Statystyczna analiza danychaniag/SAD_2012/sad_wstep.pdfSTATYSTYCZNA ANALIZA DANYCH piątek, 10...

Statystyczna analiza danych

wykład I: motywacja i organizacja

Anna Gambin Instytut Informatyki UW

piątek, 10 lutego 2012

plan wykładu

• motywacja: statystyczna bioinformatyka - dwa przykłady (z własnego podwórka)

• spektrometria mas

• mikromacierze aCGH

• organizacja: plan wykładu i reguły zaliczenia


Diagram of the microarray-based comparative genomic hybridization (aCGH)process © 2008 Nature Education

EKSPERYMENT

DANE (duża skala)

STATYSTYCZNA ANALIZA DANYCH


http://www.nature.com/scitable


MichałPiotrek

ludzie (bioputer.mimuw.edu.pl)


projekty (przykład 1: spektrometria)


2. MASS SPECTRA PREPROCESSING

• if here is exactly one candidate cluster we extend it with the active peak,

• if more than one candidate cluster exists we assign the active peak to the

cluster whose monoisotopic peak is the highest (such a situation is quite

rare but it happens when the signal coming from one peptide is artificially

split in the domain of the retention time (c.f. Fig. 2.6)).

Figure 2.6: Artificial peak separation in the retention time domain. Isotopic

envelopes visualized by Sparky tool (Goddard and Kneller, 2006). Peaks found

by NMRPipe are depicted as black Xes. Horizontal axis — mass-to-charge ratio,

vertical axis — retention time, height is color coded increasing from red to blue.

2.3.3 Automated Charge Determination

We have implemented two versions of this step, simple and fast and a more

sophisticated one. The simple version uses only information from the peak spacing

14

spektrometria maswidmo

peptydu = obwiednia izotopowa


2.3 Isotopic envelopes detection

Figure 2.8: Masses and charges calculated by our algorithm for the fragment

of the spectrum. Peaks are marked as black crosses, small arrow denotes the

monoisotopic peak in each isotopic cluster, the monoisotopic mass (M) and charge

(Q) are given for each identified peptide.

21

automatyczna interpretacja widma


DBSCAN


3.2 Alignment via clustering

Figure 3.6: Colorectal cancer data clustered with the DBSCAN algorithm, �m =

5, �rt = 30, minPts = 10. Picture on the right presents fragment of the data in

greater detail. The cluster colors are recycled.

• the upper limit for size of a preliminary cluster was 1000 elements.

In case of minPts = 0 no peaks are treated as noise, even the ones in the very

sparse regions. For minPts = 10 we assume that some of the peaks might have

noise origins. Of course another explanation for their origins can be that they

in fact correspond to real peptides, but the retention time drift was so big, that

they cannot be aligned to any peaks in this iteration. Hopefully, excluding them

at this stage does not necessarily mean they they will never be properly aligned.

If retention time correction step (discussed in Section 3.2.3) is performed after

the clustering step the drifts might become smaller.

There were 9026 preliminary groups obtained with parameter minPts = 0 and

8216 with minPts = 10 (c.f. Fig. 3.6). In the latter case 3076 points were marked

as noise.

All the models were fitted within each of the preliminary clusters in the second

stage of the algorithm. At one time the same model was assumed in all the

preliminary clusters. Hence, model selection problem was solely to select the

appropriate number of clusters, the one that minimizes the BIC value. For a

45

klastrowanie w domenie czasu retencji

metody obszarowe: DBSCAN


3.2 Alignment via clustering

a) λrBr b) λB c) λrB

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Figure 3.7: Example of clustering acquired for one of the preliminary clusters

from Figure 3.6 of size 999. a) – i) stand for fitted models: a) λrBr, b) λB, c)

λrB, d) λBr, e) – i) models have deviation in the m/z dimension fixed to 0.04,

retention time deviations are: e) 50, f) 100, g) 200, h) estimated from the data,

the same for every cluster, i) estimated from the data for each cluster.

51

klastrowaniealgorytm k-średnich

algorytm EM

wykorzystujące model probabilistyczny


ocena jakości


(jednoczesne) testowanie (wielu) hipotez statystycznych

FDR - false dicovery rate


28 A. Gambin et al. / International Journal of Mass Spectrometry 260 (2007) 20–30

Fig. 10. Results of PPC method on the colorectal cancer example. Each of the four panels in the right figure shows a histogram of peptide intensities in the training setfor one mass cluster for healthy donors (top) and cancer patients (bottom). Cluster centroid coordinates: m/z and retention time value is given. Additionally we estimatedthe density of signal abundance and calculated the PPC threshold as before. Right panel shows the false-discovery-rate (FDR) value as a function of the PPC threshold.

two lines (retention times) in the previous approach. Our algo-rithm operates on the sorted peaks list (of length n) and calculatesthe list of masses (i.e., peptides) of length k. Assuming that ev-ery vertical strip intersects constant number of isotopic clusters

(in practice this number is less than 10), we can estimate timecomplexity of the algorithm to be O(n(log n + log k)). Memoryrequirements can be bounded by O(n + k). Effectivity tests wereperformed to find the execution time and memory requirements.

selekcja cech (biomarkerów)metoda PPC


t-test (Welch)

selekcja cech (biomarkerów)


niestabilność biomarkerów


!"#$!%&%'(&)*+,%-.!"##$%!!&'())*!+,-'+ .//)-00111234567897:/;<*29560=>$=?"=#+0@0'+0'+

A<B7!==!5C!=D/0+12$'3*42)$'&,$(&)$-%,+,%&'$03)0&.2.5

The structure of the graph underlying the Markov chainMC1 is presented in Figure 7. Depicted is the nested familyof sets grouped together during the consecutive phases ofthe algorithm.

Readers interested in the details of the approximationalgorithm are referred to [19], (an extended version of it isavailable at [20]).

The hierarchical approach from [19] complies well withchain MC1. The structure of MC4 does not allow for effi-

cient aggregation, but because of the limited number offeatures selected from each input ranking, it is still tracta-ble. Table 1 summarizes the efficiency of Markov chainaggregation method. For MC1 we have 7 grouping stages;the sizes of resulting groups vary from 4 to 87. For MC4 all242 states are grouped together in the first phase and thestationary distribution vector is calculated exactly usingthe GTH algorithm [18]. The significant speed-upobtained with the approximation algorithm is crucialwhen aggregation is applied to complete rankings of fea-tures from massive datasets.

Markov chain hierarchical structureFigure 7Markov chain hierarchical structure. The structure of the state space graph for rank aggregation Markov chain MC1. The type of edge corresponds to the transition probability. Ellipses surround the top ranked features appearing in each phase (from 1 up to 3 in this example). States joined at an earlier stage have higher stationary probability, and therefore rank higher in the aggregated ranking.

modele Markowa


uliniowienie próbek


klasyfikacja


konsensus biomarkerów


!"#$!%&%'(&)*+,%-.!"##$%!!&'())*!+,-'+ .//)-00111234567897:/;<*29560=>$=?"=#+0@0'+0'+

A<B7!+!5C!=D/0+12$'3*42)$'&,$(&)$-%,+,%&'$03)0&.2.5

Ovarian cancer classification resultsFigure 3Ovarian cancer classification results. Classification results for four classifiers (random forest (RF), SVM, decision trees (DT) and LDA) on the MALDI-TOF ovarian cancer dataset are shown separately in the four panels. Classifier performance using a specified number of best features from individual scoring functions (peak probability contrast (PPC), mutual information (MI), t-statistic (TT) and random forest feature ranking (RF)) are plotted in black. Performance with features selected by MC1 rank aggregation of the four functions is shown in blue. Results for regular PCA and our modified "Consensus" version using only the best features from the four scoring functions are plotted in green and red respectively. For all methods the average accuracy (fraction of samples correctly classified) over 20 cross-validation runs is shown. See Section Results for discussion.

klasyfikacja

RF- random forest

SVM- support vector machines

DT - decision trees

LDA- linear discriminant

analysis


Introduction Model and methods Results Bibliography

Proteolysis

peptidases — enzymes cleaving polipeptide chains, divided into:

exopeptidases - cleave near the ends of thepolypeptide chainendopeptidases - cleave the polypeptide chain inthe middle

process of proteolysis — decomposition of proteins into peptidesand amino acids

modelowanie aktywności proteolitycznej


!

FT

FTS

TS

FTSS

TSS

SS

FTSST

TSST

SST

ST

FTSSTS

TSSTS

SSTS

STS

SSTSY

STSY

TSY

SY

†

Figure 2: The cleavage graph for 2 precursor peptides FTSSTS and SSTSY with source

and sink nodes added.

model I: egzopeptydazy


model II: endopepydazy


modelowanie


bayesowskie modelowanie


prawdopodobieństwoa posteriori


Metropolis-Hastings


aktywność trypsyny


!

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1)

Figure 4. (A) Inferred peptidases’ activities for sample no. 19 (colorectalcancer patient). (B-D) Same parameters for synthetic data generated fromthe model with standard deviation set to 0.1, 0.01, 0.01 respectively. Redlines correspond to model peptidases’ activities, which we aim to recover.

estimated parameters are known (red line). In those cases weonly test the accuracy of estimation procedure.

The set of identified enzymes do not vary significantlybetween all investigated samples (39). There are 9 peptidasesidentified in all samples and 22 peptidases found in at leastone sample.

For further analysis we selected 19 samples (11 healthy, 8diseased), for which acceptable estimates had been obtained(c.f. Table I). Heatmap in figure 5 presents the activities ofpeptidases identified for these samples. Hierarchical clus-

24 25 31 35 32 15 19 39 26 20 6 29 10 5 1 37 23 28 2

data set no.

membrane.type.matrix.metallopeptidase.4

elastase.1

ADAMTS5.peptidase

ADAM10.peptidase

cathepsin.S


trypsin.1


calpain.2


insulysin

neprilysin

signalase..animal..21.kDa.component

cathepsin.G

calpain.1

cathepsin.H

cathepsin.B

aminopeptidase.A

angiotensin.converting.enzyme.2

chymase...Homo.sapiens..type.

myeloblastin

matrix.metallopeptidase.20

healthydiseased

Figure 5. Peptidases’ activities for 19 samples. The red-white scalerepresents peptidase acivities in descending order (for missing peptidasesvalues are set to minimal).

tering of activity profiles groups samples into two clustersbeing in good accordance with patient’s diagnosis.

Let’s take a closer look at the set of identified peptidases.Among them we detected the family of matrix metallopep-tidases, whose role in cancer development and progressionis significant [16], [17]. The calpain enzyme is used as amarker for the early detection of colorectal carcinoma [18]and inhibitors of cathepsins as possible therapeutics incolorectal diseases [19]. Moreover, cathepsins because oftheir ability to degrade extracellular matrix proteins havebeen implicated to play a role in invasion and metastasisof colorectal cancer. Members of ADAM family are alsoknown to be involved in various biological and disease-related processes [20].

V. CONCLUSION

In this paper we significantly extend formal model of pro-tein degradation proposed in [5]. The extension is twofold:firstly current approach encompass endopeptidase activity aswell (while [5] deals with exopeptidases only), and secondlywe integrate our model with knowledge about proteolyticevents stored in MEROPS database [6]. Moreover, we for-mulate the task of inferring parameters of our model as con-strained optimization problem, which we solve by standardprocedure for non-linear least squares. This approach turnedout to be more time efficient for complex MS data whencomparing to previous Markov Chain Monte Carlo method

estymacja parametrów


grupowanie


PCA: analiza składowych głównych


projekty (przykład 2: mikromacierze aCGH)


Diagram of the microarray-based comparative genomic hybridization (aCGH)process © 2008 Nature Education

technologia aCGH




baza pacjentów w IMiD


zidentyfikowane segmenty


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Organizacja wykładu

✦ wykład ~ teoria (slajdy + notatki)

✦ zaliczenie wykładu = egzamin ustny

✦ laboratorium ~ analiza danych (język R)

✦ zaliczenie labu = projekt


literatura

http://cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf

Statistics Using R with Biological Examples Kim Seefeld, Ernst Linder, http://cran.r-project.org/doc/contrib/Seefeld_StatsRBio.pdf

Applied Statistics for Bioinformatics using R Wim P. Krijnen

Statistical Bioinformatics with RSunil K. Mathur, Elsevier Academic Press, 2010




http://cran.r-project.org/doc/contrib/

http://cran.r-project.org/doc/contrib/

http://cran.r-project.org/doc/contrib/Seefeld_StatsRBio.pdf

http://cran.r-project.org/doc/contrib/Seefeld_StatsRBio.pdf

✦ wykład 1: wstęp - organizacja wykładu, skąd przyszliśmy, dokąd zmierzamy...

✦ wykład 2 i 3: podstawowe rozkłady prawdopodobieństwa, testy parametryczne i nieparametryczne

✦ wykłady 4, 5: analiza skupień=grupowanie = klasteryzacja (ang. clustering)

✦ metody grafowe, metody hierarchiczne, relokacyjne, oparte o model.



✦ wykłady 6,7: redukcja wymiaru, selekcja cech (biomarkerów)

✦ analiza składowych głównych, skalowanie wielowymiarowe

✦ wykłady 8-11: klasyfikacja

✦ LDA, QDA, regresja liniowa, klasyfikatory drzewowe, boosting, ...

✦ wykłady 11-14: modele Markowa



✦ wykład 1: wstęp - organizacja wykładu, skąd przyszliśmy, dokąd zmierzamy...

✦ wykład 2 i 3: podstawowe rozkłady prawdopodobieństwa, testy parametryczne i nieparametryczne

✦ wykłady 4-7: statystyka bayesowska

✦ modele Markowa, symulacje stochastyczne, próbnik Gibbsa, MCMC....



✦ wykłady 8,9: modelowanie

✦ estymacja parametów modelu

✦ wykłady 10-12: modele liniowe, analiza wariancji

✦ ANOVA, regresja liniowa, ...

✦ wykłady 13-14: projektowanie eksperymentów



Statystyczna analiza danychaniag/SAD_2012/sad_wstep.pdfSTATYSTYCZNA ANALIZA DANYCH piątek, 10...

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Transcript of Statystyczna analiza danychaniag/SAD_2012/sad_wstep.pdfSTATYSTYCZNA ANALIZA DANYCH piątek, 10...