1 Canadian Bioinformatics Workshops

2Module #: Title of Module

Anna Lapuk, PhD Vancouver Prostate Centre Module 3: Clinical genomics and survival analysis

Disease characterization Module 3: Clinical genomics and survival analysis

ID race family history (yes/no) Nodal status (yes/no; number of nodes involved) Radiation Chemo Hormone therapy Protein IHC Stage Size Age at diagnosis Estrogen receptor level Progesterone level SBR grade Overall outcome (dead/alive) Overall survival time Disease specific outcome (dead/alive) Disease specific survival time Recurrence status (yes/no) time to recurrence Time to distant recurrence Distant recurrence status (yes/no) Survival times – time to a given end point Survival analysis Module 3: Clinical genomics and survival analysis

GoalTechnique Estimate the probability of individual surviving for a given time period (one year) Kaplan-Meier survival curve, life table Compare survival experience of two different groups of individuals (drug/placebo) Logrank test (comparison of different K-M curves) Detect clinical/genomic/epidemiologic variables which contribute to the risk (associated with poor outcome) Multivariate (univariate) Cox regression model Module 3: Clinical genomics and survival analysis

Survival time – is the time from a fixed point to an end point Almost never observe the event of interest in all subjects (censoring of data) Need for a special analytical techniques Starting pointEnd point SurgeryDeath/Recurrence/Relapse DiagnosisDeath/Recurrence/Relapse TreatmentDeath/Recurrence/Relapse Module 3: Clinical genomics and survival analysis

Arise whenever the dependent variable of interest represents the time to a terminal event, and the duration of the study is limited in time. Incomplete observation - the event of interest did not occur at the time of the analysis. Type I and II censoring (time fixed/proportion of subjects fixed) Right and left censoring Event of InterestCensored observation Death of the diseaseStill alive Survival of marriageStill married Drop-out-time from schoolStill in school Module 3: Clinical genomics and survival analysis

Survival probability for a given length of time can be calculated considering time in intervals. Probability of survival month 2 is the probability of surviving month 1 multiplied by the probability of surviving month 2 provided that the patient has survived month 1 (conditional probability) Survival probability = p 1 x p 2 x p 3 x p 4 x... p j p j is the probability of surviving month j of those still known to be alive after (j-1) months. In the reality time intervals contain exactly one case. p1p1 p2p2 p3p3 p4p4 Module 3: Clinical genomics and survival analysis

Survival probability Time (months) Censored observations r – still at risk f – failure (reached the end point) Module 3: Clinical genomics and survival analysis

Survival probability Time (months) Censored observations What is the probability of a patient to survive 2.5 months? Module 3: Clinical genomics and survival analysis

Survival probability Time (months) Treated patients Untreated patients Are survival experiences significantly different? Module 3: Clinical genomics and survival analysis

Is a non-parametric method to test the null hypothesis that compared groups are samples from the same population with regard to survival experience. (Doesn’t tell how different) Module 3: Clinical genomics and survival analysis

Survival probability Time (months) Treated patients Untreated patients Compare proportions at every time interval and summarize it across intervals (similar to a Chi- square test) Module 3: Clinical genomics and survival analysis

k time intervals O – observed proportion E – expected V – variance of (O-E) Then compare with the χ2 distribution with (k-1) degrees of freedom Chi-square Log-rank Module 3: Clinical genomics and survival analysis

Measures relative survival in two groups base don the complete period studied R=0.43 – relative risk (hazard) of poor outcome under the condition of group 1 is 43% of that of group 2. (tells how different) Module 3: Clinical genomics and survival analysis

investigate the effect of several variables on survival experience Multivariate proportional hazards regression model Module 3: Clinical genomics and survival analysis

X 1...X p – independent variable of interest b 1... b p – regression coefficients to be estimated Assumption: the effect of variables is constant over time and additive in a particular scale (Similarly to K-M) Hazard function is a risk of dying after a given time assuming survival thus far Cumulative function H 0 (t) – cumulative baseline or underlying function. Probability of surviving to time t is S(t) = exp[-H(t)] for every individual with given values of the variables in the model we can estimate this probability. Module 3: Clinical genomics and survival analysis

Cox regression model fitted to data from PBC trial of azathioprine vs placebo (n=216) variableRegression coef (b)SE(b)exp(b) Serum billirubin Age Cirrhosis Serum albumin Central cholestasis Therapy Altman D, 1991 Coefficient: Sign – positive or negative association with poor survival Magnitude – refers to the increase in log hazard for an increase of 1 in the value of the covariate Module 3: Clinical genomics and survival analysis

Cox regression model fitted to data from PBC trial of azathioprine vs placebo (n=216) variable Regression coef (b)SE(b)exp(b)Increase of value of the variable by 1 will result in Serum billirubin % Age % Cirrhosis % Serum albumin % Central cholestasis % Therapy % Modified from Altman D, 1991 Coefficient: Sign – positive or negative association with poor survival Magnitude – refers to the increase in log hazard for an increase of 1 in the value of the covariate. If the value changes by 1, hazard changes Exp(b) times. Module 3: Clinical genomics and survival analysis

Altman D, 1991 Module 3: Clinical genomics and survival analysis

Clinical data is a highly important component and is intrinsically different from genomic/transcriptomic data. Survival data is a special type of data requiring special methodology Main applications of survival analysis: – Estimates of survival probability of a patient for a given length of time (Kaplan- Meier survival curve) under given circumstances. – Comparison of survival experiences of groups of patients (is the drug working???) (log-rank test) – Investigation of risk factors contributing to the outcome (make a prognosis for a given patient and choose appropriate therapy) Module 3: Clinical genomics and survival analysis

Back in 20 minutes Module 3: Clinical genomics and survival analysis

Statistics for Medical Research, Douglas G Altman, 1991 Chapman & Hall/CRC Pharmacogenetics and pharmacogenomics: development, science, and translation. Weinshilboum RM, Wang L. Annu Rev Genomics Hum Genet. 2006;7: PMID: Pharmacogenomics: candidate gene identification, functional validation and mechanisms. Wang L, Weinshilboum RM. Hum Mol Genet Oct 15;17(R2):R PMID: End-sequence profiling: sequence-based analysis of aberrant genomes. Volik S, Zhao S, Chin K, Brebner JH, Herndon DR, Tao Q, Kowbel D, Huang G, Lapuk A, Kuo WL, Magrane G, De Jong P, Gray JW, Collins C. Proc Natl Acad Sci U S A Jun 24;100(13): PMID: A Review of Trastuzumab-Based Therapy in Patients with HER2-positive Metastatic Breast Cancer, David N. Church and Chris G.A. Price. Clinical Medicine: Therapeutics 2009: Other useful references: The hallmarks of cancer. Hanahan D, Weinberg RA. Cell Jan 7;100(1): PMID: Aberrant and alternative splicing in cancer. Venables JP Cancer Res Nov 1;64(21): PMID: Module 3: Clinical genomics and survival analysis