3 rd Summer School in Computational Biology September 10, 2014 Frank Emmert-Streib & Salissou Moutari Computational Biology and Machine Learning Laboratory Center for Cancer Research and Cell Biology Queen’s University Belfast, UK

Exercise – Survival Analysis Homework ~ 1.5 hours

1. Kaplan-Meier Survival Curves 3

Result: Survival Curve 4 S(t)

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 5 Problem: censoring

Small example: Leukemia 6 Chemotherapy (we use this info later) censoring Acute Myelogenous Leukemia (AML) survival time Only 5 patients

Small example: Leukemia 7 censoring Number in riskNumber of events event ???

Kaplan-Meier estimator for S(t) Estimator: n i : number of subjects at time t i d i : number of events at time t i 8 Kaplan & Meier 1958

Kaplan-Meier estimator for S(t) Estimator: n i : number of subjects at time t i d i : number of events at time t i 9

Check S(t) till t 10

Kaplan-Meier estimator for S(t) Estimator: n i : number of subjects at time t i d i : number of events at time t i 11

Check S(t) till t 12

Kaplan-Meier estimator for S(t) Estimator: n i : number of subjects at time t i d i : number of events at time t i 13 Last time seen, still alive at that time

Check S(t) till t 14

Kaplan-Meier estimator for S(t) Estimator: n i : number of subjects at time t i d i : number of events at time t i 15

Check S(t) till t 16

Kaplan-Meier estimator for S(t) Estimator: n i : number of subjects at time t i d i : number of events at time t i 17

Check S(t) till t 18

Full data set: Leukemia patients

R code 20

2. Comparing Survival Curves 21

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? 22

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? 23 Survival Analysis has a big practical relevance

Data: Leukemia patients with chemo 12 patients without Goal: compare the two SCs statistically Group 1 Group 2

R code 25

Log-rank test (Mantel-Haenszel) Hypothesis: Null hypothesis H 0 : No difference in survival between (group 1) and (group 2). Alternative hypothesis H 1 : Difference in survival between (group 1) and (group 2). 26 Mantel and Haenszel 1959

Idea of the test For each time t, estimate the expected number of events for (group 1) and (group 2). 27 Number in risk at t in i Number of events at t in i

28 The e it are obtained assuming H 0 is true. Hence, m it – e it is a measure for the deviation of the data from H 0. sum E2E2 E1E1 O 1 - E 1 O 2 – E 2

Wrapping up Test statistic: Sampling distribution: s follows a chi-square distribution with one degree of freedom 29

R code Back to our leukemia data set: 30

Data: Leukemia patients with chemo 12 patients without Goal: compare the two 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 patient to classify survival

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 analysis 2.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.Clustering 2.Survival analysis 3.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 and Vice-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?

It means first of all more data!

What does this all mean? It means first of all more data!

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Thank you to everyone for participating! We hope you enjoyed the summer school.