# Predicting Diabetes with Bayesian Neural Networks: More Than Just a Probability

**Date:** April 18, 2025
**Link:** https://swarnendu-stat.netlify.app/post/bnns-binary-classification/
**Tags:** R, Bayesian Neural Networks, Clinical Trials




> *In critical applications like healthcare, knowing the probability isn’t enough. Knowing how confident we are in that probability makes all the difference.*

---

## 🔍 The Problem

Diabetes prediction models abound, but they often give us **just a number**. Traditional classifiers like logistic regression or random forests will tell you, for instance, that there's a 73% chance someone has diabetes.

But what if we asked:
> _"How sure are we about that 73%?"_

Enter **Bayesian Neural Networks** (`bnns`), where uncertainty isn’t a bug—it’s a feature.

---

## 📊 The Data

We used the `PimaIndiansDiabetes2` dataset from the `mlbench` package, containing clinical variables (e.g., glucose, BMI, insulin) and diabetes diagnosis. Missing values were removed, and outcomes were converted to binary.


``` r
library(bnns)
library(mlbench)
library(rsample)
library(ggplot2)

set.seed(123)
data("PimaIndiansDiabetes2")
trial_data <- PimaIndiansDiabetes2 |>
  transform(diabetes = ifelse(diabetes == "pos", 1, 0)) |>
  na.omit()

trial_data_split <- initial_split(trial_data, strata = diabetes, prop = 0.8)
trial_data_train <- training(trial_data_split)
trial_data_test <- testing(trial_data_split)
```

---

## 🧠 The Model

Our BNN has two hidden layers (24 and 12 nodes) and uses Cauchy priors to encourage sparsity. We used logistic output activation (`out_act_fn = 2`) for binary classification.


``` r
bnn_model <- bnns(
  diabetes ~ .,
  data = trial_data_train,
  L = 2,
  nodes = c(24, 12),
  act_fn = c(4, 1),
  out_act_fn = 2,
  iter = 0.1e4,
  warmup = 0.05e4,
  chains = 4,
  cores = 4,
  prior_weights = list(dist = "cauchy", params = list(mu = 0, sigma = 0.3)),
  prior_bias = list(dist = "cauchy", params = list(mu = 0, sigma = 0.3))
)
```

---

## 🎯 The Prediction

We predicted probabilities on the test set and extracted the **posterior median** and **95% credible intervals**.


``` r
pred <- predict(bnn_model, newdata = trial_data_test)
pred_y <- apply(pred, MARGIN = 1, median)
pred_quantiles <- apply(pred, 1, function(x) quantile(x, probs = c(0.025, 0.975)), simplify = FALSE) |>
  do.call(rbind, args = _)
```

---

## 📏 Model Performance


``` r
measure_bin(trial_data_test$diabetes, pred)
```

```
Setting levels: control = 0, case = 1
```

```
Setting direction: controls < cases
```

```
$conf_mat
   pred_label
obs  0  1
  0 42 11
  1  7 19

$accuracy
[1] 0.7721519

$ROC

Call:
roc.default(response = obs, predictor = pred)

Data: pred in 53 controls (obs 0) < 26 cases (obs 1).
Area under the curve: 0.8353

$AUC
[1] 0.8352685
```

Performance was comparable to classical methods (AUC ~0.835), but with a massive advantage: **uncertainty quantification**.

---

## 🔬 Visualizing Predictions


``` r
plot_data <- data.frame(
  Actual = trial_data_test$diabetes,
  Predicted = pred_y,
  Lower = pred_quantiles[,1],
  Upper = pred_quantiles[,2]
) |>
  transform(width = Upper - Lower) |>
  dplyr::arrange(width)

ggplot(plot_data, aes(x = Actual, y = Predicted)) +
  geom_point(size = 2) +
  geom_errorbar(aes(ymin = Lower, ymax = Upper), width = 0.05, color = "steelblue") +
  labs(
    title = "BNN Predictions for Patient Status",
    subtitle = "Error bars show 95% credible intervals",
    x = "Test Set Patient Status",
    y = "Predicted Patient Status"
  ) +
  theme_minimal()
```

<img src="{{< blogdown/postref >}}index_files/figure-html/unnamed-chunk-5-1.png" width="672" />

---

## 🧠 Why Use `bnns`?

1. **Non-linear modeling**: Captures complex relationships among covariates without heavy pre-specification.
2. **Credible intervals**: Each prediction comes with its uncertainty.
3. **Probability of a probability**:
   - For example: _Pr(Pr(Diabetes) > 0.5) > 0.9_
   - Translation: "We are 90% confident this person has more than 50% risk."
   - That’s **clinical-grade insight**.

---

## 📣 Final Thoughts

Bayesian Neural Networks let us move beyond binary thinking and embrace **informed uncertainty**. When the stakes are high (think medicine, finance, or policy), `bnns` offers a probabilistic flashlight in the black box jungle.

> *Ready to stop guessing your predictions? Start modeling your belief about your predictions.*

🔗 [Explore the `bnns` package](https://cran.r-project.org/package=bnns)

💬 Like this blog? Share your thoughts and use-cases on [LinkedIn](https://www.linkedin.com/) and tag [me](https://www.linkedin.com/in/swarnendu-stat/)!

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