Handout: Predicting NHS OPEL-4 Status

This document provides a summary of the training course on building a Bayesian forecasting model for NHS operational pressures.

Course Objective

To build a model that predicts the probability of a hospital trust entering “Severe Acute Patient Harm” (OPEL-4) on any of the next ten days. This is achieved by using R and the probabilistic programming language Stan.

Module 1: Setting Up Your Environment

• R & RStudio: The primary tools for this analysis. R is the language; RStudio is the development environment.
• Key R Packages:
  • tidyverse: For data manipulation and visualization.
  • rstan: The interface between R and Stan.
  • lubridate: For working with dates.
  • forecast: For time-series forecasting (ARIMA models).
  • patchwork: For combining plots.
  • knitr: For report generation.

Module 2: Sourcing and Preparing the Data

• A synthetic dataset is generated to mimic real-world daily NHS data.
• Key Variables:
  • date: The date of observation.
  • daily_admissions: Simulated daily patient admissions.
  • staff_absences: Simulated daily staff absences.
  • winter_pressure: A cyclical seasonal factor.
  • opel_level: The final OPEL status (0-4), determined by a probabilistic model based on the other predictors.

Module 3: Forecasting Predictors with ARIMA

• The Need for Forecasting: To predict future OPEL status, we first need to predict the future values of our predictors (daily_admissions, staff_absences).
• ARIMA Models: An introduction to AutoRegressive Integrated Moving Average models as a powerful tool for time-series forecasting.
• Implementation: The auto.arima() function from the forecast package is used to automatically find the best ARIMA model and forecast the predictors 10 days into the future.

Module 4: An Introduction to Bayesian Modelling and Stan

• Bayesian Inference: A method of updating beliefs (Priors) with new data (Likelihood) to get an updated understanding (Posterior).
• Why Bayesian?: It excels at quantifying uncertainty, providing not just a single prediction but a range of possible outcomes (credible intervals).
• Stan: A probabilistic programming language used to define the model structure and let its algorithms handle the fitting.
• Stan Model Structure:
  • data: Declares the input data.
  • parameters: Declares the unknown quantities to be estimated.
  • model: Defines the relationship between data and parameters.
  • generated quantities: For post-fit calculations, like forecasting.

Module 5: Building the Stan Model

• The model is a logistic regression, suitable for binary outcomes (OPEL-4 or not).
• The model is saved in a file named opel_model.stan.
• Formula: P(OPEL-4) = logistic(alpha + beta1*admissions + beta2*absences)
• Key Blocks:
  • data: Defines historical data and the number of future days to predict.
  • parameters: Defines the intercept (alpha) and coefficients (betas) to be estimated.
  • model: Specifies priors for the parameters and the Bernoulli likelihood for the outcome.
  • generated quantities: Uses the fitted parameters and forecasted predictor values to generate future OPEL-4 probabilities.

Module 6: Running and Interpreting the Model

• An R script is used to:
  1. Load the synthetic data.
  2. Forecast future predictors using auto.arima().
  3. Format the data for Stan, including the future forecasts.
  4. Run the stan() function to fit the model.
  5. Extract the 10-day forecast from the generated quantities block.
  6. Visualize the forecast as a plot showing the daily probability of an OPEL-4 event with 95% credible intervals.

Module 7: Next Steps

• Automation: The script can be automated to run daily for real-time monitoring.
• Model Improvements:
  • Add more relevant predictors (e.g., bed occupancy, A&E wait times).
  • Incorporate time-series features directly into the Stan model (e.g., autoregressive effects).
  • Build hierarchical models for multi-trust analysis.
• Key Takeaway: The course provides a framework for probabilistic forecasting that can be adapted to many different problems.