1. Ameliorating Statistical Methodologies as
Genomic Data Burgeon:
Refined Proportional Odds Model with
Application to New Dravet Dataset
Ivan Rodriguez∗,⊥, †
Joseph C. Watkins, Ph.D.∗,⊥,§
∗The University of Arizona
⊥Department of Mathematics
†UROC-PREP/STAR Program
§Graduate Interdisciplinary Program in Statistics, Chair
August 5, Summer 2016

2. Focus
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 2 / 19

3. Focus
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 3 / 19

4. Research Overview
Motivation: ≈150,000 newborns diagnosed with genetic disease
annually (Nussbaum, McInnes, & Willard, 2007).
Challenge: making sense of this abundant data.
Objectives:
Match data and diagnosis by improving existing technique.
Apply model to new and exclusive dataset.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 4 / 19

5. Research Overview
Motivation: ≈150,000 newborns diagnosed with genetic disease
annually (Nussbaum, McInnes, & Willard, 2007).
Challenge: making sense of this abundant data.
Objectives:
Match data and diagnosis by improving existing technique.
Apply model to new and exclusive dataset.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 4 / 19

6. Research Overview
Motivation: ≈150,000 newborns diagnosed with genetic disease
annually (Nussbaum, McInnes, & Willard, 2007).
Challenge: making sense of this abundant data.
Objectives:
Match data and diagnosis by improving existing technique.
Apply model to new and exclusive dataset.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 4 / 19

7. Research Overview
Motivation: ≈150,000 newborns diagnosed with genetic disease
annually (Nussbaum, McInnes, & Willard, 2007).
Challenge: making sense of this abundant data.
Objectives:
Match data and diagnosis by improving existing technique.
Apply model to new and exclusive dataset.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 4 / 19

8. Research Overview
Motivation: ≈150,000 newborns diagnosed with genetic disease
annually (Nussbaum, McInnes, & Willard, 2007).
Challenge: making sense of this abundant data.
Objectives:
Match data and diagnosis by improving existing technique.
Apply model to new and exclusive dataset.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 4 / 19

9. Research Overview
Motivation: ≈150,000 newborns diagnosed with genetic disease
annually (Nussbaum, McInnes, & Willard, 2007).
Challenge: making sense of this abundant data.
Objectives:
Match data and diagnosis by improving existing technique.
Apply model to new and exclusive dataset.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 4 / 19

10. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

11. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

12. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

13. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

14. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

15. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

16. Methods: Ordinal Categorical Data Analysis
Clear ordering of categories.
Relevant example: disease severity.
Complications:
Assigning numeric values to categories.
Nonequidistance between categories.
Naïve solution: dichotomize ordinal outcome.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 5 / 19

17. Methods: Proportional Odds Model, General
Better method: the proportional odds model (McCullagh, 1980).
Extends binary logistic regression (Cox, 1958).
Celebrated method for ordinal data analysis (Bender & Grouven,
1998).
Applications: surveys, quality assurance, radiology, clinical research
(McCullagh, 1999).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 6 / 19

18. Methods: Proportional Odds Model, General
Better method: the proportional odds model (McCullagh, 1980).
Extends binary logistic regression (Cox, 1958).
Celebrated method for ordinal data analysis (Bender & Grouven,
1998).
Applications: surveys, quality assurance, radiology, clinical research
(McCullagh, 1999).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 6 / 19

19. Methods: Proportional Odds Model, General
Better method: the proportional odds model (McCullagh, 1980).
Extends binary logistic regression (Cox, 1958).
Celebrated method for ordinal data analysis (Bender & Grouven,
1998).
Applications: surveys, quality assurance, radiology, clinical research
(McCullagh, 1999).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 6 / 19

20. Methods: Proportional Odds Model, General
Better method: the proportional odds model (McCullagh, 1980).
Extends binary logistic regression (Cox, 1958).
Celebrated method for ordinal data analysis (Bender & Grouven,
1998).
Applications: surveys, quality assurance, radiology, clinical research
(McCullagh, 1999).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 6 / 19

21. Methods: Proportional Odds Model, General
Better method: the proportional odds model (McCullagh, 1980).
Extends binary logistic regression (Cox, 1958).
Celebrated method for ordinal data analysis (Bender & Grouven,
1998).
Applications: surveys, quality assurance, radiology, clinical research
(McCullagh, 1999).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 6 / 19

22. Methods: Proportional Odds Model, General
Better method: the proportional odds model (McCullagh, 1980).
Extends binary logistic regression (Cox, 1958).
Celebrated method for ordinal data analysis (Bender & Grouven,
1998).
Applications: surveys, quality assurance, radiology, clinical research
(McCullagh, 1999).
logit P(Yi ≤ j | Xi ) = θj − βT
Xi , j ∈ (1, . . . , J − 1),
logit(π) = log
π
1 − π
.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 6 / 19

23. Methods: Proportional Odds Model, Limitations
Great on paper, but not in practice.
Proportional odds assumption often violated (Long & Freese, 2006).
A standard workaround: modify the model.
Refine the latent variable.
Fine-tune the null hypothesis.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 7 / 19

24. Methods: Proportional Odds Model, Limitations
Great on paper, but not in practice.
Proportional odds assumption often violated (Long & Freese, 2006).
A standard workaround: modify the model.
Refine the latent variable.
Fine-tune the null hypothesis.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 7 / 19

25. Methods: Proportional Odds Model, Limitations
Great on paper, but not in practice.
Proportional odds assumption often violated (Long & Freese, 2006).
A standard workaround: modify the model.
Refine the latent variable.
Fine-tune the null hypothesis.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 7 / 19

26. Methods: Proportional Odds Model, Limitations
Great on paper, but not in practice.
Proportional odds assumption often violated (Long & Freese, 2006).
A standard workaround: modify the model.
Refine the latent variable.
Fine-tune the null hypothesis.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 7 / 19

27. Methods: Proportional Odds Model, Limitations
Great on paper, but not in practice.
Proportional odds assumption often violated (Long & Freese, 2006).
A standard workaround: modify the model.
Refine the latent variable.
Fine-tune the null hypothesis.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 7 / 19

28. Methods: Proportional Odds Model, Limitations
Great on paper, but not in practice.
Proportional odds assumption often violated (Long & Freese, 2006).
A standard workaround: modify the model.
Refine the latent variable.
Fine-tune the null hypothesis.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 7 / 19

29. Methods: Latent Variable
Variables that are inferred, not directly observed.
The focus is to make better inferences.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 8 / 19

30. Methods: Latent Variable
Variables that are inferred, not directly observed.
The focus is to make better inferences.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 8 / 19

31. Methods: Latent Variable
Variables that are inferred, not directly observed.
The focus is to make better inferences.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 8 / 19

32. Methods: Latent Variable
Variables that are inferred, not directly observed.
The focus is to make better inferences.
Y ∗
= βT
+ ε,
P(Y ≤ j | X) =
1
exp(βTX − θj) + 1
.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 8 / 19

33. Methods: Hypothesis Testing
Null versus alternative hypotheses: H0 against HA.
Traditionally, H0 is the status quo.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 9 / 19

34. Methods: Hypothesis Testing
Null versus alternative hypotheses: H0 against HA.
Traditionally, H0 is the status quo.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 9 / 19

35. Methods: Hypothesis Testing
Null versus alternative hypotheses: H0 against HA.
Traditionally, H0 is the status quo.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 9 / 19

36. Methods: Hypothesis Testing
Null versus alternative hypotheses: H0 against HA.
Traditionally, H0 is the status quo.
H0 : β1 = · · · = βq = 0.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 9 / 19

37. Methods: Hypothesis Testing
Null versus alternative hypotheses: H0 against HA.
Traditionally, H0 is the status quo.
H0 : β1 = · · · = βq = 0.
β = τξ, τ ∈ F,
Si = ξT
xi .
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 9 / 19

38. Methods: Hypothesis Testing
Null versus alternative hypotheses: H0 against HA.
Traditionally, H0 is the status quo.
H0 : β1 = · · · = βq = 0.
β = τξ, τ ∈ F,
Si = ξT
xi .
H0 : τ = 0,
P Y ≤ j | X =
1
exp(Sτ − θj) + 1
.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 9 / 19

39. Methods: Score Function
Allows for quantification of performance of model.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 10 / 19

40. Methods: Score Function
Allows for quantification of performance of model.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 10 / 19

41. Methods: Score Function
Allows for quantification of performance of model.
u(θ1, . . . , θJ−1, τ) = −
J
j=1
nj
i=1
Sij 1 − ψ θj − τSij − ψ θj−1 − τSij ,
ψ(t) =
1
1 + exp(−t)
.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 10 / 19

42. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

43. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

44. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

45. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

46. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

47. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

48. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

49. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

50. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

51. Methods: Simulations
Criteria: type I error frequency and power.
Algorithm:
1. Generate genotype data.
2. Obtain error terms.
3. Fix latent variables.
4. Produce ordinal categorical responses.
5. Estimate θj under modified H0.
6. Plug ˆθj into score function.
7. Receive p-values.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 11 / 19

52. Methods: Application
Response: Dravet syndrome patient severity.
Predictor: 12 stress-related single nucleotide polymorphisms.
Sample size: 22 relatively isolated Japanese observations.
Categories: 2, mild and severe.
Other data: sex, status, IQ, allele count.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 12 / 19

53. Methods: Application
Response: Dravet syndrome patient severity.
Predictor: 12 stress-related single nucleotide polymorphisms.
Sample size: 22 relatively isolated Japanese observations.
Categories: 2, mild and severe.
Other data: sex, status, IQ, allele count.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 12 / 19

54. Methods: Application
Response: Dravet syndrome patient severity.
Predictor: 12 stress-related single nucleotide polymorphisms.
Sample size: 22 relatively isolated Japanese observations.
Categories: 2, mild and severe.
Other data: sex, status, IQ, allele count.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 12 / 19

55. Methods: Application
Response: Dravet syndrome patient severity.
Predictor: 12 stress-related single nucleotide polymorphisms.
Sample size: 22 relatively isolated Japanese observations.
Categories: 2, mild and severe.
Other data: sex, status, IQ, allele count.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 12 / 19

56. Methods: Application
Response: Dravet syndrome patient severity.
Predictor: 12 stress-related single nucleotide polymorphisms.
Sample size: 22 relatively isolated Japanese observations.
Categories: 2, mild and severe.
Other data: sex, status, IQ, allele count.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 12 / 19

57. Methods: Application
Response: Dravet syndrome patient severity.
Predictor: 12 stress-related single nucleotide polymorphisms.
Sample size: 22 relatively isolated Japanese observations.
Categories: 2, mild and severe.
Other data: sex, status, IQ, allele count.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 12 / 19

58. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

59. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

60. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

61. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

62. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

63. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

64. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

65. Results: The Proposed Model Is Successful
Type I error and power comparable to:
Sequence kernel association test (Wu et al., 2011).
Optimized sequence kernel association test (Lee et al., 2012).
In terms of power, outperforms:
Variable threshold test (Price et al., 2010).
Cohort allelic sums test (Morgenthaler & Thilly, 2007).
Cumulative minor-allele test (Zawistowski et al., 2010).
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 13 / 19

66. Results: Stress and Dravet Are Intricately Correlated
Rare phenotypes prevalent for young severe patients.
Several genes protect or exacerbate Dravet.
Likely varies on case-by-case basis.
Stress-Dravet link contingent on sample heterogeneity.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 14 / 19

67. Results: Stress and Dravet Are Intricately Correlated
Rare phenotypes prevalent for young severe patients.
Several genes protect or exacerbate Dravet.
Likely varies on case-by-case basis.
Stress-Dravet link contingent on sample heterogeneity.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 14 / 19

68. Results: Stress and Dravet Are Intricately Correlated
Rare phenotypes prevalent for young severe patients.
Several genes protect or exacerbate Dravet.
Likely varies on case-by-case basis.
Stress-Dravet link contingent on sample heterogeneity.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 14 / 19

69. Results: Stress and Dravet Are Intricately Correlated
Rare phenotypes prevalent for young severe patients.
Several genes protect or exacerbate Dravet.
Likely varies on case-by-case basis.
Stress-Dravet link contingent on sample heterogeneity.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 14 / 19

70. Results: Stress and Dravet Are Intricately Correlated
Rare phenotypes prevalent for young severe patients.
Several genes protect or exacerbate Dravet.
Likely varies on case-by-case basis.
Stress-Dravet link contingent on sample heterogeneity.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 14 / 19

71. Discussion
Preliminary evaluation of model and dataset analysis.
Severe genetic disease modifying genes determine quality-of-life.
Identification of modifying genes is paramount.
Provides impetus for new medication and treatment.
Personalized care will rise with genomic information.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 15 / 19

72. Discussion
Preliminary evaluation of model and dataset analysis.
Severe genetic disease modifying genes determine quality-of-life.
Identification of modifying genes is paramount.
Provides impetus for new medication and treatment.
Personalized care will rise with genomic information.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 15 / 19

73. Discussion
Preliminary evaluation of model and dataset analysis.
Severe genetic disease modifying genes determine quality-of-life.
Identification of modifying genes is paramount.
Provides impetus for new medication and treatment.
Personalized care will rise with genomic information.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 15 / 19

74. Discussion
Preliminary evaluation of model and dataset analysis.
Severe genetic disease modifying genes determine quality-of-life.
Identification of modifying genes is paramount.
Provides impetus for new medication and treatment.
Personalized care will rise with genomic information.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 15 / 19

75. Discussion
Preliminary evaluation of model and dataset analysis.
Severe genetic disease modifying genes determine quality-of-life.
Identification of modifying genes is paramount.
Provides impetus for new medication and treatment.
Personalized care will rise with genomic information.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 15 / 19

76. Discussion
Preliminary evaluation of model and dataset analysis.
Severe genetic disease modifying genes determine quality-of-life.
Identification of modifying genes is paramount.
Provides impetus for new medication and treatment.
Personalized care will rise with genomic information.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 15 / 19

77. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

78. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

79. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

80. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

81. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

82. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

83. In Conclusion
Problems:
The proportional odds model can be improved.
The stress-Dravet link is not known.
Takeaways:
The proposed model is formidable.
A new stress-Dravet link has been established.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 16 / 19

84. Acknowledgments
Joseph C. Watkins, Ph.D.
Miao Zhang, M.S.
Michael Hammer, Ph.D., and the Hammer Lab.
Andrew Huerta, Ph.D. and Reneé Reynolds, M.A.
Andrew Carnie, Ph.D.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 17 / 19

85. Acknowledgments
Joseph C. Watkins, Ph.D.
Miao Zhang, M.S.
Michael Hammer, Ph.D., and the Hammer Lab.
Andrew Huerta, Ph.D. and Reneé Reynolds, M.A.
Andrew Carnie, Ph.D.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 17 / 19

86. Acknowledgments
Joseph C. Watkins, Ph.D.
Miao Zhang, M.S.
Michael Hammer, Ph.D., and the Hammer Lab.
Andrew Huerta, Ph.D. and Reneé Reynolds, M.A.
Andrew Carnie, Ph.D.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 17 / 19

87. Acknowledgments
Joseph C. Watkins, Ph.D.
Miao Zhang, M.S.
Michael Hammer, Ph.D., and the Hammer Lab.
Andrew Huerta, Ph.D. and Reneé Reynolds, M.A.
Andrew Carnie, Ph.D.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 17 / 19

88. Acknowledgments
Joseph C. Watkins, Ph.D.
Miao Zhang, M.S.
Michael Hammer, Ph.D., and the Hammer Lab.
Andrew Huerta, Ph.D. and Reneé Reynolds, M.A.
Andrew Carnie, Ph.D.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 17 / 19

89. Acknowledgments
Joseph C. Watkins, Ph.D.
Miao Zhang, M.S.
Michael Hammer, Ph.D., and the Hammer Lab.
Andrew Huerta, Ph.D. and Reneé Reynolds, M.A.
Andrew Carnie, Ph.D.
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 17 / 19

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Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 18 / 19

91. Questions?
Ivan Rodriguez: ivanrodriguez@email.arizona.edu .
Ivan Rodriguez (The University of Arizona) Ameliorating Statistical Methodologies August 5, 2016 19 / 19