This calculator finds the attributable risk, attributable risk percentage, and population attributable risk percentage for a given 2×2 contingency table.
Simply fill in the cells of the table below and then click “Calculate.”
| Disease | No Disease | |
|---|---|---|
| Exposed | ||
| Not Exposed |
Attributable Risk: 0.08077
Attributable Risk %: 53.30612
Population Attributable Risk %: 17.30718%
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike. My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
Hello Zach,
Thanks for disseminationg your relevant knowledge and work via the statology website- it is great.
I have a question. Did you have any content on sensitive analysis? I am browsing how to systematically address it for a logistic regression mondel.
Many thanks for considering my enquiry.
Juan
Yes, I can definitely help you with **sensitivity analysis for a logistic regression model**. Sensitivity analysis examines how the output (e.g., predicted probabilities or classification decisions) of your logistic regression model changes when inputs (features, parameters, assumptions) are varied. This is especially important in fields like epidemiology, economics, and risk modeling.
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### 🔍 **Types of Sensitivity Analysis for Logistic Regression**
Here’s a structured way to think about it:
#### 1. **Input (Predictor) Sensitivity**
* **Objective**: Assess how changes in predictor values affect the predicted probability or odds.
* **Method**: Vary one input at a time (OAT) while holding others constant, and observe the change in predicted probabilities.
* **Tool**: Partial dependence plots (PDPs) or marginal effect plots.
#### 2. **Coefficient Sensitivity**
* **Objective**: Assess how robust the model is to small perturbations in the estimated coefficients.
* **Method**: Use bootstrapping or jackknife resampling to obtain confidence intervals and test coefficient stability.
#### 3. **Assumption Sensitivity**
* **Objective**: Check sensitivity to model assumptions such as linearity, independence of errors, multicollinearity.
* **Method**:
* Run the model excluding or including interaction terms.
* Check with/without regularization (e.g., L1/L2).
* Test for multicollinearity (e.g., VIF scores).
#### 4. **Sensitivity to Missing Data Imputation**
* **Objective**: See how your choice of imputation method affects model outcomes.
* **Method**: Fit models using different imputation techniques (mean, median, multiple imputation) and compare output.
#### 5. **Outcome Classification Threshold Sensitivity**
* **Objective**: Evaluate how the classification performance (e.g., sensitivity, specificity) changes as the probability threshold varies.
* **Method**:
* Vary the threshold from 0 to 1.
* Plot ROC curve and Precision-Recall curve.
* Identify the threshold that balances sensitivity/specificity or maximizes a custom metric.
#### 6. **Influential Observation Sensitivity**
* **Objective**: Identify observations that disproportionately influence the model.
* **Method**:
* Cook’s distance, leverage statistics, DFBETA.
* Rerun model excluding influential observations.
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### 🛠️ Tools and Libraries
In **Python**:
* `statsmodels` for influence diagnostics.
* `sklearn.inspection` for PDP and permutation importance.
* `seaborn`/`matplotlib` for visualizing effects.
In **R**:
* `car` package for VIF and influence measures.
* `effects` and `rms` for plotting marginal effects.
* `boot` for coefficient stability.
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