README.md

In jameshenegan/dmsepmlr: Delta Method Standard Errors for various quantities related to the Predictive Margins of a Logistic Regression Model

dmsepmlr

Delta Method Standard Errors for various quantities related to the Predictive Margins of a Logistic Regression model with a binary main effect and any number of adjustors.

This package estimates predictive margins, along with their delta method standard errors, for a logistic regression model having a binary main effect and any number of adjustors. The margins are then used to produce additional estimates, including an “adjusted risk difference” and an “adjusted risk ratio.”

Installation

You can install the development version of dmsepmlr from GitHub with:

# install.packages("devtools")
devtools::install_github("jameshenegan/dmsepmlr")

Example 1

In this example, we will look at a simulated epidemiological dataset (containing N=10000 observations) where each observation contains information on a subject’s death status, disease status, and age.

library(dmsepmlr); data(epiDat); head(epiDat)
#>   death disease   age
#> 1     0       0 42.38
#> 2     0       0 52.29
#> 3     0       0 63.67
#> 4     0       0 48.65
#> 5     0       0 18.96
#> 6     0       0 86.83

Suppose we wish to consider the following model:

glm(formula = death ~ disease + age,
    family=binomial(link = "logit"),
    data = epiDat)
#> 
#> Call:  glm(formula = death ~ disease + age, family = binomial(link = "logit"), 
#>     data = epiDat)
#> 
#> Coefficients:
#> (Intercept)      disease          age  
#>    -9.32354      0.63888      0.08159  
#> 
#> Degrees of Freedom: 9999 Total (i.e. Null);  9997 Residual
#> Null Deviance:       1129 
#> Residual Deviance: 878.4     AIC: 884.4

Then we may use dmsepmlr::logisticMargins to obtain the predictive margins associated with disease values of 0 and 1, along with related estimates, for this model as follows:

logisticMargins(formula = death ~ disease + age,
                main_effect = "disease",
                over = FALSE,
                data = epiDat)
#>          Quantity    Estimate Delta Method SE
#> 1       MargProb0 0.009740075    0.0009832863
#> 2       MargProb1 0.017642796    0.0059259127
#> 3 RiskDiff(p1-p0) 0.007902722    0.0060069545
#> 4  RelRisk(p1/p0) 1.811361504    0.6352947138
#> 5       OddsRatio 1.825933276    0.6514774210

Note that

• the first row of the output provides the predictive margin associated with disease value of 0,
• the second row of the output provides the predictive margin associated with disease value of 1,
• the third row of the output provides the risk difference between these two margins,
• the fourth row of the output provides the risk ratio for two margins, and
• the fifth row of the output provides the odds ratio for two margins.

Comparison with Stata’s margins command

Suppose that we have epiDat loaded into Stata. Then running logistic death i.disease age followed by margins disease would produce the following results:

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     disease |
          0  |   .0097401   .0009833     9.91   0.000     .0078129    .0116673
          1  |   .0176428   .0059259     2.98   0.003     .0060282    .0292574
------------------------------------------------------------------------------

Meanwhile, running lincom _b[1.disease] - _b[0.disease] would give us the following:

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .0079027    .006007     1.32   0.188    -.0038707    .0196761
------------------------------------------------------------------------------

Also, running nlcom (RR: _b[1.disease] / _b[0.disease]) would give us the following:

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          RR |   1.811361   .6352954     2.85   0.004     .5662054    3.056517
------------------------------------------------------------------------------

Finally, running

nlcom (OR: (_b[1.disease]/(1-_b[1.disease])) ///
         / (_b[0.disease]/(1-_b[0.disease])) ///
      )

would produce

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          OR |   1.825933   .6514781     2.80   0.005     .5490597    3.102807
------------------------------------------------------------------------------

We see that these results closely resemble the results we obtained from our logisticMargins command.

Example 2

In this example, we use the same data and the same logistic model as above.

Now suppose that we ran the following command in Stata

margins, over(disease)

In this case, we would obtain the following results:

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     disease |
          0  |   .0097077   .0009798     9.91   0.000     .0077874    .0116281
          1  |   .0190476   .0064454     2.96   0.003     .0064149    .0316804
------------------------------------------------------------------------------

We can obtain these results from dmsepmlr::logisticMargins by setting the over option to TRUE:

logisticMargins(formula = death ~ disease + age,
                main_effect = "disease",
                over = TRUE,
                data = epiDat)
#>          Quantity    Estimate Delta Method SE
#> 1       MargProb0 0.009707724    0.0009797998
#> 2       MargProb1 0.019047619    0.0064453915
#> 3 RiskDiff(p1-p0) 0.009339895    0.0065194386
#> 4  RelRisk(p1/p0) 1.962109575    0.6928495929
#> 5       OddsRatio 1.980791314    0.7124808464

jameshenegan/dmsepmlr documentation built on Jan. 1, 2021, 4:27 a.m.