Immune response studies

BISP.6 - Bressanone - June 18th-20th 2009

Mixtures, clustering, spatial [ & dynamic ] point processes and big data sets

Mike WestDepartment of Statistical Science

Duke University


cellular phenotypes in vaccine adjuvant studies

Immune response studies

Lymphocyte differentiation: Multiple cell types ~ 15 cell surface marker proteins (+)

<V705-A>: CD8 Q705

<G7

10-A

>: C

D4 C

Y55P

E

57.8

36.3

0.79

i. cell subtyping

ii. spatio-temporal response


i. Cell subtyping: Flow cytometry data

LASER

OPTICS

ELECTRONICSFLUIDICS

Modest p, large n <V705-A>: CD8 Q705

<G7

10-A

>: C

D4 C

Y55P

E

57.8

36.3

0.79

Cell subset identification

Comparison across times, interventions

Comparison across patients

Comparison across treatmentsTreatment

Patient 1

Dataset 1

Cell subset 1 Cell subset n

Dataset n

Patient nMultiple experiments … - really big data - characterise data distributions - comparisons


Mixtures for flow cytometry data

mixture models (TDP version)Chan et al 2008,9

MCMC Bayesian EM

FSC-W

FSC-

H

88.3

<Violet G-A>: CD3 Amcyan<V

iole

t H-A

>: v

Amin

e CD

14PB

CD1

9 PB

41.4

Live T-cells


Non-Gaussian clusters/cell subtypesFlexible mixture model:

Subtypes: groups of componentsModal grouping

Modal clustering for non-Gaussian mixtures

Mode trace: fast iterative id of modes


Mixtures of mixtures

Cluster mixture models (TDP version)Cao & West 1993; Merl et al 2009

Cluster “anchors”


cluster locations

data by cluster

components

CFSE data: 3 of 7 dimensions: MCMC snapshot

helper Ts

cytotoxic Ts

dead cells

other Ts


Specification & computation

MCMC iteratesa. Reallocate data to components:

One “big mixture of normals”

b. Sufficient statistics: resample normal parameters

c. Probabilities: - Counts of data in clusters

- Counts in components within clusters

BIG data, many components: Exploit parallelisation in modules a, b, c

shared memory multi-threading in multi-core, multi-cpu computer

cluster: MPI interface

Prior control: Anchor cluster locations

Tie component means “close” to anchors

Stickiness: New MCMC - Split/merge? Component swapping between clusters

MAP/Bayesian EM


Inferences: Comparisons

Common interest: rare cell subsets

(e.g. antigen-specific cells << 1%)

Changes in relative abundance Changes in marker levels

Mouse cell line: HIV adjuvants


Marker 1

Mar

ker 2

Variable selection: Discriminative information

Measure fewer variables? Subtype characterising variables?

Redundant variables? Discrimination confusing variables?

discriminators:

discriminatory information: - high is good - finds useful & useless variables - ranks subsets

- involves “concordances” :


CFSE discriminative information analysis

Change in information by subtype: Drop one marker

Lose irrelevant markers: no loss in false pos/neg ratesSimpler, efficient marker subset analysis


Technology adoption: Many routine analyses

ComputationImplementation

HIV/AIDSCancer vaccines

Tropical diseases



ii. Spatial responses: Fluorescent histology/microscopy

Example: Mice lymph nodes: Compare immune response to various treatments

3 or 4 fluorescent tags – stain cell types: e.g. B220, IgM, GL-7

Many exploratory questions: Regional concentrations of types?

Overall levels of types?Interactions?

Germinal centres: relative concentrations of GL7/B220

Etc

Different time points

PA+Alum, day 1


4 cell types/4 colour channels: several treatments, several dayspixels: grid to small pixel regions

PA alone

B220 IgM

CD4 GL7

Immunofluorescent histology: BIG data

106 ¡ 108

Cells: model 2D (3D) spatial intensity hugely inhomogeneous

Noisy fluorescence

Flexible model to characterise

... intensity surfaces, … uncertain overall levels,

… noise & signal fluorescence,… compare cell types


Inhomogeneous Poisson process model

Point process

Measured fluorescence levels

B cells: GFP/B220, day 1

Intensity function

Latent


Spatial mixture & measurement model

Truncated Dirichlet process mixture [ Kottas & Sanso 07; Ji et al 09 ]

Data: noise/background vs. signal Extend “usual” priors:

- random effects- Pareto tails


Fluorescence intensity signal & noise model

Fluorescence intensity data

Mixture model - noise vs. signal

signal

noise


Components of posterior

Grid: (small) pixel regions: area

MCMC: conditionals

Gaussian mixture: Signal only observationsLarge K, large NBlock Gibbs sampler for TDP mixtures

f


MCMC progression & inferences

Signal/noise events? Pr(Signal/noise events)?

Intensity function …

… estimate…Intensity function …

B220/day 1

B220/day 11


Posterior summaries and explorations

(b) IgM(a) B220

(c) CD4 (*) B220/(B220+IgM)

Quantified germinal centres


Computation: Multi-core, multi-thread; cluster

Large K, large N mixture model

Heavy computation: Configuration indicators,

Gaussian component parameter updates

Parallelizable steps within MCMC

Parallel sub-images: conditional mixture in sub-image

a) allocate pixel to sub-image b) … then to component in sub-mixture

… use a) only for pixels “near boundaries” - reduces computation


3D


Dynamic spatial process

Confocal microscopy: Imaging fluorescence in situ

Model: quantify directional(?) drifts in intensity

Above model at each time:Intensity dynamic

- Dynamic models for Gaussian parameters- Generalized Polya Urn Scheme for random

partitions/pixel-component configurations[ Matt Taddy’s talkCaron, Davey, Doucet, 07, UAIC. Ji et al, 09 forthcoming ]

Sequential MC: Particle filtering


Dynamic spatial process


Team & Links

Lynn Lin, PhD student

Quanli Wang, comp.guru

Dan Merlpostdoc > Livermore

Cliburn ChanImmunology & Comp Bio

Chunlin Ji, PhD student

Tom KeplerImmunology & Comp Bio

Ioanna Manolopolou postdoc

Chan et al, Cytometry A, 2008Ji et al, BA 2009

New & software: www.stat.duke.edu/~mw

Documents

Immune response studies