PSC Forum 6

November 9, 2023

Nicole Erler

Assistant Professor

Department of Biostatistics

Erasmus Medical Center, Rotterdam

Nothing to disclose.

to Dynamic

Prediction

**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

the Patient’s

History

- Interval censoring

- Competing risk

- Biopsy sensitivity < 100%

**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

**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**

… 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