Modelling longitudinal biomarkers of disease progression natural history of prostate cancer
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Modelling Longitudinal Biomarkers of Disease Progression (Natural History of Prostate Cancer). Donatello Telesca Stochastic Modeling Preliminary Exam. Preview. Prostate Cancer Background Natural History Models Modeling Different Views A case study (BLSA)

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Modelling Longitudinal Biomarkers of Disease Progression (Natural History of Prostate Cancer)

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Modelling longitudinal biomarkers of disease progression natural history of prostate cancer

Modelling Longitudinal Biomarkers of Disease Progression (Natural History of Prostate Cancer)

Donatello Telesca

Stochastic Modeling Preliminary Exam


Preview

Preview

  • Prostate Cancer Background

  • Natural History Models

  • Modeling Different Views

  • A case study (BLSA)

  • Model Assessment and Conclusions


Prostate cancer

Prostate Cancer

  • Most commonly diagnosed form of cancer in USA.

  • Usually diagnosed in men over 55 and slow growing.

  • Second most common cause of cancer death in American men (after lung cancer )

  • The prostate gland plays a role in the male urinary and reproductive systems.


Natural history of prostate cancer

Natural History of Prostate Cancer

Clinical Stage

(Size and Extent of the tumor)

Histologic Grade

(Cell differentiation)

Local

Metastasis

Gleason score 1

Gleason score 5


Natural history models

Natural History Models

  • Natural history models aim to chart the progression of a disease.

  • They provide critical information about the early stages of a disease.

  • They provide recommendations for cancer screening and detection.

  • The challenge is related to the latency of the main events comprising disease progression.

  • They usually rely on the availability of a biomarker associated to the presence and progression of the disease.


Psa and prostate cancer

PSA and Prostate Cancer

  • PSA (Prostate Specific Antigen) is a protein produced by the prostate gland to keep the semen in a liquid state.

Disease Onset

Cancer

PSA Level

Normal

Puberty

AGE


Different views on disease progression

Different Views on Disease Progression

  • Prostate adenocarcinomas have a different natures directly from onset. Some are more aggressive (Low cell differentiation), others are less aggressive (Good cell differentiation).

  • Prostate adenocarcinomas have a progressive nature. They start out as well differentiated tumor cells and they progress with time to more aggressive forms, with poorly differentiated tumor cells.


A model with no grade progression

A model with no grade progression

TM : Metastasis (Advanced)

TM : Metastasis (Local)

High Grade

Low Grade

Log(PSA+α)

Tc : Clinical Diagnosis

T0 : Onset Time

AGE


Psa trajectories

PSA Trajectories

Subject level

Population level


Disease onset

Disease Onset

Hazard

Cumulative Hazard

Density


Time to diagnosis and metastasis

Time to Diagnosis and Metastasis

Time to Metastasis

Hazard

Cumulative Hazard

Monotonicity

Time to Clinical Diagnosis

Hazard

Cumulative Hazard


A causal diagram of grade progression

A causal diagram of grade progression

Onset

Grade trans.

t0

tG

PSA

tC

tM

Metastasis

Diagnosis


A model with grade progression

A model with grade progression

tg : Grade transition

Log(PSA + α)

tM : Metastasis

 

t0 : Onset

tc : Diagnosis

AGE


Psa trajectories1

PSA Trajectories

Subject level

Population level


Grade transition

Grade Transition

Hazard

t0


Time to metastasis

Time to Metastasis

Hazard

Monotonicity:


Likelihood

Likelihood

yi: log(PSA + const) for individual i

θ : parameter vector

x : stage(1=local, 2=metastasis)

Local stage

Advanced Stage


Bayesian estimation

Bayesian Estimation

POSTERIOR

Chained data augmentation

  • i) Given (t0(k-1), tM(k-1)) , θ(k) ~ π(θ|y, tc, x, t0(k-1) ,tM(k-1));

  • Given θ(k) , (t0(k-1) , tM(k-1))~ π(θ|y, tc, x, t0(k-1) ,tM(k-1) );

  • Iterate (i), (ii).


Dealing with constrained parameter spaces example

Dealing with constrained parameter spaces (Example)

Growth rates full conditional:

With constraints:

  • bi0 ~ bi0|yi,θ(-bi0)

  • bi1 ~ bi1|yi,θ(-bi1) in (bi1>-bi2)

  • bi2 ~ bi2|yi,θ(-bi2) in (bi2>-bi1)

  • bi3 ~ bi3|yi,θ(-bi3) in (bi3>-(bi1+bi2))

bi2=-bi1

bi3 = -(bi1+bi2)

bi2

bi1+bi2

bi1

bi3


Case study blsa

Case Study (BLSA)


Model fit comparison

Model Fit Comparison

Subject with local disease and high grade

Progressive grade

No grade progression

Log(PSA + 0,03)

Log(PSA + 0,03)

Age

Age


Model fit comparison1

Model Fit Comparison

Subject with advanced disease and high grade

Progressive grade

No grade progression

Log(PSA + 0,03)

Log(PSA + 0,03)

Age

Age


Model fit comparison2

Model Fit Comparison

Subject with local disease and low grade

Progressive grade

No grade progression

Log(PSA + 0,03)

Log(PSA + 0,03)

Age

Age


Posterior predictive assessment

Posterior Predictive Assessment

Posterior predictive distributions for transition times and median predictive PSA

trajectories, assuming no grade progression .

(High GS)

Log(PSA + 0.03)

(Low GS)

Density

4ng/ml

Age


Posterior predictive assessment1

Posterior Predictive Assessment

Posterior predictive distributions for transition times and median predictive PSA

trajectory, assuming grade progression .

Log(PSA + 0.03)

Density

4ng/ml

Age


Model assessment

Model Assessment

M1: No grade progression

M2: Grade progression

● Bayes Factor

→ Strong evidence against M2


Cpo analysis

CPO Analysis

● No Grade progression

● Grade progression

o

Log( CPO ) = Log( f(yi, tci, xi|y-i, tc,-i ,x-i) )

Log(CPO)

Subject


Concluding

Concluding

  • We proposed a way to translate scientific hypotheses about the progression of prostate cancer into a statistical model for the disease main biomarker (PSA).

  • The BLSA data provides evidence in favor of the hypothesis of no grade progression as opposed to that of grade progression.

  • Limitations of this approach :

    - Difficult validation of the hazard models for the latent transition times.

    - Prior sensitivity.

  • Extensions may consider :

    - Misclassified diagnosis of the normal subjects.

    - Non-parametric formulation of the problem.


Acknowledgements

Acknowledgements

  • Julian Besag

  • Lourdes Inoue

  • Stat518(2005): Congley, Haoyuan, Liang, Nate, Yanming.


Adaptive slice sampling r m neal 2000

Adaptive Slice Sampling (R.M. Neal, 2000)

f(x0)

S

y ~ U[0,f(x0)]

x1 ~ U(S)

x0


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