Bayesian Survival and Multistate Models using R and Stan

Time-to-event analysis with patient preferences

Statistical Methods

Bayesian

Advanced

Authors

Eric Novik (Founder & CEO, Generable)

Jacqueline Buros-Novik (Generable)

Juho Timonen (Computational Scientist, Generable)

Overview

Advanced Bayesian Survival Analysis

Bayesian inference and Stan offer many advantages for time-to-event data: incorporating prior knowledge, propagating uncertainty, and integrating patient utility functions for optimal decision-making. Learn multistate models for competing events in cardiovascular and oncology trials.

What You’ll Learn

🔄 Bayesian workflow - Typical analysis steps
⏱️ Survival models - Single and competing events
🔀 Multistate models - Bleeding, stroke, death pathways
🎯 Patient preferences - Utility function integration
📊 Decision analysis - Optimal treatment selection

Prerequisites

Required Knowledge:

Intermediate R programming
Basic survival analysis concepts
Some Bayesian exposure helpful

Recommended:

Stan familiarity (not required)
Clinical trial experience

Key Tools

Stan

{bmstate}

{rstan}

{cmdstanr}

Workshop Materials

Resources

GitHub Package: github.com/generable/bmstate

Why Bayesian for Survival Analysis?

Advantages

1. Prior Information Integration

Use historical trial data
Expert knowledge incorporation
Borrowing strength across studies

2. Uncertainty Quantification

Full posterior distributions
Credible intervals
Probability statements

3. Patient Preferences

Utility function integration
Trade-offs between outcomes
Personalized decision-making

4. Complex Models

Multistate transitions
Competing risks
Time-varying effects

Bayesian Workflow

Step 1: Prior Specification

parameters {
  real log_baseline_hazard;
  real treatment_effect;
}

model {
  // Priors
  log_baseline_hazard ~ normal(-2, 1);
  treatment_effect ~ normal(0, 0.5);
}

Step 2: Prior Predictive Checks

Simulate data from priors to verify reasonableness.

Step 3: Fit Model

library(bmstate)

fit <- fit_survival_model(
  formula = Surv(time, status) ~ treatment,
  data = clinical_data,
  prior = prior_spec
)

Step 4: Posterior Diagnostics

Check convergence (R-hat)
Effective sample size
Trace plots
Posterior predictive checks

Step 5: Inference

Extract posterior summaries and make decisions.

Single-Event Survival Models

Exponential Model

Constant hazard over time.

Weibull Model

Flexible hazard shape (increasing/decreasing).

Piecewise Exponential

Different hazards in time intervals.

Cox-Like Models

Semi-parametric baseline with covariates.

Multistate Models

Example: Cardiovascular Trial

States:

Healthy
Bleeding event
Stroke event
Death

Transitions:

Healthy → Bleeding
Healthy → Stroke
Healthy → Death
Bleeding → Death
Stroke → Death

Oncology Trial

States:

Stable disease
Progressive disease
Death

Allows:

Different treatment effects on each transition
Competing risks modeling
Illness-death models

Patient Utility Functions

Incorporating Preferences

Patients may value outcomes differently:

Prefer minor bleeding over stroke
Trade survival time for quality
Different risk tolerances

Example Utility

# Patient preferences
utility <- function(state, time) {
  switch(state,
    "healthy" = 1.0,
    "bleeding" = 0.8,  # 20% quality loss
    "stroke" = 0.3,    # 70% quality loss
    "death" = 0.0
  )
}

Decision Analysis

Use utilities to:

Compare treatment strategies
Calculate quality-adjusted survival
Optimize individual decisions

Workshop Exercises

Exercise 1: Single-Event Model

Fit Weibull survival model to trial data.

Exercise 2: Multistate Model

Cardiovascular trial with bleeding/stroke competing events.

Exercise 3: Utility Integration

Incorporate patient preferences into decision analysis.

Practical Example

library(bmstate)

# Fit multistate model
fit <- fit_multistate(
  formula = list(
    bleeding ~ treatment + age,
    stroke ~ treatment + age + prior_stroke,
    death ~ treatment + age
  ),
  data = cardio_data,
  transitions = transition_matrix
)

# Extract hazard ratios
hr_bleeding <- exp(posterior_summary(fit, "treatment_bleeding"))
hr_stroke <- exp(posterior_summary(fit, "treatment_stroke"))

# Decision analysis with utilities
qaly <- calculate_qaly(
  fit = fit,
  utilities = patient_utilities,
  horizon = 5  # years
)

Advantages in Pharma

Regulatory

Explicit uncertainty quantification
Transparent assumptions (priors)
Flexible for complex designs

Scientific

Accumulate knowledge across trials
Handle small samples better
Natural borrowing of information

Patient-Centered

Individual risk-benefit
Preference integration
Personalized medicine

Learning Outcomes

✅ Understand Bayesian workflow for survival data
✅ Fit single-event survival models in Stan
✅ Build multistate models for competing risks
✅ Integrate patient utility functions
✅ Perform Bayesian decision analysis
✅ Interpret and communicate Bayesian results

Advanced Topics (Time Permitting)

Cure models
Recurrent events
Joint models (longitudinal + survival)
Hierarchical models

Resources

{bmstate} documentation
Bayesian Survival Analysis (Ibrahim et al.)
Stan User’s Guide - Survival chapter
Statistical Rethinking (McElreath)

Similar Workshops

Debugging Stan - Stan troubleshooting skills
rpact Trial Design - Frequentist designs

Next Steps

Prerequisites: Debugging Stan workshop highly recommended
Career value: Bayesian expertise opens doors

Last updated: November 2025 | R/Pharma 2025 Conference

--- title: "Bayesian Survival and Multistate Models using R and Stan" subtitle: "Time-to-event analysis with patient preferences" author: - "Eric Novik (Founder & CEO, Generable)" - "Jacqueline Buros-Novik (Generable)" - "Juho Timonen (Computational Scientist, Generable)" categories: [Statistical Methods, Bayesian, Advanced] --- ## Overview [Advanced]{.badge .badge-advanced} [Bayesian]{.badge .badge-category} [Survival Analysis]{.badge .badge-category} Bayesian inference and Stan offer many advantages for time-to-event data: incorporating prior knowledge, propagating uncertainty, and integrating patient utility functions for optimal decision-making. Learn multistate models for competing events in cardiovascular and oncology trials. ### What You'll Learn - 🔄 **Bayesian workflow** - Typical analysis steps - ⏱️ **Survival models** - Single and competing events - 🔀 **Multistate models** - Bleeding, stroke, death pathways - 🎯 **Patient preferences** - Utility function integration - 📊 **Decision analysis** - Optimal treatment selection ## Prerequisites ::: requirements **Required Knowledge:** - Intermediate R programming - Basic survival analysis concepts - Some Bayesian exposure helpful **Recommended:** - Stan familiarity (not required) - Clinical trial experience ::: ## Key Tools ::: tool-tag Stan ::: ::: tool-tag {bmstate} ::: ::: tool-tag {rstan} ::: ::: tool-tag {cmdstanr} ::: ## Workshop Materials ::: callout-note ## Resources **GitHub Package:** [github.com/generable/bmstate](https://github.com/generable/bmstate) ::: ## Why Bayesian for Survival Analysis? ### Advantages **1. Prior Information Integration** - Use historical trial data - Expert knowledge incorporation - Borrowing strength across studies **2. Uncertainty Quantification** - Full posterior distributions - Credible intervals - Probability statements **3. Patient Preferences** - Utility function integration - Trade-offs between outcomes - Personalized decision-making **4. Complex Models** - Multistate transitions - Competing risks - Time-varying effects ## Bayesian Workflow ### Step 1: Prior Specification ``` stan parameters { real log_baseline_hazard; real treatment_effect; } model { // Priors log_baseline_hazard ~ normal(-2, 1); treatment_effect ~ normal(0, 0.5); } ``` ### Step 2: Prior Predictive Checks Simulate data from priors to verify reasonableness. ### Step 3: Fit Model ``` r library(bmstate) fit <- fit_survival_model( formula = Surv(time, status) ~ treatment, data = clinical_data, prior = prior_spec ) ``` ### Step 4: Posterior Diagnostics - Check convergence (R-hat) - Effective sample size - Trace plots - Posterior predictive checks ### Step 5: Inference Extract posterior summaries and make decisions. ## Single-Event Survival Models ### Exponential Model Constant hazard over time. ### Weibull Model Flexible hazard shape (increasing/decreasing). ### Piecewise Exponential Different hazards in time intervals. ### Cox-Like Models Semi-parametric baseline with covariates. ## Multistate Models ### Example: Cardiovascular Trial **States:** 1. Healthy 2. Bleeding event 3. Stroke event 4. Death **Transitions:** - Healthy → Bleeding - Healthy → Stroke - Healthy → Death - Bleeding → Death - Stroke → Death ### Oncology Trial **States:** 1. Stable disease 2. Progressive disease 3. Death **Allows:** - Different treatment effects on each transition - Competing risks modeling - Illness-death models ## Patient Utility Functions ### Incorporating Preferences Patients may value outcomes differently: - Prefer minor bleeding over stroke - Trade survival time for quality - Different risk tolerances ### Example Utility ``` r # Patient preferences utility <- function(state, time) { switch(state, "healthy" = 1.0, "bleeding" = 0.8, # 20% quality loss "stroke" = 0.3, # 70% quality loss "death" = 0.0 ) } ``` ### Decision Analysis Use utilities to: - Compare treatment strategies - Calculate quality-adjusted survival - Optimize individual decisions ## Workshop Exercises ### Exercise 1: Single-Event Model Fit Weibull survival model to trial data. ### Exercise 2: Multistate Model Cardiovascular trial with bleeding/stroke competing events. ### Exercise 3: Utility Integration Incorporate patient preferences into decision analysis. ## Practical Example ``` r library(bmstate) # Fit multistate model fit <- fit_multistate( formula = list( bleeding ~ treatment + age, stroke ~ treatment + age + prior_stroke, death ~ treatment + age ), data = cardio_data, transitions = transition_matrix ) # Extract hazard ratios hr_bleeding <- exp(posterior_summary(fit, "treatment_bleeding")) hr_stroke <- exp(posterior_summary(fit, "treatment_stroke")) # Decision analysis with utilities qaly <- calculate_qaly( fit = fit, utilities = patient_utilities, horizon = 5 # years ) ``` ## Advantages in Pharma ### Regulatory - Explicit uncertainty quantification - Transparent assumptions (priors) - Flexible for complex designs ### Scientific - Accumulate knowledge across trials - Handle small samples better - Natural borrowing of information ### Patient-Centered - Individual risk-benefit - Preference integration - Personalized medicine ## Learning Outcomes ✅ Understand Bayesian workflow for survival data\ ✅ Fit single-event survival models in Stan\ ✅ Build multistate models for competing risks\ ✅ Integrate patient utility functions\ ✅ Perform Bayesian decision analysis\ ✅ Interpret and communicate Bayesian results ## Advanced Topics (Time Permitting) - Cure models - Recurrent events - Joint models (longitudinal + survival) - Hierarchical models ## Resources - **{bmstate} documentation** - *Bayesian Survival Analysis* (Ibrahim et al.) - Stan User's Guide - Survival chapter - *Statistical Rethinking* (McElreath) ------------------------------------------------------------------------ ### Similar Workshops - [Debugging Stan](debugging-stan.qmd) - Stan troubleshooting skills - [rpact Trial Design](rpact-trial-design.qmd) - Frequentist designs ### Related Presentations - [BayesERtools](../presentations/europe-us-sessions.qmd#bayesertools-bayesian-exposure-response-analysis) - Exposure-response with Stan ### Next Steps - **Prerequisites:** [Debugging Stan workshop](debugging-stan.qmd) highly recommended - **Career value:** [Bayesian expertise](../summary/career-insights.qmd#5-bayesian-methods) opens doors ------------------------------------------------------------------------ *Last updated: November 2025 \| R/Pharma 2025 Conference*