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 (possibly through an approximate conversion) as well as E-values for the point estimate and the confidence interval limit closer to the null.

1 |

`est` |
The effect estimate that was observed but which is suspected to be
biased. A number of class "estimate" (constructed with |

`lo` |
Optional. Lower bound of the confidence interval. If not an object
of class "estimate", assumed to be on the same scale as |

`hi` |
Optional. Upper bound of the confidence interval. If not an object
of class "estimate", assumed to be on the same scale as |

`se` |
The standard error of the point estimate, for |

`delta` |
The contrast of interest in the exposure, for |

`true` |
A number to which to shift the observed estimate to. Defaults to
1 for ratio measures ( |

`...` |
Arguments passed to other methods. |

An E-value for unmeasured confounding is minimum strength of association, on the risk ratio scale, that unmeasured confounder(s) would need to have with both the treatment and the outcome to fully explain away a specific treatmentâ€“outcome association, conditional on the measured covariates.

The estimate is converted appropriately before the E-value is calculated. See conversion functions for more details. The point estimate and confidence limits after conversion are returned, as is the E-value for the point estimate and the confidence limit closest to the proposed "true" value (by default, the null value.)

For an `OLS()`

estimate, the E-value 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`

.

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).

Ding & VanderWeele (2016). Sensitivity analysis without assumptions.

*Epidemiology.*27(3), 368.VanderWeele & Ding (2017). Sensitivity analysis in observational research: Introducing the E-value.

*Annals of Internal Medicine.*27(3), 368.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | ```
# compute E-value for leukemia example in VanderWeele and Ding (2017)
evalue(RR(0.80), 0.71, 0.91)
# you can also pass just the point estimate
# and return just the E-value for the point estimate with summary()
summary(evalue(RR(0.80)))
# demonstrate symmetry of E-value
# this apparently causative association has same E-value as the above
summary(evalue(RR(1 / 0.80)))
# E-value for a non-null true value
summary(evalue(RR(2), true = 1.5))
## Hsu and Small (2013 Biometrics) Data
## sensitivity analysis after log-linear or logistic regression
head(lead)
## log linear model -- obtain the conditional risk ratio
lead.loglinear = glm(lead ~ ., family = binomial(link = "log"),
data = lead[,-1])
est_se = summary(lead.loglinear)$coef["smoking", c(1, 2)]
est = RR(exp(est_se[1]))
lowerRR = exp(est_se[1] - 1.96*est_se[2])
upperRR = exp(est_se[1] + 1.96*est_se[2])
evalue(est, lowerRR, upperRR)
## logistic regression -- obtain the conditional odds ratio
lead.logistic = glm(lead ~ ., family = binomial(link = "logit"),
data = lead[,-1])
est_se = summary(lead.logistic)$coef["smoking", c(1, 2)]
est = OR(exp(est_se[1]), rare = FALSE)
lowerOR = exp(est_se[1] - 1.96*est_se[2])
upperOR = exp(est_se[1] + 1.96*est_se[2])
evalue(est, lowerOR, upperOR)
## linear regression
# standardizing conservatively by SD(Y)
ols = lm(age ~ income, data = lead)
est = OLS(ols$coefficients[2], sd = sd(lead$age))
# for a 1-unit increase in income
evalue(est = est,
se = summary(ols)$coefficients['income', 'Std. Error'])
# for a 0.5-unit increase in income
evalue(est = est,
se = summary(ols)$coefficients['income', 'Std. Error'],
delta = 0.5)
# E-value for Cohen's d = 0.5 with SE = 0.25
evalue(est = MD(.5), se = .25)
# compute E-value for HR = 0.56 with CI: [0.46, 0.69]
# for a common outcome
evalue(HR(0.56, rare = FALSE), lo = 0.46, hi = 0.69)
# for a rare outcome
evalue(HR(0.56, rare = TRUE), lo = 0.46, hi = 0.69)
``` |

```
point lower upper
RR 0.800000 0.71 0.910000
E-values 1.809017 NA 1.428571
[1] 1.809017
[1] 1.809017
You are calculating a "non-null" E-value, i.e., an E-value for the
minimum amount of unmeasured confounding needed to move the estimate
and confidence interval to your specified true value rather than to the
null value.
[1] 2
id smoking lead age male edu.lt9 edu.9to11 edu.hischl edu.somecol
1 41493 1 FALSE 77 0 0 1 0 0
2 41502 1 FALSE 29 1 0 0 1 0
3 41512 1 FALSE 80 0 0 0 0 1
4 41545 1 FALSE 40 0 1 0 0 0
5 41556 1 FALSE 38 1 0 1 0 0
6 41558 1 FALSE 50 0 0 1 0 0
edu.college edu.unknown income income.mis white black mexicanam otherhispan
1 0 0 1.57 0 1 0 0 0
2 0 0 3.41 0 0 0 1 0
3 0 0 1.24 0 1 0 0 0
4 0 0 1.27 0 0 0 1 0
5 0 0 1.24 0 1 0 0 0
6 0 0 1.22 0 0 1 0 0
otherrace
1 0
2 0
3 0
4 0
5 0
6 0
Warning message:
glm.fit: algorithm did not converge
point lower upper
RR 2.488840 1.672007 3.704724
E-values 4.413804 2.732008 NA
Warning message:
glm.fit: algorithm did not converge
point lower upper
RR 1.642884 1.315436 2.051843
E-values 2.670591 1.959590 NA
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
point lower upper
RR 1.576173 1.010050 2.459603
E-values 2.529142 1.110803 NA
point lower upper
RR 0.670084 0.585935 0.7735267
E-values 2.349531 NA 1.9080039
point lower upper
RR 0.560000 0.46 0.690000
E-values 2.970223 NA 2.256198
```

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