1. Unit of Statistical Genetics, Kyoto University
Statistical Analyses of Life Science and Pathology from Genomic Perspective
Unit of Statistical Genetics, Kyoto University
Ryo Yamada

2. Contents of Today
2 Genotypes and Phenotypes ～Data Records for Statistical Analyses～
1 Overview of Statistical Methods

3. Goals of Today Get a perspective covering many topics .
Grab the idea of each topics. Do not attempt to understand their details.
Make a list of terms some of which you might learn further after today’s lecture.
Understand some ideas appear in multiple analysis settings. Multiple basic ideas are combined to analyze specific tasks in various settings.

4. Overview of Statistical Methods

5. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

6. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

7. Quality Control of Noisy High-Throughput Data
Systematic errors/ biases; samples, reagents, date/machine/personnel effects
How to Correct or control the noises
Outsider detection
Transformation of all records with a function
Normalization for “locational effects”
“Control samples”

8. Outsider detection

9. Transformation of all records with a function
Genomic control
for
GWAS
Preprocessing Micorarray Data
Median-based correction
Log-transformation

10. Normalization for “locational effects”
Tendency should be considered.
Batch effects should be considered.
Non-data-driven
Data-driven

11. Quality Control of High-Throughput Data Correction/control
Systematic errors/ biases; samples, reagents, date/machine/personnel effects
Correction/control
Outsider detection
Transformation of all records with a function
Normalization for “locational effects”
“Control samples”

12. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

13. Tests, Estimation/Inference, Classification/Clustering
Significance, Error Controlling, Multiple-testing issue
Estimation/Inference
Interval, Models, Bayes
Classification/Clustering
Unsupervised Learning vs. Supervised Learning

14. Tests, Estimation/Inference, Classification/Clustering
Significance, Error Controlling, Multiple-testing issue
Estimation/Inference
Interval, Models, Bayes
Classification/Clustering
Unsupervised Learning vs. Supervised Learning

15. Multiple Comparison
P-value vs. Q-value

16. Multiple Comparison
Almost all hypotheses are NULL

17. Small p-values are likely when testing many hypotheses
1 test : Uniform between 0 and 1
10 tests : Minimum p should be close to 0, or around 0.1
100 tests : Closer to 0, or around 0.01 …

18. Uniform distribution

19. 2 tests
How do smaller p values distribute? p2 p1

20. Minimum p-value distribution
Mean
2^10
Min-p may take quite larger value than the mean.
In many cases, min-p value is smaller than the mean.
Such small value are not rare.

21. Minimum p-value distribution
1,2,4,8,… ^6
1,2,4,8,… ^6

22. NON-NULL, FDR (False Discovery Rate)
Many hypotheses are NON-NULL, or Almost all hypotheses are NON- NULL

23. P-value n <- 2^(0:20) n.iter <- 10^5
minps <- matrix(0,n.iter,length(n))
for(i in 1:length(n)){
ps <- matrix(runif(n[i]*n.iter),ncol=n[i])
minps[,i] <- apply(ps,1,min) }
boxplot(minps)
boxplot(log(minps,10))
hist(minps[,11],main="2^10")
N <- 9000
n <- 1000
K <- rchisq(N,1)
k <- rchisq(n,1,ncp=6)
hist(c(K,k),density=15)
hist(K,density=17,col=3,add=TRUE)
hist(k,add=TRUE,col=2,density=21)
P <- pchisq(K,1,lower.tail=FALSE)
p <- pchisq(k,1,lower.tail=FALSE)
hist(c(P,p),density=15)
hist(p,density=21,col=2)
hist(P,density=17,add=TRUE,col=3)
Pp <- c(P,p)
col <- c(rep(1,N),rep(2,n))
ord <- order(Pp)
plot(Pp[ord],col=col[ord],pch=20,cex=0.1,type="h")
plot(Pp[ord],col=col[ord],pch=20,cex=0.1,type="h",ylim=c(0,0.1),xlim=c(0,3*10^3))

24. Combination of two distributions
Uniform p-values
Small p-values

28. Pick smaller p-values. Threshold value should be changed for the ranks of p-values. The fraction of “true positives” is controlled.

29. Large-scale inference
When you observed many at once, their distribution is informative.
The estimates of each observation using the information are different from the estimates not using the information.
q-value of FDR is one type of such estimates.
Use information of distribution when observed many together
Empirical Bayes

30. Tests, Estimation/Inference, Classification/Clustering
Significance, Error Controlling, Multiple-testing issue
Estimation/Inference
Interval, Models, Bayes
Classification/Clustering
Unsupervised Learning vs. Supervised Learning

31. Estimation/Inference
Models, Parameters, Interval, Bayes
Uniform p-values
Small p-values
Assuming the mixture of two distributions;
This is a model.

32. Estimation/Inference
Samples　→　Point estimates, Interval estimates
Sample distribution, Theoretical estimates, unbiased estimates,…

33. Estimation/Inference
Samples　→　Point estimates, Interval estimates
Sample distribution, Theoretical estimates, unbiased estimates,…
The statement “The star’s weight is between a and b” will be right 9 times out of 10 times.

34. Estimation/Inference
Samples　→　Point estimates, Interval estimates
Sample distribution, Theoretical estimates, unbiased estimates,…
Frequentist
The statement “The star’s weight is between a and b” will be right 9 times out of 10 times.

35. Estimation/Inference
Frequentists　vs. 　Bayesians
Frequentists approaches are difficult for students not good at mathematics and their thinking processes are not easy to follow.
Instead Bayesian thinking processes tend to be easy to follow for many.

36. Estimation/Inference
Bayesian
Model has parameter(s)
Dara　＋　Model　→　Estimation of parameter value
Likelihood-based; Maximum-likelihood estimates; Interval estimates based on likelihood

37. Estimation/Inference
Frequentists　vs. 　Bayesians
Use both, not select one of them, it is the way in 21-st century
Bayesian approaches seem to be used more and more, because
Models became more complicated.
Computers’ assists・・・Complicated distributions can be handled simulationally
Large-scale data ・・・Empirical Bayes approaches can be applied

38. Estimation/Inference
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs
Estimation/Inference
Frequentists　vs. 　Bayesians
Use both, not select one of them, it is the way in 21-st century
Bayesian approaches seem to be used more and more, because
Models became more complicated.
Computers’ assists・・・Complicated distributions can be handled simulationally
Large-scale data ・・・Empirical Bayes approaches can be applied

39. Estimation/Inference
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs
Estimation/Inference
Frequentists　vs. 　Bayesians
Use both, not select one of them, it is the way in 21-st century
Bayesian approaches seem to be used more and more, because
Models became more complicated.
Computers’ assists・・・Complicated distributions can be handled simulationally
Large-scale data ・・・Empirical Bayes approaches can be applied

40. Estimation/Inference
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs
Estimation/Inference
Frequentists　vs. 　Bayesians
Use both, not select one of them, it is the way in 21-st century
Bayesian approaches seem to be used more and more, because
Models became more complicated.
Computers’ assists・・・Complicated distributions can be handled simulationally
Large-scale data ・・・Empirical Bayes approaches can be applied

41. Estimation/Inference
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs
Estimation/Inference
Frequentists　vs. 　Bayesians
Use both, not select one of them, it is the way in 21-st century
Bayesian approaches seem to be used more and more, because
Models became more complicated.
Computers’ assists・・・Complicated distributions can be handled simulationally
Large-scale data ・・・Empirical Bayes approaches can be applied

42. Estimation/Inference
Frequentists　vs. 　Bayesians
“Prior” distribution is necessary
What is the “appropriate prior”?

43. Success rate：No information at all
Somebody you don’t know at all will take an exam on which you have no information at all. How likely do you think (s)he will pass it?

44. Success rate：No information at all
Somebody you don’t know at all will take an exam on which you have no information at all. How likely do you think (s)he will pass it?
Jeffreys prior
One of non-subjective priors

45. Estimation/Inference
Frequentists　vs. 　Bayesians
Use both, not select one of them, it is the way in 21-st century
Large scale inference
Prior can be set based on the data set ~ empirical Bayesian

46. Tests, Estimation/Inference, Classification/Clustering
Significance, Error Controlling, Multiple-testing issue
Estimation/Inference
Interval, Models, Bayes
Classification/Clustering
Unsupervised Learning vs. Supervised Learning

47. Classification/Clustering
Multi-dimension/High-dimension, first.

48. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

49. Multi-dimensional/High-dimensional Data
No way to visualize high-dimensional data
Almost impossible for US to understand in high-dimensional data themselves

50. Multi-dimensional/High-dimensional Data
How many dimensions can we handle?
2D space or 3D space
Extra dimensions
Gray/Color scale
Arrows
Time

51. Multi-dimensional/High-dimensional Data
Dimension reduction
Pick up 2 or 3 dims seemingly important, then visualization is easy and we feel we can understand them.

52. Multi-dimensional/High-dimensional Data
Dimension reduction
Pick up 2 or 3 dims seemingly important, then visualization is easy and we feel we can understand them.
PCA (Principal Component Analysis)

53. Multi-dimensional/High-dimensional Data
Dimension reduction
Pick up 2 or 3 dims seemingly important, then visualization is easy and we feel we can understand them.
Only few dims are truly meaningful and all the others are noize. Pick the true dims.

54. Multi-dimensional/High-dimensional Data
Dimension reduction
Pick up 2 or 3 dims seemingly important, then visualization is easy and we feel we can understand them.
Only few dims are truly meaningful and all the others are noize. Pick the true dims.
LASSO, Compression sensing

55. Multi-dimensional/High-dimensional Data
Space is high dimensional but data is low
Manifold learning
Put data into higher dimensional space and pull them back to low dim space.

56. High-dimensionality
Many genes, many biomarkers, many features

57. Multi-dimensional/High-dimensional Data
Life-science data are high- dimensional
Number of observed items are huge.
But the items are mutually strongly correlated , and their dimension is much smaller in reality.
FACS
Ethnic diversity

58. Multi-dimensional/High-dimensional Data
Objects with low dimensions in higher dimensional space
Topology

59. Multi-dimensional/High-dimensional Data
Objects with low dimensions in higher dimensional space
Topology
Graph, network and topology

60. Multi-dimensional/High-dimensional Data
Graph: Itemize and connect items with relation
Pairwise relations are cared.

61. Multi-dimensional/High-dimensional Data
Graph: Itemize and connect items with relation
Pairwise relations are cared.
No care for trio-wise or higher relations.

62. Multi-dimensional/High-dimensional Data
Graph and its matrix representation and linear algebra

63. Multi-dimensional/High-dimensional Data
Graph and its matrix representation and linear algebra
Graph tends to be sparse
… Sparse analysis

64. Multi-dimensional/High-dimensional Data
Two important features
No “common” individuals
Sparse

65. High-dimensionality No commons 3.14 / 4 = 0.785
Central area : a sphere in a cubic
3.14 / 4 = 0.785

66. High-dimensionality Sparse
To estimate density, you need reasonable number of samples per small cubic volume, but…
Dim = 1 : 0.1
Dim = 2 : 0.01
Dim = 3 : 0.001 ….
Dime = 6 :

67. High-dimensionality Quite spacious, but reasonably dense distribution.
Distribution should be low dimensional.

68. Multi-dimensional/High-dimensional Data
Life-science data are high- dimensional
Number of observed items are huge.
But the items are mutually strongly correlated , and their dimension is much smaller in reality.
FACS
Ethnic diversity

69. Low dimensional distribution in higher dimensional space and its local density
Regular density estimation method does not work.
Small cubic are still spacious in high dimensional space
How to estimate local density
k-nearest neighbor method
In graph theory, similar idea is applicable.
Minimum-spanning tree

70. Sparse in highly dimensional space

71. Sparse in highly dimensional space
How sparse?
One-dimensional manifolds
But significant variance

72. Sparse in highly dimensional space
How sparse?
One-dimensional manifolds
But significant variance

73. Sparse in highly dimensional space
How sparse?
One-dimensional manifolds
But significant variance
Clustering

74. Tests, Estimation/Inference, Classification/Clustering
Significance, Error Controlling, Multiple-testing issue
Estimation/Inference
Interval, Models, Bayes
Classification/Clustering
Unsupervised Learning vs. Supervised Learning

75. Two types of clustering methods
Hierarchical
Non-hierarchical

76. Hierarchical Tree structure --- Graph, again
Its structure has information
Its structure is related with dimension
On the tree, distance is defined.
Some phenomena have reasons to be analyzed hierarchically.

77. Classification Separate something difficult to segregate.
J. Med. Imag. 1(3), (Oct 09, 2014). doi: /1.JMI

78. Classification/Clustering
Unsupervised Learning
Supervised Learning

79. Classification/Clustering
Unsupervised Learning
Supervised Learning
No teacher, but want to check whether the classification criteria is reliable or not.
Cross-validataion: One of resampling methods

80. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

81. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs
A bit more high-dimension issue

82. Small n Large p Sample size 100
Test association between a trait and expression of A gene.
N = 100, p = 1
Large n Small p
Test association between a trait and expression of MANY genes.
N = 100, p = 25000
Small n Large p

83. n = p then, you can find the perfect regression answer
q = a x; q = 3, x = 2 → Solvable
q1 = a x1 + b y1
q2 = a x2 + b y2 　→　Solvable
q1 = a x1 + b y1 + c z1
q2 = a x2 + b y2 + c z2　
q3 = a x3 + b y3 + c z3 →　Solvable

84. n << p One set of variables gives the perfect answer.
Another set of variables gives the perfect but different answer.
Which answer is the truth?
Closer fitting is not always the best.
AIC ～ Simpler model is better
LASSO, Sparse
The assumption k << n variables should be the answer, that is “prior” belief of Bayesian

85. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

86. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches　～　Monte-Carlo method
Others : Experimental Designs

87. Resampling Estimation based on samples Statistical significance
Jack-knife（Subsets）、Bootstrap(Replacement)
Statistical significance
Permutation ～ Exact probability
Cross-validation

88. Resampling Estimation based on samples Statistical significance
Jack-knife（Subsets）、Bootstrap(Replacement)
Statistical significance
Permutation ～ Exact probability
Cross-validation
Pseudo-random generators from computers

89. Pseudo-random number sequences
From uniform distribution
From other known distributions

90. Pseudo-random number sequences
From uniform distribution
From other known distributions
From arbitrary distributions … Gibbs sampling

91. Psuedo-random number sequences
From uniform distribution
From other known distributions
From arbitrary distributions … Gibbs sampling
Using Gibbs sampler,
Based on a stochastic model, estimate parameters of distributions and generate random values form the estimated distributions…
BUGS (Bayesian inference using Gibbs Sampling)

92. Example Fraction of red vs. green is repeatedly estimated
Based on the assumption that the red is non-central chi- square distribution and its non-central parameter value is repeatedly estimated.
Eventually estimate both unknown parameter values

93. Psuedo-random number sequences
From uniform distribution
From other known distributions
From arbitrary distributions … Gibbs sampling
Using Gibbs sampler,
Based on a stochastic model, estimate parameters of distributions and generate random values form the estimated distributions…
BUGS (Bayesian inference using Gibbs Sampling)
MCMC(Markov-Chain Monte-Carlo)
With Stan (a Bayesian estimation application)

94. Pseudo-random numbers, Monte-Carlo
Computer-driven methods

95. Roles of statistics/data science for genome/omics
Quality Control of Noisy High-Throughput Data
Tests, Estimation/Inference, Classification/Clustering
Multi-dimensional/High-dimensional Data
Random value-based approaches
Others : Experimental Designs

96. Experimental designs Various data sets
Using all kinds of them, what can we state?

98. Individual analysis/interpretation is tough enough Integration of them is tougher
Construct a model/assumption to integrate multiple sets
There are variations how to combine; order of combination, structure of combination ….
Use raw data sets from multiple resources.
Integrate primary outputs from each data set; so called meta-analyses
Narrow-sense meta-analyses only combine outputs from similar data sets analyses.
Difficulties are rooted to the heterogeneity among various data- resources.
Each data-resource has its own way of analysis. The variations among analyses make the integration difficult. Then, make each analysis method unified???

99. Some resources http://statgenet-kyotouniv.wikidot.com/MasterCourse2017
Its linked sites would be helpful to broaden and deepen your understandings of todays lecture.

100. Genotypes and Phenotypes ～Data Records for Statistical Analyses～

101. Childhood
Birth
Death
Phenome
Adolescent
Phenotypes
Aging
Development
Adult
Individual
Fertilized
Egg
Metabolites
Metabolome
Organ
Gametes
Cell
Tissue
Genes
Molecules
DNA
Proteins
Molecular
Genetics at
a glance
RNA
Proteome
Genome
Transcriptome
Omics
Heredity
Big Data
Phenotypic diversity
Stochastics
Genetic diversity
Statistics
Diversity

102. Genotypes and Phenotypes
Only one Spatio-Temporally
Heterogeneous Chronologically and Spatially

103. DNA/Chromosome modification
DNA,Genome, Consistent
Genotype
Phenotype
DNA/Chromosome modification
Transcriptome
Intermediate phenotype
Protein/Proteome
Phenotype/Phenome
Phenotypes of Individuals
Terminal phenotype

104. Time x Space of Individual
Cancer
Functional Somatic Mutations
Somatic Mosaicism
Parents
Germline
Fertilized Egg
Mutations

105. Diversity in Phenotypes
Easy to measure vs. Not-easy to measure
Representatives vs. Distribution itself
Many but Mutually Independent vs. Mutually Correlated

106. Representatives vs. Distribution itself
Temperature
A representative of molecular population
Independent and Identically Distributed Variable Observation
Good-shaped distribution→Representatives→Parametric approach
Bad-shaped distribution→Distribution itself →Non-parametric approach
One sample is a set of observations
One sample gives a distribution→Representatives enough?
ThermoFisher Scientific社

107. Many but Mutually Independent vs. Mutually Correlated
Multiple items mutually correlated.
Chronological data(time-line)
Shape data(space continuity)
Movement data(Time x Space)
Patten data(Informational axies)
横河電機
Nature 465, 918–921 (17 June 2010)

108. Estimation of parameter values
Data　＋　Model　
Estimation of parameter values ↓　

109. Summary for Genotypes and Phenotypes
Data　＋　Model　
Estimation of parameter values ↓　
To start your analysis
Record “Values”
“Values” take various shapes
“Simple value” : a Number
“Number”
Natural Number, Integer, Rationals, Reals, Complex,Vector,Matrix …
“Values” for analysis but not “Numbers”
Mathematical models
Biological phenomena have random errors
Stochastic models, Statistical models
Models have parameters, then
“Values” for parameters are “Numbers” again
“Simple values” are values of parameters in simple models.
Complex models and their parameters can be also values for your analysis.

110. Summary for Genotypes and Phenotypes
To start your analysis
Record “Values”
“Values” take various shapes
“Simple value” : a Number
“Number”
Natural Number, Integer, Rationals, Reals, Complex,Vector,Matrix …
“Values” for analysis but not “Numbers”
Mathematical models
Biological phenomena have random errors
Stochastic models, Statistical models
Models have parameters, then
“Values” for parameters are “Numbers” again
“Simple values” are values of parameters in simple models.
Complex models and their parameters can be also values for your analysis.

111. Contents of Today
Genotypes and Phenotypes ～Data Records for Statistical Analyses～
Overview of Statistical Methods