  risk_dec = FALSE,
  ...
)

Arguments

est	The point estimate: a risk, odds, or hazard ratio. An object of class "estimate", it should be constructed with functions RR(), OR(), or HR().
lo	The lower limit of the confidence interval
hi	The upper limit of the confidence interval
true	The true value to which to shift the observed point estimate. Typically set to 1 to consider a null true effect.
sel_pop	Whether inference is specific to selected population (TRUE) or entire population (FALSE). Defaults to FALSE.
S_eq_U	Whether the unmeasured factor is assumed to be a defining characteristic of the selected population. Defaults to FALSE.
risk_inc	Whether selection is assumed to be associated with increased risk of the outcome in both exposure groups. Defaults to FALSE.
risk_dec	Whether selection is assumed to be associated with decreased risk of the outcome in both exposure groups. Defaults to FALSE.
...	Arguments passed to other methods.

Details

A selection bias E-value is a summary measure that helps assess susceptibility of a result to selection bias. Each of one or more parameters characterizing the extent of the bias must be greater than or equal to this value to be sufficient to shift an estimate (est) to the null or other true value (true). The parameters, as defined in Smith and VanderWeele 2019, depend on assumptions an investigator is willing to make (see arguments sel_pop, S_eq_U, risk_inc, risk_dec). The function prints a message about which parameters the selection bias E-value refers to given the assumptions made. See the cited article for details.

Examples

# Examples from Smith and VanderWeele 2019

# Zika virus example
selection_evalue(OR(73.1, rare = TRUE), lo = 13.0)
#> This selection bias E-value refers to RR_UY|A=0, RR_UY|A=1, RR_SU|A=0,
#> and RR_SU|A=1 (see documentation)
#>                            point     lower upper
#> RR                      73.10000 13.000000    NA
#> Selection bias E-values 16.58416  6.670588    NA

# Endometrial cancer example
selection_evalue(OR(2.30, rare = TRUE), true = 11.98, S_eq_U = TRUE, risk_inc = TRUE)
#> You are calculating a "non-null" selection bias E-value, i.e., an
#> E-value for the minimum amount of selection bias needed to move the
#> estimate and confidence interval to your specified true value rather
#> than to the null value.
#> This selection bias E-value refers to RR_UY|A = 1 (see documentation)
#>                            point lower upper
#> RR                      2.300000    NA    NA
#> Selection bias E-values 5.208696    NA    NA

# Obesity paradox example
selection_evalue(RR(1.50), lo = 1.22, sel_pop = TRUE)
#> This selection bias E-value refers to RR_UY|S=1 and RR_AU|S=1 (see
#> documentation)
#>                            point    lower upper
#> RR                      1.500000 1.220000    NA
#> Selection bias E-values 2.366025 1.738073    NA