Statistical methods in detecting differential expressed genes, analyzing insertion tolerance for

109 Pages·2017·1.4 MB·English

by  Fangfang Liu

Iowa State University Capstones, Theses and
Graduate Theses and Dissertations
Dissertations
2015
Statistical methods in detecting differential
expressed genes, analyzing insertion tolerance for
genes and group selection for survival data
Fangfang Liu
Iowa State University
Follow this and additional works at:https://lib.dr.iastate.edu/etd
Part of theStatistics and Probability Commons
Recommended Citation
Liu, Fangfang, "Statistical methods in detecting differential expressed genes, analyzing insertion tolerance for genes and group
selection for survival data" (2015).Graduate Theses and Dissertations. 14514.
https://lib.dr.iastate.edu/etd/14514
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Statistical methods in detecting differential expressed genes, analyzing insertion
tolerance for genes and group selection for survival data
by
Fangfang Liu
A dissertation submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Major: Statistics
Program of Study Committee:
Peng Liu, Co-major Professor
Chong Wang, Co-major Professor
Kenneth Koehler
Dan Nettleton
Susan J. Lamont
Iowa State University
Ames, Iowa
2015
Copyright (cid:13)c Fangfang Liu, 2015. All rights reserved.
ii
To my family.
iii
TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
CHAPTER 1. GENERAL INTRODUCTION . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Next-Generation Sequencing Technology . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 RNA-seq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Tn-seq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 False Discovery Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Benjamini and Hochberg Method . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 The q-value Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.3 BFDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Non-parametric Bayesian method . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Dirichlet Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Gamma Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
CHAPTER 2. ZERO-INFLATED POISSON MODEL FOR INSERTION
TOLERANCE ANALYSIS OF GENES BASED ON TN-SEQ DATA . . . 10
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
iv
2.2.1 Tn-seq data at the level of locations . . . . . . . . . . . . . . . . . . . . 15
2.2.2 The ZIP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 The EM Algorithm for Maximum Likelihood Estimation . . . . . . . . . 17
2.2.4 Hypothesis Testing to Classify the Tolerance Status of Bacterial Genes . 21
2.3 A Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Analysis of a Real Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 APPENDIX: DERIVATION OF THE SECOND DERIVATIVE MATRIX . . . 27
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
CHAPTER3. ASEMI-PARAMETRICBAYESIANAPPROACHFORDIF-
FERENTIAL EXPRESSION ANALYSIS OF RNA-SEQ DATA . . . . . . 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 A Semi-parametric Bayesian Model . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 A Poisson-Gamma Mixture model . . . . . . . . . . . . . . . . . . . . . 40
3.2.2 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Prior Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Posterior Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Markov Chain Monte Carlo Simulation . . . . . . . . . . . . . . . . . . 45
3.3.2 Bayesian FDR for Multiple Hypothesis Testing . . . . . . . . . . . . . . 48
3.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 Simulation A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.2 Simulation B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.5 Real Maize Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.7 APPENDIX: GENERATE POSTERIOR CONDITIONAL DISTRIBUTIONS . 60
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
v
CHAPTER 4. A BAYESIAN METHOD FOR GROUP SELECTION IN
THE COX MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Prior Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.1 Prior for Λ (·) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
0
4.3.2 Prior for γ and θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.3 Criteria to Choose Parameter π . . . . . . . . . . . . . . . . . . . . . . . 75
4.4 Bayesian Group Selection Method . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Extension to the overlap case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.6 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6.1 Description of the Models for Simulating the Data . . . . . . . . . . . . 77
4.6.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.7 PRRS Survey Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.7.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
CHAPTER 5. GENERAL CONCLUSIONS . . . . . . . . . . . . . . . . . . . . 93
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
vi
LIST OF TABLES
Table 1.1 Outcomes when testing m null hypotheses. . . . . . . . . . . . . . . . . 3
Table 2.1 Summary statistics for the simulation study. ”True Diff” is the true
difference between mean abundance of normal genes and pseudogenes
(d = µ −µ ). ”Est Diff” is the estimated difference averaged over the
g g 0
100 repeated simulations, and ”SE” is the corresponding standard error. 30
Table 2.2 Summary of the IA3902 Tn-seq data. . . . . . . . . . . . . . . . . . . 30
Table 2.3 Statistical results for the regression coefficients (β’s) in the logistic re-
gression model for the insertion rate. P-values were obtained by testing
the null hypothesis that the corresponding regression coefficient equals
zero. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Table 2.4 The number of genes in each tolerance class at different FDR levels. . 31
Table 2.5 Leave-one-out analysis for the pseudogenes. We treated each one of the
pseudogenes as normal and classify this gene’s tolerance status while
using the remaining pseudogenes to estimate µ . Each row corresponds
0
to the result of a pseudogene when it was treated as a normal gene. . . 33
Table 4.1 A scale for interpretation of Bayes factor K introduced by Kass and
Raftery (1995). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Table 4.2 Results from Simulation A based on 20 replications: Overall average of
operating characteristics (standard deviations in parentheses). . . . . 81
vii
Table 4.3 Model error comparison for different methods under the simulation A.
The numbers before the parentheses are the average of model errors,
the numbers in the parentheses are the standard errors corresponding
to the model errors. The columns denoted with “Median” are results
when the posterior median is used as the estimated parameter βˆ , while
the columns denoted with “Mean” are results when the posterior mean
is used as the estimated parameter βˆ. . . . . . . . . . . . . . . . . . . 81
Table 4.4 Results from Simulation B based on 20 replications: Overall average of
operating characteristics (standard deviations in parentheses). . . . . 82
Table 4.5 Model error comparison for different methods under the Simulation B.
The numbers before the parentheses are the average of model errors,
the numbers in the parentheses are the standard errors corresponding
to the model errors. The columns denoted with “Median” are results
when the posterior median is used as the estimated parameter βˆ , while
the columns denoted with “Mean” are results when the posterior mean
is used as the estimated parameter βˆ. . . . . . . . . . . . . . . . . . . 82
Table 4.6 Thirty-three questions considered and their descriptions in the data
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Table 4.7 Use different priors for the indicator parameters γ ’s when different π is
k
chosen. Compare the selected questions and DIC using different values
of π. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Table 4.8 Marginalposteriormeanandstandarddeviationforvariableswithinthe
selected groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
viii
LIST OF FIGURES
Figure 2.1 Percentages of genes being classified into each of the three different
status (tolerant; hypo-tolerant and hyper-tolerant) for simulated data
plotted against true values of mean abundance (µ ). The mean for
g
pesudogenes µ was set to be 8 (indicated by the solid vertical bar). . 29
0
Figure 2.2 Volcano plot. The y axis corresponds to −log(pval+2−20) while the x
axis corresponds to estimated d ’s. . . . . . . . . . . . . . . . . . . . . 31
g
Figure 2.3 The left panel is histogram of the estimated µ ’s for the normal genes,
g
the right panel is for the subset of normal genes with estimated mean
lessthan20. Theverticaldottedlineinbothplotsdenotestheestimated
mean for pseudogenes (7.0552). . . . . . . . . . . . . . . . . . . . . . . 32
Figure 3.1 Histogram of the empirical estimated fold change (ρˆ ) from one maize
g
data set (Tausta et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . 43
Figure 3.2 Histogram for the logarithm of the simulated fold change ρ ’s. The
g
dashed line denotes the estimated density from the simulated log fold
changes and the sold line denotes the density plot for the mixtures of
the lognormal distributions with mean −log(4) and standard deviation
1 and the lognormal distributions with mean log(4) and standard devi-
ation 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
ix
Figure 3.3 ROC curves resulting from simulations A and B. For each level of FPR,
the TPRs were averaged across the 30 simulated datasets. The percent-
age annotated for each method is the average AUC, represented as the
percentage of the total area 0.1 in the range of FPR< 0.1, and the per-
centage in each set of parentheses is the standard error of the estimated
AUC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Figure 3.4 False discovery curves, depicting the average number of false positives
encounteredamongthetop-rankedgenesbythefiveevaluatedmethods.
Genes are ranked according to their P-value or posterior probabilities,
and the number of false positives are averaged over 30 simulated datasets. 54
Figure 3.5 Plot of the actual FDR versus the nominal level of FDR. Given a
method,theproportionoffalsediscoveriesamongthedeclaredDEgenes
wascalculatedforeachdatasetwhenwecontrolFDRatanominallevel,
and the actual FDR is calculated by averaging such proportions over 30
simulated datasets at each nominal FDR level. . . . . . . . . . . . . . . 55
Figure 3.6 Using the second simulated data set for simulation B (n = 3) to check
the effect of estimating FDR using different treatment conditions as the
baseline. The x axis is the estimated FDR using the first treatment
condition as the baseline while y axis denotes the estimated FDR using
thesecondoneasthebaseline. “Circle”denotesthecorrespondingtruly
non-DEgeneswhile“rectangle”denotesthecorrespondingtrulyDEgenes. 56
Figure 3.7 TheVenndiagramontheleftshowstheresultsofdetecteddifferentially
expressed genes from the Bayseq method, the AMAP test and our pro-
posed method when the FDR was controlled at 0.1%, the Venn diagram
on the right shows the corresponding results when FDR was controlled
at 1%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Figure 4.1 The scatter plot of DIC v.s. different values of parameter π in the prior
model (4.13) for γ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85