### Syllabus del corso

#### Obiettivi

**Expcted Learning Outcomes**

Types of Survival data - classical, competing risks, multistate, illness-death

Features of Survival data - Censoring, delayed entry, time varying covariates, treatment switch

Time functions for Classical Survival data – Survival, Incidence, Hazard, Dynamic Incidence

Time functions for Competing Risks data – Crude Incidences, Cause-specific Hazards

Time functions for Multistate data – State Probabilities, Transition hazards

Assumption for the Transition hazard – Markov, Semi-Markov, Extended Semi-Markov

Counterfactual Time functions for Competing risks data – Net Incidence, Cause-specific Hazards

Counterfactual Time functions for Illness(tr switch)-death data – Survival “as if” under the initial treatment, Survival “as if” treatment is switched at baseline

Non parametric estimation for Competing risks data – Aalen-Johansen estimator of the Crude Incidences, Nelson-Aalen estimator for the Cause-specific hazards

Non parametric estimation for Illness-death data – Aalen Johansen estimator of the State Probabilities, Nelson-Aalen estimator for the Cause-specific hazards

Validation of Assumptions for the Transition hazard – Graphical with non parametric smoothing, by Cox model, by Poisson model

Non parametric estimation of Counterfactual Time functions for Illness(trt switch)-death data – Kaplan Meier estimator

Semi-parametric modelling of the Transition hazards – Cox model, Poisson model, role of time scales

#### Contenuti sintetici

**Competing Risks and
Multistate models** are widely used in medical research when survival data involve
composite outcomes with absorbing events (competing risks) and possible intermediate
events (multistate). These models can be used to obtain risk prediction on
future outcome development and to assess the prognostic impact of patient
characteristics and therapeutic interventions on the outcome development

**Prediction**. The incidence
function is generalized to competing risks data by its decomposition into
absolute risks of each absorbing event. Absolute risks are called “crude
probabilities” emphasizing the indirect protection that each absorbing event
determines on the others. In the presence of multistate data, the intermediate
events are included in the absolute risks which are called “state probabilities”,
emphasizing that subjects may sojourn in intermediate states in the multistate
process that takes to the absorbing events

**Prognostic Impact**. The
hazard function is generalized to competing risks data by its decomposition
into cause specific hazard of each absorbing event. In the presence of
multistate data, the intermediate events are included among the hazard
functions that are called “transition hazard” between the states, to emphasize
the motion among the intermediate and absorbing states

The
course will deal first with the clinical questions and corresponding
theoretical quantities. This link will be crucial to guide the student in the approach
to estimation and inference to be adopted

#### Programma esteso

**SURVIVAL DATA**

Brief reminder

**ABSOLUTE RISKS AND STATE PROBABILITIES**

Motivating examples

Clinical Questions

Non parametric analysis

Semi-Parametric models

Practical session with R

**TRANSITION HAZARDS**

Motivating examples

Clinical Questions

Markov, Semimarkov, Extended Semi Markov concepts

Non parametric analysis

Semi-Parametric models

**PRACTICAL SESSIONS**

Theoretical reasoning and appications using the R software

#### Prerequisiti

Basic knowledge of survival analysis

Participants are required to bring their own laptops with the most recent copy of R and RStudio installed

The following R packages will be used in the tutorial: mstate, cmprsk, survival, epi

#### Modalità didattica

Interactive lectures and practicals

#### Materiale didattico

Handouts and R code

#### Periodo di erogazione dell'insegnamento

**October 15th **

9.00-10:30 Lecture and Practical

10.50-12:30 Lecture and Practical

14:00-15.30 Lecture and Practical

15:50-17.00 Lecture and Practical

**October 16th **

9.00-10:30 Lecture and Practical

10.50-12:30 Lecture and Practical

14:00-15.30 Lecture and Practical

15:50-17.00 Lecture and Practical

#### Modalità di verifica del profitto e valutazione

#### Orario di ricevimento

#### Aims

**Expcted Learning Outcomes**

Types of Survival data - classical, competing risks, multistate, illness-death

Features of Survival data - Censoring, delayed entry, time varying covariates, treatment switch

Time functions for Classical Survival data – Survival, Incidence, Hazard, Dynamic Incidence

Time functions for Competing Risks data – Crude Incidences, Cause-specific Hazards

Time functions for Multistate data – State Probabilities, Transition hazards

Assumption for the Transition hazard – Markov, Semi-Markov, Extended Semi-Markov

Counterfactual Time functions for Competing risks data – Net Incidence, Cause-specific Hazards

Counterfactual Time functions for Illness(tr switch)-death data – Survival “as if” under the initial treatment, Survival “as if” treatment is switched at baseline

Non parametric estimation for Competing risks data – Aalen-Johansen estimator of the Crude Incidences, Nelson-Aalen estimator for the Cause-specific hazards

Non parametric estimation for Illness-death data – Aalen Johansen estimator of the State Probabilities, Nelson-Aalen estimator for the Cause-specific hazards

Validation of Assumptions for the Transition hazard – Graphical with non parametric smoothing, by Cox model, by Poisson model

Non parametric estimation of Counterfactual Time functions for Illness(trt switch)-death data – Kaplan Meier estimator

Semi-parametric modelling of the Transition hazards – Cox model, Poisson model, role of time scales

#### Contents

**Competing Risks and
Multistate models** are widely used in medical research when survival data involve
composite outcomes with absorbing events (competing risks) and possible intermediate
events (multistate). These models can be used to obtain risk prediction on
future outcome development and to assess the prognostic impact of patient
characteristics and therapeutic interventions on the outcome development

**Prediction**. The incidence
function is generalized to competing risks data by its decomposition into
absolute risks of each absorbing event. Absolute risks are called “crude
probabilities” emphasizing the indirect protection that each absorbing event
determines on the others. In the presence of multistate data, the intermediate
events are included in the absolute risks which are called “state probabilities”,
emphasizing that subjects may sojourn in intermediate states in the multistate
process that takes to the absorbing events

**Prognostic Impact**. The
hazard function is generalized to competing risks data by its decomposition
into cause specific hazard of each absorbing event. In the presence of
multistate data, the intermediate events are included among the hazard
functions that are called “transition hazard” between the states, to emphasize
the motion among the intermediate and absorbing states

The
course will deal first with the clinical questions and corresponding
theoretical quantities. This link will be crucial to guide the student in the approach
to estimation and inference to be adopted

#### Detailed program

**SURVIVAL DATA**

Brief reminder

**ABSOLUTE RISKS AND STATE PROBABILITIES**

Motivating examples

Clinical Questions

Non parametric analysis

Semi-Parametric models

Practical session with R

**TRANSITION HAZARDS**

Motivating examples

Clinical Questions

Markov, Semimarkov, Extended Semi Markov concepts

Non parametric analysis

Semi-Parametric models

**PRACTICAL SESSIONS**

Theoretical reasoning and appications using the R software

#### Prerequisites

Basic knowledge of survival analysis

Participants are required to bring their own laptops with the most recent copy of R and RStudio installed

The following R packages will be used in the tutorial: mstate, cmprsk, survival, epi

#### Teaching form

Interactive lectures and practicals

#### Textbook and teaching resource

Handouts and R code

#### Semester

**October 15th **

9.00-10:30 Lecture and Practical

10.50-12:30 Lecture and Practical

14:00-15.30 Lecture and Practical

15:50-17.00 Lecture and Practical

**October 16th **

9.00-10:30 Lecture and Practical

10.50-12:30 Lecture and Practical

14:00-15.30 Lecture and Practical

15:50-17.00 Lecture and Practical

#### Assessment method

On line quiz