# Dynamic Prediction

PSC Forum 6

November 9, 2023

Assistant Professor

Department of Biostatistics
Erasmus Medical Center, Rotterdam

## Conflicts of Interest

Nothing to disclose.

# From Static to Dynamic   Prediction

## Random Effects Models

Linear Regression Model $y_i = \mathbf x_i^\top \boldsymbol\beta + \varepsilon_i$

$\color{grey}{ \text{e.g.: }\log(\text{bili}_i) = \beta_0 + \beta_1 \text{age}_i + \beta_2\text{sex}_i + \beta_3 \text{time}_i + \ldots + \varepsilon_i}$

Random Effects Model $y_i(t) = \underset{\substack{\text{fixed effects}\\\text{(population level)}}}{\underbrace{\mathbf x_i(t)^\top \boldsymbol\beta}} + \bbox[#400020, 5pt]{\underset{\substack{\text{random effects}\\\text{(patient level)}}}{\underbrace{\mathbf z_i(t)^\top \mathbf b_i}}} + \varepsilon_i(t)$

medication

AST

platelets

ALP

bilirubin

IBD

medication

AST

platelets

ALP

bilirubin

IBD

# Example

## Personalized Biopsy Schedules: Challenges

• Interval censoring
• Competing risk
• Biopsy sensitivity < 100%

## Personalized Biopsy Schedules: Features

• Dynamic prediction of cancer progression risk
• Multiple predictors, measured at different times
• Creation of a entire (tentative) biopsy schedule
• Patient- & time-specific risk thresholds
⇨ Minimize number of biopsies & detection delay

## Possible Applications

Optimal patient-specific timing:

• time of the outcome measurement
• time of biomarker measurements
• time of an intervention

“What-if” analyses:

• expected outcomes under different (treatment) scenarios
• estimate causal effects

## In Summary: Dynamic Prediction …

… makes better use of the available information.

• Time as additional dimension of the data
• Model relevant features of the biomarker trajectories
• Filter out short term fluctuations and measurement error
• Patient-specific predictions
• Model complex & time-dependent structures between multiple markers and outcomes