# Introduction to Program MARK

Program MARK
Slide 1 of 54

Models in MARK
Slide 2 of 54

Slide 3 of 54

#### Knowledge Required of the User

Knowledge Required of the User
Slide 4 of 54

#### Data are Required to Gain Reliable Knowledge

Data are Required to Gain Reliable Knowledge
Slide 5 of 54

#### Vocabulary of MARK

Vocabulary of MARK
Slide 6 of 54

#### Likelihood Function

Likelihood Function
Slide 7 of 54

Basic Data
Slide 8 of 54

Live Encounters
Slide 9 of 54

Live Encounters
Slide 10 of 54

Live Encounters
Slide 11 of 54

Live Encounters
Slide 12 of 54

Live Encounters
Slide 13 of 54

Live Encounters
Slide 14 of 54

Live Encounters
Slide 15 of 54

Live Encounters
Slide 16 of 54

Live Encounters
Slide 17 of 54

Live Encounters
Slide 18 of 54

Live Encounters
Slide 19 of 54

Model Building
Slide 20 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 21 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 22 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 23 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 24 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 25 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 26 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 27 of 54

#### Parameter Index Matrix – PIM

Parameter Index Matrix – PIM
Slide 28 of 54

Design Matrix
Slide 29 of 54

#### Individual Covariates

Individual Covariates
Slide 30 of 54

#### PIMs for Design Matrix Examples

PIMs for Design Matrix Examples
Slide 31 of 54

#### Model {theta(g*t)}

Model {theta(g*t)}
Slide 32 of 54

Slide 33 of 54

Design Matrix
Slide 34 of 54

Design Matrix
Slide 35 of 54

Design Matrix
Slide 36 of 54

Model {theta(.)}
Slide 37 of 54

Model {theta(g)}
Slide 38 of 54

Model {theta(t)}
Slide 39 of 54

#### Model {theta(g + t)}

Model {theta(g + t)}
Slide 40 of 54

#### Model {theta(g*t)}

Model {theta(g*t)}
Slide 41 of 54

Model {theta(T)}
Slide 42 of 54

#### Model {theta(g + T)}

Model {theta(g + T)}
Slide 43 of 54

#### Model {theta(g*T)}

Model {theta(g*T)}
Slide 44 of 54

Model Selection
Slide 45 of 54

Model Selection
Slide 46 of 54

#### Selecting “Best” Model

Selecting “Best” Model
Slide 47 of 54

#### Program MARK Assumption

Program MARK Assumption
Slide 48 of 54

#### Variance Components

Variance Components
Slide 49 of 54

#### Process Variance €2

Process Variance €2
Slide 50 of 54

Example
Slide 51 of 54

#### Example Continued

Example Continued
Slide 52 of 54

#### Program Documentation

Program Documentation
Slide 53 of 54

#### Program Availability

Program Availability
Slide 54 of 54