Discrete Structural Statistics:
A Data-centric Framework for
Empowering Cancer Science
離散構造統計学の創出と癌科学への展開

Koji Tsuda (U. Tokyo)
Kenji Kadomatsu (Nagoya U.)
Ichiro Takeuchi (Nagoya Inst. Tech.)
Jun Sese (AIST)
Ryo Yamada (Kyoto U.)
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Publishing	  system	  in	  life	  sciences
Hypotheses	  Set

Gene	  2	  causes	  disease
Gene	  3	  causes	  disease…
Gene	  N	  causes	  diseaseSignificant?

Statistical	  Test

Gene	  1	  causes	  disease	  Data×◎

OK,	  publish!

×◎

OK,	  publish!
2Reproducibility Crisis!
(and statistics is to blame)• Biological	  results	  reported	  in	  journals	  cannot	  be	  reproduced– Bayer:	  could	  not	  reproduce	  43	  of	  67	  studies– Amgen:	  could	  not	  reproduce	  47	  of	  53	  studies

J.	  Ioannidis	   (Stanford)

Data	  that	  are	  multidimensional	  (ie contain	  manyfeatures)	  are	  particularly	  at	  risk	  of	  false	  positives	  and	  overfitting,	  particularly	  when	  analyzed	  by	  inexperienced	  or	  untrained	  analysts.	  
(Lancet,	  2014)3

Curse	  of	  Dimensionality	  in	  Testing
New	  Machines

Huge increase in explanatory variablesNo increase in examples

False	  positive	  more	  likely	  →Have	  to	  apply	  stricter	  criterion	  →Fewer	  discovery	  (!)
cheating
4

BAD	  NEWS: Combinatorial	  Hypotheses
N	  Genes

M Environments

Gene	  1	  causes	  disease	  Environment	  1	  causes	  disease	  Gene	  2	  causes	  disease

Environment	  2	  causes	  disease

Gene	  3	  causes	  disease

Environment	  3	  causes	  disease…

…

Gene	  N	  causes	  disease

Environment	  M	  causes	  disease

In	  Environment	  i,	  Gene	  j	  causes	  disease	  NM	  hypotheses
fromN+M	  variables	  5

BAD	  NEWS: Combinatorial	  Hypotheses
N	  Genes

M Environments

Gene	  1	  causes	  disease	  Environment	  1	  causes	  disease	  Gene	  2	  causes	  disease

Environment	  2	  causes	  disease

Gene	  3	  causes	  disease…
Gene	  N	  causes	  disease

Hypothesis
Explosion	  In	  Environment	  i,	  Gene	  j	  causes	  disease	  Environment	  3	  causes	  disease…

Environment	  M	  causes	  disease

NM	  hypotheses
from
N+M	  variables	  6

Good statistical test with stronger detection power= better estimation of false positive probability
Existing	  Test

Existing	  Test

False	  Positive	  Probability

No	  significant	   genes	  foundGood	  Test	  True	  (Unknown)	  Good	   Test
Genes	  X,Y,Z	  found	  significant!

Number	  of	  Hypotheses
7

Discrete Algorithms for	  Estimating	  Accurate False Positive Probability• Tarone-­‐Bonferroni test
– Estimating	  effective	  number	  of	  hypothesis– Discrete	  counting• Westfall-­‐Young test
– Find best hypothesis
under randomly	  permuted	  labels	  – Discrete	  optimization• Discrete	  Algorithms– SAT-­‐based	  approximate	  counting	  (WISH)– Binary	  Decision	  Diagrams– Closure	  Operation– Reverse	  Search– Pattern	  Mining– Sampling	  8

CREST	  Project	  Overview
Hypotheses	   SetDiscrete	  Mathematics
ZDD,	  SAT,	  WISH	  etcStatistics
FDR,Permutation

Discrete	  Structural
Statistics	  Structure	  Introduced	  ⊥⊥Cancer	  Science	  Closure	  Operator
Statistical	  Pruning
9First	  Step	  Taken:	  Limitless	  Arity Multiple	  testing	  Procedure	  (LAMP)	  Terada,	  Okada-­‐Hatakeyama,	  Tsuda and	  Sese,	  PNAS (2013)• Effective	  number	  of	  hypotheses	  counted	  by	  itemset mining• Big	  improvement	  in	  detection	  power– Combination	  of	  eight	  genes	  found	  significant	  in	  breast	  cancer• Much	  to	  improve– Slow	  – Compatible	  with	  limited	  types	  of	  statistical	  tests– Cannot	  utilize	  domain	  information	  (e.g.,	  regulatory	  pathways)
OCT1>18-Motif

CTTTAAR>1>1 C/EBP
0.0137 >1EVI1

EGF>10.5nM NFAT
15min>1
LEF1>1
GR>1FOXO4>1
1.0
0.5
0.05
0.025
0.010Can	  Statistics	  cure	  Neuroblastoma?
• One	  in	  5000	  new	  born	  babies• 20%	  cure	  autonomously• No	  driver	  mutations	  known• Combinatorial	  anomaly	  in	  differentiation	  program	  ?
11

Comprehensive  Measurement  • Genomics:  Mutations,  chromosomal  aberrations,   SNPs,  etc.
• Epi-‐‑‒genomics:  DNA  methylation,  Histone  modification,  etc.
• Transcriptomics:  mRNA,  non-‐‑‒coding  RNA,  etc.

Discrete  Structural Statistics

Extraction  of  factors/combinations  vital  for  carcinogenesis  and  de-‐‑‒carcinogenesis

Interventional  studiesin  vitro experiments→→in  vivo experiments-‐‑‒ Cell  growth-‐‑‒ Cell  death-‐‑‒ Differentiationetc.

-‐‑‒ Knockout/Transgenic  mice-‐‑‒ Tumorigenesis-‐‑‒ Drug  treatment
etc.  
12

Research	  Groups	  and	  Collaborators
Koji	  Tsuda

Toshikazu	  Ushijima	  • University	   of	  Tokyo,	  Professor• Statistics,	   Discrete	   Algorithms,	  Bioinformatics（National	  Cancer	  Center）

Jun	  Sese

（National	  Cancer	  Center）• AIST,	  Senior	   Research	   Scientist• Data	   Mining,	   Sequence	   Analysis

Takehiko Kamijo

Ryo	  Yamada

Miki	  Ohira• Kyoto	  University,	  Professor• Statistics（Saitama	  Cancer	  Center）

Ryuichi Sakai（Saitama	  Cancer	  Center）

Ichiro	  Takeuchi• Nagoya	  Institute	  of	  Technology,	   Professor• Machine	   Learning,	   Medical	   Informatics

Kenji	  Kadomatsu• Nagoya	  University,	  Professor• Cancer	   Science,	   Molecular	   Biology

13

Conclusion• Statistics:	  BEST	  strategy	  to	  improve	  scientific	  productivity
ENGINE:
High-­‐throughput
Measurement
Devices

BRAKE:
Statistics• Selective Inference / Adaptive Data Analysis• High Performance Computing

14

高次交互作用モデルの Selective Inference
鈴村真也，中川和也，津田宏治，竹内一郎（津田 CREST チーム）

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▶

高次交互作用モデル（cf. パターンマイニング）
▶

線形モデル

y = β1 x1 + β2 x2 + β3 x3▶

2 次交互作用モデル
y = β1 x1 + β2 x2 + β3 x3 + β12 x1 x2 + β13 x1 x3 + β23 x2 x3▶

3 次交互作用モデル
y = β1 x1 + β2 x2 + β3 x3 + β12 x1 x2 + β13 x1 x3 + β23 x2 x3 + β123 x1 x2 x3▶

Selective Inference（新しいタイプの統計的検定）▱㆑㸪⤒㦂௬ㄝᑐ㇟௬ㄝ௬ㄝ᳨ᐃ

ᑐ㇟

昔からの統計的検定,௬ㄝ᳨ᐃ

ࣅࢵࢢࢹ࣮ࢱࢧࣥࣉࣜࣥࢢ௬ㄝ⏕ᡂ
E\ᶵᲔᏛ⩦

ࢹ࣮ࢱ཰㞟ࢹ࣮ࢱ

Selective Inference
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