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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

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Exercise – Survival Analysis Homework ~ 1.5 hours

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1. Kaplan-Meier Survival Curves 3

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Result: Survival Curve 4 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 5 Problem: censoring

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

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

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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

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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

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Check S(t) till t 10

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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

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Check S(t) till t 12

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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

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Check S(t) till t 14

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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

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Check S(t) till t 16

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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

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Check S(t) till t 18

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Full data set: Leukemia 19 23 patients

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R code 20

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2. Comparing Survival Curves 21

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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? 22

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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? 23 Survival Analysis has a big practical relevance

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Data: Leukemia 24 11 patients with chemo 12 patients without Goal: compare the two SCs statistically Group 1 Group 2

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R code 25

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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

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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

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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

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

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R code Back to our leukemia data set: 30

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Data: Leukemia 31 11 patients with chemo 12 patients without Goal: compare the two SCs statistically Group 1 Group 2

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Survival Analysis & Biomarkers

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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.

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

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

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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!

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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

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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

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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

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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

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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

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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!

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Summary & Outlook to Genome and Network Medicine Almost there!

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Schedule 17 lectures

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Interdisciplinary summer school

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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

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A look 5 years ahead

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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

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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.

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1. Single cell experiments PacBio (Pacific Biosciences) SMRT: Single molecule real time sequencing

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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.

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2. Personalized Medicine 2012

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What does this all mean?

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It means first of all more data!

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

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Survey Please participate in the survey about the summer school in order to help us to improve. We will send it early next week.

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

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