*! version 1.0.1 26Feb2024

*! version 1.0.0 24Sept2019

Title

evalue_estat -- Postestimation tool for conducting sensitivity analyses of unmeasured confounding in observational studies

Syntax

E-value for testing against a null effect (equaling a rate ratio of 1.0):

evalue_estat
coef_name

E-value for testing against a different value:

evalue_estat
coef_name
==
#

coef_name identifies a coefficient in the preceding estimation model. coef_name is typically a variable name with or without a level indicator (see fvvarlist). The easiest
way to identify the coef_name assigned by the estimation model is to specify the coeflegend option; see estimation options.

For continuous outcomes estimated with regress, tobit, truncreg, { helpb hetregress}, xtreg, intreg, meintreg, or metobit,
coef_name must be a binary variable, as evalue_estat computes the standardized mean difference between 2 levels of a variable.

Description

evalue_estat is a postestimation command that performs sensitivity analyses for unmeasured confounding in observational studies using the methodology
proposed by VanderWeele and Ding (2017). evalue_estat reports E-values, defined as the minimum strength of association on the risk ratio scale that an
unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific treatment-outcome association, conditional
on the measured covariates.

evalue_estat computes E-values for point estimates and confidence limits for several common outcome types, including risk and rate ratios,
odds ratios with common or rare outcomes, hazard ratios with common or rare outcomes, and standardized mean differences in outcomes. Estimation models currently supported by
evalue_estat are logistic, logit, cloglog, scobit, clogit, melogit, mecloglog, stcox, streg,
mestreg, poisson, cpoisson, tpoisson, nbreg, zip, zinb, mepoisson, menbreg,
regress, tobit, truncreg, hetregress, intreg, xtreg, metobit and meintreg.

See evalue for a comprehensive discussion of how to interpret results produced by evalue_estat.

Examples

1) E-value for a risk ratio

Set-up

. webuse dollhill3, clear

Estimate a Poisson model

. poisson deaths smokes i.agecat, exposure(pyears) irr

Compute the E-value for the coefficient smokes.

. evalue_estat smokes

Same as above but assessing the amount of confounding needed to shift the point estimate (1.43) to 1.10.

. evalue_estat smokes==1.1

2) E-value for an odds ratio

Set-up

. webuse lbw, clear

Estimate a logistic regression model. Note that, in this example, the exposure variable smoke is specified as a factor variable.

. logistic low age lwt i.race i.smoke ptl ht ui

Compute the E-value for the coefficient i.smoke

. evalue_estat 1.smoke

3) E-value for a hazard ratio

Set-up

. webuse drugtr, clear

Estimate a Cox regression model.

. stcox drug age

Compute the E-value for the coefficient drug

. evalue_estat drug

Estimate a survival regression model with a Weibull distribution.

. streg drug age, dist(weibull)

Compute the E-value for the coefficient drug

. evalue_estat drug

4) E-value for a standardized mean difference

Set-up

. sysuse auto, clear

Estimate a linear regression model

. regress mpg weight foreign

Compute the E-value for the coefficient foreign

. evalue_estat foreign

Stored results

evalue_estat stores the following in r():

Scalars

r(est) Model coefficient for the point estimate

r(ll) Model lower confidence limit

r(ul) Model upper confidence limit

r(eval_est) E-value for the point estimate

r(eval_ci) E-value for the confidence interval

When regress, tobit, truncreg, hetregress, xtreg, intreg, meintreg, or metobit is the estimation model, these scalars are also added:

r(d) Cohen's d

r(se_d) standard error of the Cohen's d estimate

r(sdy) e(sample) standard deviation of the outcome variable

r(n0) sample size of the control group in e(sample)

r(n1) sample size of the treatment group in e(sample)

References

Linden, A., Mathur, M.B., and T. J. VanderWeele. Conducting Sensitivity Analysis for Unmeasured Confounding in Observational Studies using E-values: The evalue package.
Stata Journal, Forthcoming.

VanderWeele, T. J., and Ding, P. (2017). Sensitivity analysis in observational research: introducing the E-value. Annals of Internal Medicine, 167(4): 268-274.

Citation of evalue_estat

evalue_estat is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such:

Linden A. (2019). EVALUE_ESTAT: Stata module for conducting postestimation sensitivity analyses of unmeasured confounding in observational studies.

Authors

Ariel Linden

President, Linden Consulting Group, LLC

alinden@lindenconsulting.org

Also see

Online: evalue if installed, esizereg if installed