Compute E-value for a linear regression coefficient estimate

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) as well as E-values for the point estimate and the confidence interval limit closer to the null.

evalues.OLS(est, se = NA, sd, delta = 1, true = 0, ...)

Arguments

est	The linear regression coefficient estimate (standardized or unstandardized)
se	The standard error of the point estimate
sd	The standard deviation of the outcome (or residual standard deviation); see Details
delta	The contrast of interest in the exposure
true	The true standardized mean difference to which to shift the observed point estimate. Typically set to 0 to consider a null true effect.
...	Arguments passed to other methods.

Details

A true standardized mean difference for linear regression would use sd = SD( Y | X, C ), where Y is the outcome, X is the exposure of interest, and C are any adjusted covariates. See Examples for how to extract this from lm. A conservative approximation would instead use sd = SD( Y ). Regardless, the reported E-value for the confidence interval treats sd as known, not estimated.

Examples

# first standardizing conservatively by SD(Y)
data(lead)
ols = lm(age ~ income, data = lead)

# for a 1-unit increase in income
evalues.OLS(est = ols$coefficients[2],
            se = summary(ols)$coefficients['income', 'Std. Error'],
            sd = sd(lead$age))
#> Confidence interval crosses the true value, so its E-value is 1.
#>             point     lower   upper
#> RR       1.015465 0.9952602 1.03608
#> E-values 1.140780 1.0000000      NA

# for a 0.5-unit increase in income
evalues.OLS(est = ols$coefficients[2],
            se = summary(ols)$coefficients['income', 'Std. Error'],
            sd = sd(lead$age),
            delta = 0.5)
#> Confidence interval crosses the true value, so its E-value is 1.
#>             point     lower   upper
#> RR       1.007703 0.9976273 1.01788
#> E-values 1.095805 1.0000000      NA

# now use residual SD to avoid conservatism
# here makes very little difference because income and age are
# not highly correlated
evalues.OLS(est = ols$coefficients[2],
            se = summary(ols)$coefficients['income', 'Std. Error'],
            sd = summary(ols)$sigma)
#> Confidence interval crosses the true value, so its E-value is 1.
#>             point     lower    upper
#> RR       1.015468 0.9952593 1.036086
#> E-values 1.140795 1.0000000       NA