Description Usage Arguments Details References Examples

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.

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

`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. |

This function is for linear regression with a continuous exposure
and outcome. Regarding the continuous exposure, the choice of `delta`

defines essentially a dichotomization in the exposure between hypothetical
groups of subjects with exposures equal to an arbitrary value *c* versus
to another hypothetical group with exposures equal to *c* +
`delta`

. Regarding the continuous outcome, the function uses the
effect-size conversions in Chinn (2000) and VanderWeele (2017) to
approximately convert the mean difference between these exposure "groups" to
the odds ratio that would arise from dichotomizing the continuous outcome.

For example, if resulting E-value is 2, this means that unmeasured
confounder(s) would need to double the probability of a subject's having
exposure equal to *c* + `delta`

instead of *c*, and would also
need to double the probability of being high versus low on the outcome, in
which the cutoff for "high" versus "low" is arbitrary subject to some
distributional assumptions (Chinn, 2000).

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.

Chinn, S (2000). A simple method for converting an odds ratio to
effect size for use in meta-analysis. *Statistics in Medicine*, 19(22),
3127-3131.

VanderWeele, TJ (2017). On a square-root transformation of the odds ratio for
a common outcome. *Epidemiology*, 28(6), e58.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
# 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$age))
# for a 0.5-unit increase in income
evalues.OLS(est = ols$coefficients[2],
se = summary(ols)$coefficients['income', 'Std. Error'],
sd = sd(lead$age),
delta = 0.5)
# 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 1.015465 0.9952602 1.03608
E-values 1.140780 1.0000000 NA
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
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
```

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