Predic'ng ALS Progression with Bayesian Addi've Regression Trees
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1 Predic'ng ALS Progression with Bayesian Addi've Regression Trees Lilly Fang and Lester Mackey November 13, 2012 RECOMB Conference on Regulatory and Systems Genomics
2 The ALS Predic'on Prize Challenge: Predict progression of ALS over 'me Dis'nguish fast from slow progressors Measure: ALS Func'onal Ra'ng Scale (ALSFRS) Score ranges from 0-40 Based on 10 ques'ons (Speech, Dressing, Handwri'ng, ) Rate of progression = slope of ALSFRS score The Data 918 training test pa'ents 12 months of data (demographic, ALSFRS, vital sta's'cs, lab tests) Time series: roughly monthly measurements 625 valida'on pa'ents Given first 3 months of data Goal: Predict future ALSFRS slopes for valida'on pa'ents Error metric: Root mean squared devia'on (RMSD)
3 Outline Featuriza6on Sta'c Data Temporal Data Modeling and Inference Bayesian Addi've Regression Trees Evalua6on BART Performance Feature Selec'on Model Comparison
4 Featuriza'on Goal: Compact numeric representa'on of each pa'ent Features will serve as covariates in a regression model Most extracted features will be irrelevant Rely on model selec'on / methods robust to irrelevant features
5 Featuriza'on Goal: Compact numeric representa'on of each pa'ent Features will serve as covariates in a regression model Most extracted features will be irrelevant Rely on model selec'on / methods robust to irrelevant features Sta6c Data Demographics Age, Race, Sex ALS History Time from onset, Site of onset Family History Mother, Father, Grandmother, Uncle 49 Categorical variables encoded as binary indicators
6 Featuriza'on Goal: Compact numeric representa'on of each pa'ent Features will serve as covariates in a regression model Most extracted features will be irrelevant Rely on model selec'on / methods robust to irrelevant features Time Series Data Repeated measurements of variables over 'me ALSFRS ques'on scores Alterna've ALS measures (forced and slow vital capacity) Vital signs (weight, height, blood pressure, respiratory rate) Lab tests (blood chemistry, hematology, urinalysis) Number and frequency of measurements vary across pa'ents
7 Featuriza'on Goal: Compact numeric representa'on of each pa'ent Features will serve as covariates in a regression model Most extracted features will be irrelevant Rely on model selec'on / methods robust to irrelevant features Time Series Data Compute summary sta's'cs from each 'me series Mean value, standard devia'on, slope, last recorded value, maximum value Compute pairwise slopes (difference quo'ents between adjacent measurements) Induces a deriva've 'me series Extract same summary sta's'cs
8 Featurizing Time Series Data ALSFRS Score Months
9 Featurizing Time Series Data ALSFRS Score Features extracted Mean = SD = Max = 40 Min = 37 Last = 37 etc Months
10 Featurizing Time Series Data ALSFRS Score Months Features extracted Mean = SD = Max = 40 Min = 37 Last = 37 Slope = - 1 etc.
11 Featurizing Time Series Data ALSFRS Score slope - 1 slope slope Months
12 Featurizing Time Series Data ALSFRS Score 40 Deriva6ve 6me series ALSFRS Slope 0 39 slope - 1 slope Months slope
13 Featurizing Time Series Data ALSFRS Score 40 Deriva6ve 6me series ALSFRS Slope 0 39 slope - 1 slope Months slope
14 Featurizing Time Series Data ALSFRS Score Deriva6ve 6me series ALSFRS Slope Features extracted Mean = - 1 SD = 1 Max = 0 Min = - 2 Last = - 2 Slope = etc Months - 2.5
15 Featurizing Time Series Data 435 temporal features extracted Problem: Missing data Average pa'ent missing 10% of features One pa'ent missing 55% of features! Missing values imputed using median heuris'c Problem: Outliers Nonsense values: Number of liters recorded as MDMD Units incorrectly recorded Wrong conversions Extreme values Treated as missing if > 4 standard devia'ons from mean
16 Modeling and Inference Regression model Future ALSFRS Slope = f(features) + noise Unknown regression func'on Goal: infer f from data Bayesian: Place a prior on f, infer its posterior Bonus: Uncertainty es'mates for each predic'on What prior? Flexible and nonparametric Avoid restric've assump'ons about func'onal form Favor simple, sparse models Avoid overfijng to irrelevant features
17 Bayesian Addi've Regression Trees * f(features) = sum of simple decision trees Days since onset > 705 Past ALSFRS slope > Simplicity = tree depends on few features Irrelevant features seldom selected Similar to frequen'st ensemble methods Boosted decision trees, random forests * Chipman, George, and McCulloch (2010)
18 BART Inference Es6ma6ng f: Markov Chain Monte Carlo R package bart available on CRAN ^ ^ ^ ^ 10,000 posterior samples: f 1, f 2, f 3, f 4, ^ f i = + 10 minutes on MacBook Pro (2.5 GHz CPU, 4GB RAM) Predic6on: Posterior mean trees ^ ^ ^ f 1 (features), f 2 (features), f 3 (features), Average of Variance reduc6on Average predic'ons of 10 BART models
19 Accuracy of BART Inference 1 sample: Validation RMSD samples: samples: samples: Number of BART Samples
20 BART Feature Selec'on All 484 Features Ordered by Usage Top Ten Features Ordered by BART Usage Onset Delta Max Dressing Score ALSFRS Slope Last Systolic Blood Pressure Slope Mean Weight Slope Last FVC Slope Last Weight Slope Last ALSFRS Min Turning Score Mean ALSFRS Average usage Average usage Many pairwise slope features Lab data excluded
21 BART on Feature Subsets Effect of Adding Each Feature in Order of BART Usage Validation RMSD max.dressing Onset.Delta 1 feature: last.slope.bp.systolic alsfrs.score.slope mean.slope.weight last.slope.fvc.liters 6 features: last.alsfrs.score 21 features: features: last.speech 14 features: last.handwriting meansquares.speech Features Added in Order of Usage
22 Model Comparison How do other models perform using our feature set? Model Our RMSD (Test) Our RMSD (Valida6on) Compe6tor RMSD Lasso Regression Random Forests Boosted Trees BART Addi6ve decision tree models especially effec've Featuriza6on is a main differen'ator of compe'tors
23 The End Ques'ons?
24 Onset Delta vs. Target Onset.Delta versus ALSFRS Slope on Train and Test Data Future ALSFRS Slope Onset.Delta
25 Past ALSFRS Slope vs. Target alsfrs.score.slope versus ALSFRS Slope on Train and Test Data Future ALSFRS Slope alsfrs.score.slope
26 Last Systolic BP Slope vs. Target last.slope.bp.systolic versus ALSFRS Slope on Train and Test Data Future ALSFRS Slope last.slope.bp.systolic
27 Max Dressing Score vs. Target max.dressing versus ALSFRS Slope on Train and Test Data Future ALSFRS Slope max.dressing
28 Mean Weight Slope vs. Target mean.slope.weight versus ALSFRS Slope on Train and Test Data Future ALSFRS Slope mean.slope.weight
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