Thesis Presentation

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Thank you Sir/Madam Rector, dear committee members, colleagues, family and friends.

I would like to thank you all for being here today, and I would like to take this opportunity to give you an overview of the research that forms my doctoral dissertation.

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# MOTIVATION
## Heart Function & Disease

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Let me start with the motivation of my research which concerns the heart, its function and disease.

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# Heart Function & Disease

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The heart is a muscular organ that consists of two atria and two ventricles.

The right-atrium receives the blood from the veins and sends it to the right ventricle. From there the blood is sent to the lungs to become oxygenated.

The oxygen-rich blood is then sent to the rest of the body by the contractions of the left ventricle.

The ideal flow of the blood depends mainly on the function of the four valves of the heart which ensure that blood flows in the right direction through the heart.

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# Heart Function & Disease

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This ideal flow of the blood may be disrupted, however, causing our health to deteriorate and increase our risk of dying. Unfortunately, there are several causes for such disruptions such as:

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# Heart Function & Disease

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Congenital Heart Disease (CHD)


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Congenital Heart Disease, which is the most common type of congenital disability and refers to a broad range of defects and symptoms.

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# Heart Function & Disease

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Heart Failure 


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and Heart Failure, a chronic and progressive condition in which the heart cannot fulfill the body's needs for blood and oxygen.

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# MOTIVATION
## Datasets

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While Congenital Heart Disease and Heart failure are only two such examples, they may lead to many different complications and health risks.

Let me, therefore, describe in a bit more detail two of the studies that motivated our research and concern patients suffering from these two diseases .

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# Pulmonary Valve

- CHD:

- 20% `\(\rightarrow\)` RVOT complications: pulmonary atresia, pulmonary valve stenosis, tetralogy of fallot.

- RVOT reconstruction with a pulmonary valve replacement.
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The first study focuses on the pulmonary valve.

1 out of 5 Congenital Heart Disease patients may suffer from complications with the Right Ventricular Outflow Tract such as

- pulmonary atresia: a birth defect where the pulmonary valve does not fully form.

- pulmonary valve stenosis: a narrowing of the pulmonary valve that disrupts the blood flow.

- tetralogy of fallot: which is characterized by four defects including stenosis of the pulmonary valve.

These patients will most likely undergo Right Ventricular Outflow Tract reconstruction with a pulmonary valve replacement.

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# Pulmonary Valve

- CHD:

- 20% `\(\rightarrow\)` RVOT complications: pulmonary atresia, pulmonary valve stenosis, tetralogy of fallot.

- RVOT reconstruction with a pulmonary valve replacement.

- ROSS patients:

- Pulmonary valve used as a transplant for the aortic valve.

- Pulmonary valve replacement needed for the pulmonary position.
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Pulmonary valve replacement is also needed for ROSS patients as according to the ROSS procedure their own pulmonary valve is used as a replacement for their diseased aortic valve.

That means that a substitute is then needed for the pulmonary position.

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# Pulmonary Valve

- Pulmonary valve replacements do not last forever.

- Echocardiographic follow-up to measure the pulmonary gradient.

- More than one replacements might be necessary during lifetime:

- Too early: `\(\rightarrow\)` more replacements necessary.
  - Too late: `\(\rightarrow\)` increased risk of dying.
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These pulmonary valve replacements may not last forever and additional valve replacements might be necessary for these patients in the future.

Therefore, these patients are monitored closely over time. Measures such as their pulmonary gradient, which represents the pressure at which the blood flows through the pulmonary valve are being recorded over time in order to assess whether additional interventions are necessary.

The timing of such interventions is crucial as if done too early then more replacements might be needed while if done too late the risk of dying increases.

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# Heart Failure

- High Risk of complications: thrombosis, embolic events, dialysis.

- Liver function `\(\rightarrow\)` monitor total bilirubin.

- Kidney function `\(\rightarrow\)` monitor creatinine.

- Left Ventricular Assist Device (LVAD).

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The second study concerns heart failure.

End-stage heart failure patients are in high risk of several and serious complications such as thormbosis, embolic events and dialysis.

Treating physicians follow these patients closely and collect biomarker measurements for their liver and kidney function and may consider to intervene with a Left Ventricular Assist Device.

This device takes over the heart function and is also used as a bridge therapy while waiting for a heart transplant.

While the Left Ventricular Assist Device considerably increases the chance of survival for these patients it might also increase the risk for complications.

It is therefore very important to understand the impact of this device at different stages after heart failure in order to improve the health management of these patients.

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# MOTIVATION
## Joint Modeling

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While the two examples I described, seem and are very different in clinical terms, they also have a lot of features in common, when viewed from a statistical point of view. Let me explain what I mean.

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# General idea

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In both situations we are dealing with a disease which may increase the risk for experiencing a negative health related outcome.

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# General idea

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As soon as we diagnose the problem, we start to follow-up the patient and record longitudinal outcomes that are associated with their risk as they have the potential to help us manage these patients better and prevent negative outcomes for their health.

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# Joint Model

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Risk is a continuous function that changes over time. It can increase, decrease or stay constant depending on other factors.

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# Joint Model

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Since we cannot measure risk directly, we monitor other markers repeatedly over time, which can help us estimate it instead.

However, these repeated measurements are subject to measurement error and are only fragments, snapshots of a continuous process that may change faster than we are able to measure it.

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# Joint Model

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We therefore use a specific class of statistical models, known as mixed-effects models, to recover the true underlying subject-specific trajectory which is also a continuous function of time.

By doing so, we not only account for the measurement error but also for the fact that measurements from the same subjects are potentially more similar than measurements from different subjects.

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# Joint Model

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After recovering the true underlying trajectory of the longitudinal outcome we need to think of a way to link it to the risk. There are several options for doing so.

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# Joint Model

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We can assume that the value of the the longitudinal outcome at each time point is associated with the risk at that same time point.

This could mean that higher values of the longitudinal outcome translate to higher risk in the case of a positive association, for example.

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# Joint Model

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Another option is to assume that the rate of increase or decrease of the longitudinal outcome at each time point, is associated with the risk at that same time point.

This means that the speed at which the longitudinal outcome changes can tell us something about the risk.

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# Joint Model

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Finally, in other situations it might be more realistic to assume that the risk at a certain time point is associated with the area under the trajectory of the longitudinal outcome up to that time point.

The area under the curve can also be seen as the overall burden of the disease as it summarizes the whole history of the marker up to a specific time-point.

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# Dynamic Prediction

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After the form of the association between the two processes is established, we can use our estimates to predict the risk for new patients.

Most importantly we can do so dynamically as time is incorporated in our models. This means that with every new measurement of the longitudinal outcome we can update our prediction for the risk accordingly.

Let me now highlight the contents of some of the chapters of my dissertation which discuss extensions of the joint modeling framework I just outlined and applications to the datasets I briefly introduced.

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# PART I
## INTERMEDIATE EVENTS

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PART I of the dissertation deals with the occurrence of intermediate events.

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# Pulmonary Valve & RE-OPERATION

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To undertsand what I mean with this term, let's go back to the pulmonary valve dataset and the repeated measurements of the pulmonary gradient.

What we observe here is that the pulmonary gradient of these patients is increasing over time, indicating higher pressure which suggests that the condition of the pulmonary valve is deteriorating.

When the gradient becomes too high this is an indication that an additional valve replacement might be necessary.

After this re-operation takes place, the pulmonary gradient drops back to normal levels.

In this case re-opereation is an intermediate event that changes the trajectory of the longitudinal outcome and reduces the risk of dying.

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# Pulmonary Valve & RE-OPERATION

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We therefore adapt our model accordingly so it is able to capture these changes under different scenarios with respect to re-operation.

This means that the trajectory of the longitudinal outcome, that we recover for each subject, will be different depending on whether and when re-operation took place.

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# Dynamic & Adaptive Predictions

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By capturing these different trajectories with respect to the occurrence or not of the intermediate event

we can now create prediction tools that are not only dynamic with respect to time,

but also adaptive to different scenarios concerning the occurrence of the intermediate event in the future.

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# Predictive Performance

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Finally we also showed via an extensive simulation study, that when intermediate events are incorporated in our models the accuracy of the predictions is considerably improved.

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# PART II
## MULTI-STATE MODELS & SHRINKAGE

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PART II of the dissertation, deals with multiple-event states and the selection of the association structure between the longitudinal and the multi-state processes.

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# Multiple states

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Sometimes, as it is the case with the heart failure dataset, we are interested to study the risk of transitioning between multiple health states of interest.

In this specific case for example we are interested to study the risk of transitioning: 
- from heart failure to death or transplantation, 
- from heart failure to complications 
- and to transplantation or death after experiencing complications.

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# Multiple states and Intermediate Events

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An intermediate event can still occur of course.

In this case, intervention with an LVAD is considered as an intermediate event and can happen at any point changing the trajectories of the longitudinal markers and the risk for each transition between the states of interest.

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# Total Bilirubin & LVAD

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We therefore specify our models accordingly so they can capture these changes and quantify the impact of LVAD in the longitudinal markers.

In this particular case, LVAD implantation reduces total bilrubin

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# Creatinine & LVAD

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same holds for creatinine, but only temporarily as it seems to return back to its pre-LVAD levels over time.

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# Feature selection

- Challenges:
  - Multiple longitudinal outcomes
  - Multiple transitions
  - Which association structure to choose?
  
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#Longitudinal Outcomes &#215 #Transitions &#215 #Association Structures
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After modeling the longitudinal outcomes we need to link them to the risk for each transition.

This creates an additional challenge in this case as now the number of parameters that describe the association structure can become quite high.

For example if we have three candidate structures: 
- the value, the rate of change and the area under the longitudinal trajectory, 
- but for two longitudinal outcomes and 
- for three transitions,

we end up with 18 association parameters in total making the selection of the most important ones, difficult.

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# Feature selection

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To address this challenge we investigated and proposed the use of Bayesian shrinkage priors.

These priors impose a penalty to weaker signals, shrinking them towards zero, while stronger signals are not penalized which can help to identify the most relevant parameters for the specification of the association structure.

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# PART III
## MISSING DATA

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In PART III of the dissertation we looked at missing data in the context of the joint modeling framework.

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# PART III: MISSING DATA

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Ideally, when we plan a study, we want to have complete information for every subject that is included in it.

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# PART III: MISSING DATA

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However, this is rarely the case in practice as patients may drop-out from a study for many different reasons such as moving to another country or due to their own decision because of severe side-effects for example.

This leaves us with partial information at hand instead of the full information we wanted to gather.

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# PART III: MISSING DATA

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Unfortunately, the missing data can never be fully recovered and we have to rely on assumptions regarding the reasons that they are missing.

Different assumptions for the causes of missingness will lead to different conclusions while certain causes of missingness are more difficult to deal with than others.

Unfortunately, since we can never be sure which assumption is true we have to explore all possibilities with sensitivity analyses.

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# PART III: MISSING DATA

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In this context we used joint models for longitudinal and time-to-event data as a tool for conducting such sensitivity analysis.

We discussed how these models can be used to investigate different assumptions for the causes of missingness on the subject-specific level.

Our results indicated minimal sensitivity in parameter estimates and standard deviations but differences in subject-specific predictions.

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## SOFTWARE IMPLEMENTATION

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Finally, for our methods to be useful and most importantly accessible in practice we implemented them in R packages: JMbayes and JMbayes2.

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# SOFTWARE IMPLEMENTATION

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D. Rizopoulos, G. Papageorgiou, P.M. Afonso
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JMbayes2, which is our latest package can be used to apply the extensions I discussed today among many other features that it offers.  It is also built with future extensions in mind and is

available for download from The Comprehensive R Archive Network and GitHub.

It also has its own website with detailed documentation and tutorials to make it more accessible to everyone.

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Thank you for your attention. I give the word back to you, Sir/Madam Rector.