Biostatistical modelling in genomics for clinical cancer studies

Transcription

1 This work was supported by Entente Cordiale Cancer Research Bursaries Biostatistical modelling in genomics for clinical cancer studies Philippe Broët JE 2492 Faculté de Médecine Paris-Sud In collaboration with S. Richardson Imperial College London Statistical Latent Variables Models in the Health Sciences Perugia, Italy, 6-8 September 2006

2 Outline Genomic biotechnologies in clinical research Introduction Comparative Genomic Hybridization (CGH) Spatial mixture model-based approach Model Performance Clinical example: Lung carcinoma study Conclusion

3 Introduction

4 Genomic-oriented biotechnologies thousands of information from one sample

5 Genomic-oriented biotechnologies thousands of information from one sample CGH µarray DNA

6 Genomic-oriented biotechnologies thousands of information from one sample CGH µarray DNA cdna/oligo µarray mrna

7 Genomic-oriented biotechnologies thousands of information from one sample CGH µarray DNA cdna/oligo µarrayµ mrna Protein µarray Protein

8 Context: Cancer Research Analysis of copy number changes of genomic sequences Loss Gain Tumor supressor gene Oncogene Amplification of an oncogene or Deletion of a tumor suppressor gene important mechanisms for tumorigenesis

9 Tumor suppressor gene = Break - Oncogene = Accelerator + Normal cell

10 Tumor suppressor genes - (e.g. p15)

11 Tumor suppressor genes - Oncogenes +++ (e.g. p15) (e.g. EGFR)

12 Tumor suppressor genes - Oncogenes +++ (e.g. p15) (e.g. EGFR) Cancer cell

13 Tumor Normal 1. Extraction (DNA) 2. Labelling (fluo) 3. (Co)-hybridization (oligo/bac) 4. Scanning

14 Tumor Normal 1. Extraction (DNA) 2. Labelling (fluo) 3. (Co)-hybridization (oligo/bac) 4. Scanning Quantitative measures of DNA content Statistical challenges Provide genomic status information (deletion/gain/modal) Estimate the error rate of the allocation

15 Spatial mixture model

16 Mixture model approach Z ik (observed log-ratio) measurement for the i th GS ordered along the chromosome k 3 latent states (mixture model): loss / modal / gain copy state loss gain modal Z ik

17 Mixture model approach Z ik (observed log-ratio) measurement for the i th GS ordered along the chromosome k 3 latent states (mixture model): loss / modal / gain copy state loss f(./θ L ) modal f(./θ M ) gain f(./θ G ) Z ik

18 Mixture model approach Z ik (observed log-ratio) measurement for the i th GS ordered along the chromosome k 3 latent states (mixture model): loss / modal / gain copy state loss f(./θ L ) modal f(./θ M ) gain f(./θ G ) Z i-k Z ik Z i+k

19 Mixture model framework c=-1,0,1 c w c i k : mixing proportion (or weight) for state c f c (./θ): conditional density for state c Latent structure for mixture model L ik an unobserved (latent) categorical variable taking the values (c=-1,0,1) with probability w c i k f c (./θ): N(./µ c, 2 c) Z ik /L ik =c ~ f c (./θ)

20 Spatial structure on the weights (w c i k w c ) Introduce 3 centred Markov random fields {x c i k } with nearest neighbours along the chromosomes Spatial neighbours of GS g x x x g -1 g g+1 Define weights (mixture proportions) to depend on the chromosomic location via a logistic model: with x c i k (latent) spatial variable => favours allocation of nearby GS to same component

21 Three latent Markov random fields x k c = {x c 1 k ;...; x c I k } having Intrinsic Gaussian conditional autoregression (ICAR) prior for δ ik = neighbour of i (m ik = #h), with constraint Σ ik x c 1 k = 0 Variance parameters τ c k2 of the ICAR act as a smoothing prior Switching structure between the states can be different between chromosomes Conditional density f c (./θ): N(./µ c, 2 c) Mean and variances (µ c,η c2 ) of the mixture components are common to all chromosomes borrowing information

22 Inference & quantities of interest Bayesian inference via MCMC In particular, latent state allocations, L ik of GS are sampled during the MCMC run Compute posterior probabilities p c ik= P(L ik = c data), c =-1,0,1 Estimated within the algorithm by counting the number of times where the GS is in state c divided by the length of the simulation run

23 Probabilistic allocation We allocate a sequence to a modified state (loss/gain copy state) if its posterior probability is above a threshold (otherwise allocate to modal state) =>Subset S of genomic sequences classified as modified (deleted/amplified) Error rate estimate FDR S = (1/M)Σ m S p* 0m M is the size of set S P* 0 = posterior probability of not being allocated to the modal state -> Can adjust the threshold to get a desired FDR and vice versa

24 Performance of the model

25 Simulation set-up 200 fake genomic sequences loss : Z ik /L c i =-1 k ~ N(./µ -1 =(-0.7;-0.4), 2 = ) modal : Z ik /L c i =0 k ~ N(./µ 0 =0, 2 = ) gain : Z ik /L c i =+1 k ~ N(./µ +1 = (+0.7;+0.4), 2 = ) 50 simulated sets

26 Simulation set-up 200 fake genomic sequences loss : Z ik /L c i =-1 k ~ N(./µ -1 =(-0.7;-0.4), 2 = ) modal : Z ik /L c i =0 k ~ N(./µ 0 =0, 2 = ) gain : Z ik /L c i =+1 k ~ N(./µ +1 = (+0.7;+0.4), 2 = ) 50 simulated sets Pattern of genomic alterations

27 Calculate the realized (estimated) FDR, TPF, TNF realized FDR = realized TPF = (Se) realized TNF = (Sp) # realized false discoveries (belonging to the modal copy state but claimed as modified) # discoveries # realized discoveries # true positives (truly modified sequences) # realized non discoveries # true negatives (truly unmodified sequences) Compare Spatial mixture-model Classical mixture model (without spatial structure) Spatial agglomerative clustering (CGH-Miner, Wang et al., 2005) same FDR target (FDR default of 1% for CGH-Miner)

28 Model performance Operational characteristics

29 Model performance Operational characteristics

30 Model performance FDR estimation threshold threshold threshold

31 Model performance FDR estimation threshold threshold threshold

32 Results Spatial mixture model-based approach Good operating characteristics: Better Se/Sp than the independent mixture model Powerful detection of genomic changes Reliable FDR estimate

33 Clinical example

34 Lung Cancer Study In collaboration with GIS/NCC-Singapore (L. Miller, P. Tan) Samples selection Primary lung adenocarcinoma (pt2n0) Quality of frozen tissue (presence of tumor cells) was checked by cytological apposition CGH technology 32K BAC arrays (2 Chips) Co-hybridization tumoral/normal sample

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37 Individual threshold related to 5% FDR target

38 Cyclin D1 Immunohistochemistry Gene amplification and protein overexpression No gene amplification no protein expression

39 Conclusion

40 Spatial mixture model Interesting operational performance Selection of interesting GS based on an error criteria More powerful than independent mixture model Extension Incorporating genomic location information (distance function) Incorporate additional components Consider other selection rules

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