Analysis of the NonHuman Primate Study: Update

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Analysis of the Non-Human Primate Study Update
David Madigan Rutgers University
stat.rutgers.edu/madigan
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Goal of the Analysis

• Are measurable aspects of the state of the immune
  system predictive of survival?
• Problem hundreds of different assay timepoints
  but fewer than one hundred macaques
• Initial descriptive analysis
• Regularized predictive modeling
• New functional decision tree modeling

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IgG
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ED50
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IFNeli
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SI
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IL4eli
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IFNm
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r_ED-IgG
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Logistic Regression Model

• Linear model for log odds of category membership

p(y1xi)
log ? bj xij bxi
p(y-1xi)

• Conditional probability model

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Maximum Likelihood Training

• Choose parameters (bj's) that maximize
  probability (likelihood) of class labels (yi's)
  given documents (xis)

• Tends to overfit
• Not defined if d gt n
• Feature selection

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Shrinkage Methods

• Feature selection is a discrete process
  individual variables are either in or out.
  Combinatorial nightmare.
• This method can have high variance a different
  dataset from the same source can result in a
  totally different model
• Shrinkage methods allow a variable to be partly
  included in the model. That is, the variable is
  included but with a shrunken co-efficient
• Elegant way to tackle over-fitting

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Ridge Logistic Regression
Maximum likelihood plus a constraint
Lasso Logistic Regression
Maximum likelihood plus a constraint
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s
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• L1 Logistic Regression
• complete imputation
• common weeks only (0,4,8,26,30,38,42,46,50)
• no interactions

IGG_38 -0.16 (0.17) ED50_30 -0.11
(0.14) SI_8 -0.09 (0.30) IFNeli_8 -0.07
(0.24) ED50_38 -0.03 (0.35) ED50_42 -0.03
(0.36) IFNeli_26 -0.02 (0.26) IL4/IFNeli_0 0.04
(0.36)
bbrtrain -p 1 -s --autosearch --accurate
commonBBR.txt commonBBR.mod
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• L1 Logistic Regression
• limited imputation
• common weeks only (0,4,8,26,30,38,42,46,50)
• no interactions

IGG_34 -0.16 ED50_30 -0.06 SI_8 -0.03
bbrtrain -p 1 -s --autosearch --accurate
commonBBRreduced.txt commonBBRreduced.mod
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Tree Models

• Easy to understand recursively divide predictor
  space into regions where response variable has
  small variance
• Can model complex interactions
• Hypothesis generation

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Groups 1-3
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Work in Progress

• Data summary visualization ?
• Regularized logistic regression ?
• Characterize assay trajectories rather than
  individual time points ?
• Assessment of out-of-sample predictive
  performance ?
• Report ?