Analysis of acgh data: statistical models and computational challenges
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1 : statistical models and computational challenges Ramón Díaz-Uriarte Díaz-Uriarte, R. acgh analysis: models and computation / 38
2 Outline 1 Introduction Alternative approaches What we really want RJaCGH There is math (just so you believe us) RJaCGH: typical output RJaCGH: performance 2 Statistical methods need software Introduction ADaCGH Can we make it fast? MPI et al. Díaz-Uriarte, R. acgh analysis: models and computation / 38
3 1 Introduction Alternative approaches What we really want RJaCGH There is math (just so you believe us) RJaCGH: typical output RJaCGH: performance 2 Statistical methods need software Introduction ADaCGH Can we make it fast? MPI et al. Díaz-Uriarte, R. acgh analysis: models and computation / 38
4 Introduction Log 2 (T/ R) Barrett et al., 2004 Calling gains and losses: hypothesis testing Olshen, 2005 Hupe & Barillot, 2005 Arrays: but location in chromosome matters Inferring number of copy gains/losses: estimation Chromosome Díaz-Uriarte, R. acgh analysis: models and computation / 38
5 Alternative approaches Available methods Hypothesis testing based Circular Binary Segmentation CGHExplorer acghsmooth SWArray CLAC Wavelet-based smoothing Copy number estimation Hidden markov models Quantile smoothing GLAD (adaptive nonparametric kernel smoothing) Gaussian mixtures Bayes regression CGHMIX Díaz-Uriarte, R. acgh analysis: models and computation / 38
6 What we really want Is this status of affairs OK? What is it we really want? Díaz-Uriarte, R. acgh analysis: models and computation / 38
7 What we really want What is it we really want? 1. Probabilities of alteration. Díaz-Uriarte, R. acgh analysis: models and computation / 38
8 What we really want What is it we really want? 1. Probabilities of alteration. The direct answer (to is this gene/region gained/lost? No, p-values and smoothed means are not a direct answer.) Usable in contexts from clinical to basic research: modify your thresholds as needed. Probabilities: of genes, of regions, of regions across subjects, etc. (No, not easy, but doable). Probabilities: incorporate uncertainty. Díaz-Uriarte, R. acgh analysis: models and computation / 38
9 What we really want What is it we really want? 2. Account for distance between probes. Díaz-Uriarte, R. acgh analysis: models and computation / 38
10 What we really want What is it we really want? 2. Account for distance between probes. Most platforms widely variable distance between probes. The larger the distance, the more likely a change. The larger the distance, the less information a probe provides about state of nearby probes. Use distance so that the information that consecutive probes provide is adequately accounted for. Díaz-Uriarte, R. acgh analysis: models and computation / 38
11 What we really want What is it we really want? 3. Genome-wide and chromosome-wide analysis. Díaz-Uriarte, R. acgh analysis: models and computation / 38
12 What we really want What is it we really want? 3. Genome-wide and chromosome-wide analysis. Chromosome-wide: alterations wrt chromosome s mean ploidy. Genome-wide: only way to detect whole chromosome gains/loses. Díaz-Uriarte, R. acgh analysis: models and computation / 38
13 What we really want Do available methods give that to us? No Díaz-Uriarte, R. acgh analysis: models and computation / 38
14 What we really want Do available methods give that to us? No Most don t provide probabilities. Most don t use distance between probes. Many ad-hoc, with parameters without intuitive meaning. No single methods fulfills the above three. Díaz-Uriarte, R. acgh analysis: models and computation / 38
15 What we really want... thus we will have to develop a new method Díaz-Uriarte, R. acgh analysis: models and computation / 38
16 RJaCGH Model: characteristics Finite number of different copy gains / losses, number of gains/losses not measured directly, state of every gen related to the state of its neighbours: Hidden Markov Model (HMM) with Gaussian emissions. Influence larger the closer the genes are: non-homogeneous HMM with Gaussian distributions Díaz-Uriarte, R. acgh analysis: models and computation / 38
17 RJaCGH Model: estimation Well known machinery for homogeneous HMM with known number of states Díaz-Uriarte, R. acgh analysis: models and computation / 38
18 RJaCGH Model: estimation Well known machinery for homogeneous HMM with known number of states We have: non-homogeneous HMM with unknown number of states and want probabilistic statements about likely state and flexible specification of model: Bayesian inference through Markov Chain Monte Carlo Díaz-Uriarte, R. acgh analysis: models and computation / 38
19 RJaCGH Model: estimation Well known machinery for homogeneous HMM with known number of states We have: non-homogeneous HMM with unknown number of states and want probabilistic statements about likely state and flexible specification of model: Bayesian inference through Markov Chain Monte Carlo Number of states not known in advance number of parameters different for different models need to jump between models during MCMC for automatic selection and probab. asses. of number of states: reversible jump MCMC Díaz-Uriarte, R. acgh analysis: models and computation / 38
20 RJaCGH Model: estimation Well known machinery for homogeneous HMM with known number of states We have: non-homogeneous HMM with unknown number of states and want probabilistic statements about likely state and flexible specification of model: Bayesian inference through Markov Chain Monte Carlo Number of states not known in advance number of parameters different for different models need to jump between models during MCMC for automatic selection and probab. asses. of number of states: reversible jump MCMC Model uncertainty must be taken into account: models averaged using Bayesian Model Averaging (improved mean square error too!). Díaz-Uriarte, R. acgh analysis: models and computation / 38
21 There is math (just so you believe us) Statistical model Díaz-Uriarte, R. acgh analysis: models and computation / 38
22 There is math (just so you believe us) Bayesian model Díaz-Uriarte, R. acgh analysis: models and computation / 38
23 There is math (just so you believe us) Reversible Jump Díaz-Uriarte, R. acgh analysis: models and computation / 38
24 RJaCGH: typical output Díaz-Uriarte, R. acgh analysis: models and computation / 38
25 RJaCGH: typical output Díaz-Uriarte, R. acgh analysis: models and computation / 38
26 RJaCGH: performance Does it really work better? Compare against best-performing methods (two reviews tell us which are best ). Data NOT simulated under our model: Willenbrock and Fridlyand. Díaz-Uriarte, R. acgh analysis: models and computation / 38
27 RJaCGH: performance Adding variable distances to the data Díaz-Uriarte, R. acgh analysis: models and computation / 38
28 RJaCGH: performance Adding variable distances to the data Location of gaps: Uniform (100) Length of gaps: Poisson. Increasing lambda of Poisson (recall: mean = variance = λ) increases variance of inter-probe distance and % of gaps. Díaz-Uriarte, R. acgh analysis: models and computation / 38
29 RJaCGH: performance RJaCGH: and how does it do? Correct classification rate ACE BIOHMM DNACopy + Merge levels HMM RJaCGH 0 % 10 % 25 % 50 % 65 % Proportion of genes missing Díaz-Uriarte, R. acgh analysis: models and computation / 38
30 RJaCGH: performance RJaCGH: and how does it do? (II) 0 % 10 % 25 % 50 % 65 % Std.Dev.Sample : (0.18,0.19] Std.Dev.Sample : (0.19,0.2] ACE BIOHMM DNA Copy + Merge Levels HMM RJaCGH 0.96 Std.Dev.Sample : (0.14,0.15] Std.Dev.Sample : (0.15,0.16] Std.Dev.Sample : (0.16,0.17] Std.Dev.Sample : (0.17,0.18] Correct classification Std.Dev.Sample : (0.09,0.11] Std.Dev.Sample : (0.11,0.12] Std.Dev.Sample : (0.12,0.13] Std.Dev.Sample : (0.13,0.14] % 10 % 25 % 50 % 65 % Proportion of missing genes 0 % 10 % 25 % 50 % 65 % Díaz-Uriarte, R. acgh analysis: models and computation / 38
31 RJaCGH: performance acgh analyses: what next? Minimal common regions (joint product of marginals!!!) Computation: many MCMCs... Díaz-Uriarte, R. acgh analysis: models and computation / 38
32 Statistical methods need software 1 Introduction Alternative approaches What we really want RJaCGH There is math (just so you believe us) RJaCGH: typical output RJaCGH: performance 2 Statistical methods need software Introduction ADaCGH Can we make it fast? MPI et al. Díaz-Uriarte, R. acgh analysis: models and computation / 38
33 Statistical methods need software Introduction Statistical methods need software (...) a reference implementation, some code which is warranted to give the authors intended answers in a moderately-sized problem. It need not be efficient, but it should be available to anyone and everyone. Brian D. Ripley, RSS 2002 Plenary Lecture. (...) publishing figures or results without the complete software environment could be compared to a mathematician publishing an announcement of a mathematical theorem without giving the proof. Jonatahn B. Buckeit and David L. Donoho. Wavelab and Reproducible Research. Díaz-Uriarte, R. acgh analysis: models and computation / 38
34 Statistical methods need software Introduction Need not be efficient? Or who is our audience? Díaz-Uriarte, R. acgh analysis: models and computation / 38
35 Statistical methods need software Introduction Need not be efficient? Or who is our audience? Statisticians, bioinformaticians Wet-lab researchers Díaz-Uriarte, R. acgh analysis: models and computation / 38
36 Statistical methods need software Introduction For wet-lab researchers Implementing a user friendly tool for a Bayesian-based approach not easy Díaz-Uriarte, R. acgh analysis: models and computation / 38
37 Statistical methods need software Introduction For wet-lab researchers Implementing a user friendly tool for a Bayesian-based approach not easy Will the user get tired of waiting (faster, faster) All the extra stuff (convergence, restarting chains, etc) Díaz-Uriarte, R. acgh analysis: models and computation / 38
38 Statistical methods need software Introduction For wet-lab researchers Implementing a user friendly tool for a Bayesian-based approach not easy Will the user get tired of waiting (faster, faster) All the extra stuff (convergence, restarting chains, etc) Working on it. In the meantime... Díaz-Uriarte, R. acgh analysis: models and computation / 38
39 Statistical methods need software ADaCGH A simpler problem ADaCGH: A web-based tool for the analysis of acgh data. Common interface Implements all decently performing methods: CBS, HMM, BioHMM, GLAD, cghseg, ACE, PSW, Wavelet-based smoothing. Dynamic graphics and links to additional functional information. And it is FAST. Díaz-Uriarte, R. acgh analysis: models and computation / 38
40 Statistical methods need software Can we make it fast? How fast is fast? (I) Small data set (2271 genes) HMM GLAD CBS Sequential code User wall time (seconds) Parallelized code Number of arrays (samples) Díaz-Uriarte, R. acgh analysis: models and computation / 38
41 Statistical methods need software Can we make it fast? How fast is fast? (II) Medium data set (10,000 genes) HMM GLAD CBS Sequential code User wall time (seconds) Parallelized code Number of arrays (samples) Díaz-Uriarte, R. acgh analysis: models and computation / 38
42 Statistical methods need software Can we make it fast? How many users? HMM Small data set (2271 genes, 10 arrays) Wavelets User wall time (seconds) CBS GLAD Number of simultaneous users Díaz-Uriarte, R. acgh analysis: models and computation / 38
43 Statistical methods need software MPI et al. Underneath Combine MPI with web-service load-balancing plus systematic rotation of MPI master and slave nodes. Díaz-Uriarte, R. acgh analysis: models and computation / 38
44 Statistical methods need software MPI et al. Díaz-Uriarte, R. acgh analysis: models and computation / 38
45 Statistical methods need software MPI et al. What can we parallelize? Díaz-Uriarte, R. acgh analysis: models and computation / 38
46 Statistical methods need software MPI et al. What can we parallelize? Segmentation (heavy number crunching) and figures... Díaz-Uriarte, R. acgh analysis: models and computation / 38
47 Statistical methods need software MPI et al. What can we parallelize? Segmentation (heavy number crunching) and figures... over arrays, or chromosomes, or chromosomes by arrays. Díaz-Uriarte, R. acgh analysis: models and computation / 38
48 Statistical methods need software MPI et al. What can we parallelize? Segmentation (heavy number crunching) and figures... over arrays, or chromosomes, or chromosomes by arrays.... for everything else, there is load-balancing. Díaz-Uriarte, R. acgh analysis: models and computation / 38
49 Statistical methods need software MPI et al. Is this the way to go? (I) Gains are spectacular. Díaz-Uriarte, R. acgh analysis: models and computation / 38
50 Statistical methods need software MPI et al. Is this the way to go? (I) Gains are spectacular. Strange (Striking?): we seem to be the only ones to use, systematically, parallelization for bioinfo/biostats web-based applications. Díaz-Uriarte, R. acgh analysis: models and computation / 38
51 Statistical methods need software MPI et al. Medium data set (10,000 genes) HMM GLAD CBS Sequential code User wall time (seconds) Parallelized code Number of arrays (samples) Díaz-Uriarte, R. acgh analysis: models and computation / 38
52 Statistical methods need software MPI et al. Is this the way to go? (II) Hard to tell. Díaz-Uriarte, R. acgh analysis: models and computation / 38
53 Statistical methods need software MPI et al. Is this the way to go? (II) Hard to tell. (Automatically) managing, monitoring, sanitizing MPI and R + MPI a pain Díaz-Uriarte, R. acgh analysis: models and computation / 38
54 Statistical methods need software MPI et al. Is this the way to go? (II) Hard to tell. (Automatically) managing, monitoring, sanitizing MPI and R + MPI a pain MPI is fragile (use a fault-tolerant PVM instead?) Díaz-Uriarte, R. acgh analysis: models and computation / 38
55 Statistical methods need software MPI et al. Is this the way to go? (II) Hard to tell. (Automatically) managing, monitoring, sanitizing MPI and R + MPI a pain MPI is fragile (use a fault-tolerant PVM instead?) I wish R were Erlang... Díaz-Uriarte, R. acgh analysis: models and computation / 38
56 Statistical methods need software MPI et al. Is this the way to go? (II) Hard to tell. (Automatically) managing, monitoring, sanitizing MPI and R + MPI a pain MPI is fragile (use a fault-tolerant PVM instead?) I wish R were Erlang... However it is every day more evident that The Free Lunch Is Over: A Fundamental Turn Toward Concurrency in Software : H. Sutter. Díaz-Uriarte, R. acgh analysis: models and computation / 38
57 Statistical methods need software MPI et al. Acknowledgements Oscar Rueda: for the work on RJaCGH. Funding from Fundación de Investigación Médica Mutua Madrileña and Project TIC C02-02 of the Spanish Ministry of Education and Science Ramón y Cajal Programme of the Spanish Ministry of Education and Science CNIO users for interesting problems and tool testing users and developers for a vibrant statistical computing community and amazing platform Díaz-Uriarte, R. acgh analysis: models and computation / 38
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