3 rd Summer School in Computational Biology September 10, 2014

3rd Summer Schoolin Computational Biology

September 10, 2014

Frank Emmert-Streib & Salissou MoutariComputational Biology and Machine Learning Laboratory

Center for Cancer Research and Cell Biology Queen’s University Belfast, UK

Exercise – Survival Analysis

Homework ~ 1.5 hours

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1. Kaplan-Meier Survival Curves

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Result: Survival Curve

S(t)

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Goal: estimate S(t) from data

• A survival curve shows S(t) as a function of t.– S(t): survival function (survivor function)– t: time

S(t) gives the probability that the random variable T is larger than a specified time t, i.e.,S(t) = Pr(T>t)T: is the event

Problem: censoring

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Small example: Leukemia

Chemotherapy(we use this info later)

censoring

Acute Myelogenous Leukemia (AML)

survival time

Only 5 patients

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Small example: Leukemia

censoring

Number in risk Number of events

event

???

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Kaplan-Meier estimator for S(t)

• Estimator:

ni: number of subjects at time ti

di: number of events at time ti

Kaplan & Meier 1958

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Kaplan-Meier estimator for S(t)

• Estimator:

ni: number of subjects at time ti

di: number of events at time ti

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Check S(t) till t

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Kaplan-Meier estimator for S(t)

• Estimator:

ni: number of subjects at time ti

di: number of events at time ti

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Check S(t) till t

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Kaplan-Meier estimator for S(t)

• Estimator:

ni: number of subjects at time ti

di: number of events at time ti

Last time seen,still alive at thattime

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Check S(t) till t

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Kaplan-Meier estimator for S(t)

• Estimator:

ni: number of subjects at time ti

di: number of events at time ti

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Check S(t) till t

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Kaplan-Meier estimator for S(t)

• Estimator:

ni: number of subjects at time ti

di: number of events at time ti

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Check S(t) till t

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Full data set: Leukemia

23 patients

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R code

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2. Comparing Survival Curves

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Reasons for comparing survival curves (SC)

• Treatment vs no treatment:– Compare a SC for patients that have been treated

with a certain medication with the SC for patient that have not been treated.

– Result: Has the treatment an effect on the survival of the patients?

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Reasons for comparing survival curves

• Chemotherapy vs no chemotherapy :– Compare a SC for patients that had chemotherapy

with the SC for patient that have not had chemotherapy.

– Result: Has the chemotherapy an effect on the survival of the patients?

Survival Analysis has a big practical relevance

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Data: Leukemia

11 patients with chemo12 patients without

Goal: compare thetwo SCs statistically

Group 1

Group 2

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R code

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Log-rank test (Mantel-Haenszel)

• Hypothesis:Null hypothesis H0: No difference in survival between (group 1) and (group 2).

Alternative hypothesis H1: Difference in survival between (group 1) and (group 2).

Mantel and Haenszel 1959

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Idea of the test

• For each time t, estimate the expected number of events for (group 1) and (group 2).

Number in risk at t in i Number of events at t in i

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The eit are obtained assuming H0 is true.Hence, mit – eit is a measure for the deviation of the data from H0.

sum

E2E1 O1 - E1 O2 – E2

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Wrapping up

• Test statistic:

• Sampling distribution:s follows a chi-square distribution with one degree of freedom

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R code

• Back to our leukemia data set:

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Data: Leukemia

11 patients with chemo12 patients without

Goal: compare thetwo SCs statistically

Group 1

Group 2

Survival Analysis & Biomarkers

NIH Definition of Biomarker

A characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacologic responses to therapeutic intervention.

FDA Definition of Biomarker

Any measurable diagnostic indicator that is used to assess the risk or presence of disease

What is a biomarker?

These definitions are very broad and do not help in finding practical implementations for a particular disease.

Our “definition”

Remark: We do not want to address all possible problems that can involve biomarkers but focus on a particular application.

Application: Identify a set of genes that can be used for a prognostic analysis.

…that are good!

Definition of ‘prognosis’

A prognosis is a medical term denoting the prediction of how a patient will progress over time.

For instance, a patient with a diagnosed disease can have:– Long time survival– Short time survival

Our “definition”

Remark: We do not want to address all possible problems that can involve biomarkers but focus on a particular application.

Application: Identify a set of genes that can be used for a prognostic analysis.

• Set of genes: we call biomarkers • Use biomarkers to predict the prognostic outcome of

a patientto classifysurvival

Underlying idea to identify biomarkers

The identification of biomarkers is a composite approach (or a procedure) that is based on a couple of other methods.

In the previous example:1. Survival analysis2. Differential expression of genes 3. Classification

Underlying idea to identify biomarkers

The identification of biomarkers is a composite approach (or a procedure) that is based on a couple of other methods.

In the previous example:1. Clustering2. Survival analysis3. Differential expression of genes 4. Classification

Our “definition”

Remark: We do not want to address all possible problems that can involve biomarkers but focus on a particular application.

Application: Identify a set of genes that can be used for a prognostic analysis.

Structured patient groups vs unstructured patient groups

Statistics: Feature selection problem

Underlying idea to identify biomarkers

The identification of biomarkers is a composite approach (or a procedure) that is based on a couple of other methods.

The definition of the procedure is part of the experimental design of the whole experiment.

Yes, the experimental design includes the analysis of the data!

Summary & Outlook to Genome

and Network Medicine

Almost there!

Schedule

17 lectures

Interdisciplinary summer school

Vision of the VC

Universities require interdisciplinary engagement in the educational and research

effort

Professor Patrick Johnston of President andVice-Chancellor (VC) of Queen’s University

A look 5 years ahead

1. Single cell experiments

Experimental measurements of– DNA– Gene expression (mRNA)– Protein binding

within single cells.

What do the other high-throughput data provide information for? Populations of cells.

NGS

1. Single cell experiments

Experimental measurements of– DNA– Gene expression (mRNA)– Protein binding

within single cells.

What do the other high-throughput data provide information for? Populations of cells.

NGS

Study the heterogeneity of cancer tumors.

1. Single cell experiments

PacBio (Pacific Biosciences)SMRT: Single molecule real time sequencing

2. Personalized Medicine

The idea behind Personalized medicine is to provide a customization of healthcare using molecular analysis - with medical decisions, practices etc, which are tailored to the needs of the individual patient.

One drug for all customized treatment.

2. Personalized Medicine

2012

What does this all mean?

What does this all mean?

It means first of all more data!

What does this all mean?

It means first of all more data!

Survey

Please participate in the survey about the summer school in order to help us to improve.

We will send it early next week.

Thank you to everyone for participating!

We hope you enjoyed the summer school.