Running Margin On Two Part Model With Exposure

by ADMIN 47 views

Introduction

When analyzing healthcare costs, it's common to encounter outcomes that are skewed and have a large number of zeros. A two-part model (twopm) is a popular approach to handle such outcomes, where the first part models the probability of incurring costs (i.e., being a non-zero spender) and the second part models the amount spent among those who incur costs. In this article, we will discuss how to run margins on a two-part model with exposure in Stata.

Two Part Model with Exposure

A two-part model with exposure is an extension of the traditional two-part model. It takes into account the exposure or the number of times an individual is at risk of incurring costs. For example, in a study on healthcare costs, the exposure might be the number of doctor visits or hospital admissions. The two-part model with exposure can be represented as follows:

  1. First Part: Logit Model

    The first part of the two-part model is a logit model that estimates the probability of incurring costs. The logit model can be represented as:

    P(Y > 0 | X) = 1 / (1 + exp(-Xβ))

    where P(Y > 0 | X) is the probability of incurring costs given the covariates X, and β is the vector of coefficients.

  2. Second Part: GLM with Gamma Distribution and Log Link

    The second part of the two-part model is a Generalized Linear Model (GLM) with a gamma distribution and log link. The gamma distribution is suitable for modeling skewed outcomes, and the log link is used to model the log of the costs. The GLM can be represented as:

    E(Y | X) = exp(Xβ)

    where E(Y | X) is the expected value of costs given the covariates X, and β is the vector of coefficients.

Running Margins on Two Part Model with Exposure

To run margins on a two-part model with exposure in Stata, we can use the margins command. The margins command calculates the marginal effects of the covariates on the outcome variable. To calculate the marginal effects of the covariates on the probability of incurring costs, we can use the following syntax:

margins, at(X = x_value) predict(p)

This will calculate the marginal effect of the covariate X at the value x_value on the probability of incurring costs.

To calculate the marginal effects of the covariates on the expected value of costs among those who incur costs, we can use the following syntax:

margins, at(X = x_value) predict(exp)

This will calculate the marginal effect of the covariate X at the value x_value on the expected value of costs among those who incur costs.

Example

Suppose we have a dataset with the following variables:

id doctor_visits hospital_admissions healthcare_cost
1 5 2 1000
2 3 1 500
3 2 0 0
... ... ... ...

We can estimate the two-part model with exposure using the following syntax:

twopm (1) (2) (doctor_visits hospital_admissions), exposure(doctor_visits hospital_admissions)

This will estimate the two-part model with exposure, where the first part is a logit model and the second part is a GLM with a gamma distribution and log link.

We can then run margins on the two-part model with exposure using the following syntax:

margins, at(doctor_visits = 5) predict(p)
margins, at(doctor_visits = 5) predict(exp)

This will calculate the marginal effect of the covariate doctor_visits at the value 5 on the probability of incurring costs and the expected value of costs among those who incur costs.

Conclusion

In this article, we discussed how to run margins on a two-part model with exposure in Stata. We showed how to estimate the two-part model with exposure using the twopm command and how to run margins on the model using the margins command. We also provided an example of how to use the margins command to calculate the marginal effects of the covariates on the probability of incurring costs and the expected value of costs among those who incur costs.

References

  • StataCorp. (2022). Stata User's Guide. Stata Press.
  • Greene, W. H. (2018). Econometric Analysis. Pearson Education.

Code

// Estimate the two-part model with exposure
twopm (1) (2) (doctor_visits hospital_admissions), exposure(doctor_visits hospital_admissions)

// Run margins on the two-part model with exposure
margins, at(doctor_visits = 5) predict(p)
margins, at(doctor_visits = 5) predict(exp)


**Q&A: Running Margin on Two Part Model with Exposure**
=====================================================

**Q: What is a two-part model with exposure?**
-----------------------------------------

A: A two-part model with exposure is an extension of the traditional two-part model. It takes into account the exposure or the number of times an individual is at risk of incurring costs. For example, in a study on healthcare costs, the exposure might be the number of doctor visits or hospital admissions.

**Q: What is the difference between a two-part model and a two-part model with exposure?**
-----------------------------------------------------------------------------------

A: The main difference between a two-part model and a two-part model with exposure is that the latter takes into account the exposure or the number of times an individual is at risk of incurring costs. This is particularly useful in studies where the outcome variable is skewed and has a large number of zeros.

**Q: How do I estimate a two-part model with exposure in Stata?**
---------------------------------------------------------

A: To estimate a two-part model with exposure in Stata, you can use the `twopm` command. The syntax for the `twopm` command is as follows:

```stata
twopm (1) (2) (exposure_variable), exposure(exposure_variable)
</code></pre>
<h2><strong>Q: How do I run margins on a two-part model with exposure in Stata?</strong></h2>
<p>A: To run margins on a two-part model with exposure in Stata, you can use the <code>margins</code> command. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<h2><strong>Q: What is the difference between the <code>predict(p)</code> and <code>predict(exp)</code> options in the <code>margins</code> command?</strong></h2>
<p>A: The <code>predict(p)</code> option in the <code>margins</code> command calculates the marginal effect of the covariate on the probability of incurring costs. The <code>predict(exp)</code> option calculates the marginal effect of the covariate on the expected value of costs among those who incur costs.</p>
<h2><strong>Q: How do I interpret the results of the <code>margins</code> command?</strong></h2>
<p>A: The results of the <code>margins</code> command can be interpreted as follows:</p>
<ul>
<li>The marginal effect of the covariate on the probability of incurring costs is the change in the probability of incurring costs for a one-unit change in the covariate, while holding all other covariates constant.</li>
<li>The marginal effect of the covariate on the expected value of costs among those who incur costs is the change in the expected value of costs for a one-unit change in the covariate, while holding all other covariates constant.</li>
</ul>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of multiple covariates?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of multiple covariates. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a categorical variable?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a categorical variable. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a continuous variable?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a continuous variable. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a binary variable?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a binary variable. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a time-varying variable?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a time-varying variable. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a variable with missing values?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a variable with missing values. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a variable with outliers?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a variable with outliers. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a variable with non-normal distribution?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a variable with non-normal distribution. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a variable with interaction terms?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a variable with interaction terms. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a variable with polynomial terms?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a variable with polynomial terms. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>
<p>This will calculate the marginal effects of the covariate exposure_variable on the probability of incurring costs and the expected value of costs among those who incur costs, while holding all other covariates constant.</p>
<h2><strong>Q: Can I use the <code>margins</code> command to calculate the marginal effects of a variable with categorical interactions?</strong></h2>
<p>A: Yes, you can use the <code>margins</code> command to calculate the marginal effects of a variable with categorical interactions. The syntax for the <code>margins</code> command is as follows:</p>
<pre><code class="hljs">margins, at(exposure_variable = x_value) predict(p)
margins, at(exposure_variable = x_value) predict(exp)
</code></pre>