Implications Of Longitudinal Data In Machine Learning For Medicine And .

Implications of Longitudinal Data in MachineLearning for Medicine and EpidemiologyBilly Heung Wing Chang, Yanxian Chen, Mingguang HeZhongshan Ophthalmic Center, Sun Yat-sen UniversityBiostatistics SeminarDalla Lana School of Public HealthFeb 3, 2015Longitudinal PredictionFeb 3, 20151 / 33

Outline1Myopia and Myopia Prediction2Supervised Machine Learning and Prediction3Myopia Progression4Principal Component Analysis5ConclusionLongitudinal PredictionFeb 3, 20152 / 33

MyopiaCommonly known as short-sightedness.Measured by Spherical Equivalence (SE), units Dioptres (D).0 D: emmetropia (no myopia).0 D to -3 D: low myopia.Correctable by wearing glasses.Morgan et. al. (2012) Lancet 379:1739-1748Longitudinal PredictionFeb 3, 20153 / 33

Myopia ProgressionCOMET (2013) IOVS 54:7871-7883Emmetropic at early ages.Myopia onset during elementary school.Myopia stabilization during secondary school.Age of onset, age of stabilization, and progression rates varies.Longitudinal PredictionFeb 3, 20154 / 33

Risk Factors for MyopiaLargely believed to be genetic in the past.Prevalence in certain countries on rapid rise recently.Lin, et al (2004) Ann Acad Med Singapore, 33, 27-33.Education, near work, outdoor time.Longitudinal PredictionFeb 3, 20155 / 33

High MyopiaAn extreme level of myopia. SE -6.0 D.Increased risk of blindness.Irreversible.Prevention.Longitudinal PredictionFeb 3, 20156 / 33

Preventive Treatment of High MyopiaTo arrest myopia progression towards high myopia.Popular treatment: Atropine eye drops, specialized contact lens.Shih et. al. (2002) Acta Ophthalmologica Scandinavica 79:3, 233-236Long-term treatment with risk of severe side-effects.Idea: target only children at risk of high myopia.Longitudinal PredictionFeb 3, 20157 / 33

Prediction of Children At-RiskGiven SE at early ages (10-13 years old). Predict the SE at age15.Longitudinal PredictionFeb 3, 20158 / 33

Outline1Myopia and Myopia Prediction2Supervised Machine Learning and Prediction3Myopia Progression4Principal Component Analysis5ConclusionLongitudinal PredictionFeb 3, 20159 / 33

Supervised Machine LearningConstruct a prediction model based on a “training" sample ofpredictors and responses {xi , yi }Ni 1 , (xi , yi ) (X, Y ).At prediction time: input the test case xtest (x1test , x2test , .) intothe fitted model to obtain the prediction y test .E.g. linear regression.IIIE(Y X ) β0 β1 X1 β2 X2 .Training data {xi , yi }Ni 1 to estimate β̂0 , β̂1 , β̂2 , .testtestŷ β̂0 β̂1 x1 β̂2 x2test .Longitudinal PredictionFeb 3, 201510 / 33

Criterion for a Good Prediction ModelGeneralization Ability:IIICan the model make accurate prediction for data unused fortraining?Can the model be applied for prediction in the future?Can the model be applied for other population?Longitudinal PredictionFeb 3, 201511 / 33

Existing WorksFollow the above scheme:Training Data Prediction Model PredictionIssues of Generalization:IIMust use data from the past.Rely on population parameters.Also need Y endpoint SE: unrealistic.Longitudinal PredictionFeb 3, 201512 / 33

Prediction using Longitudinal DataWith longitudinal data, we can extrapolate using SE at early ages.Endpoint SE not needed for model building.But this naive approach ignores myopia stabilization.SESEAgeAgeLongitudinal PredictionFeb 3, 201513 / 33

Change-point ModelMyopia progression will stabilize during adolescence.Use a Change-point Regression Model to imitate stabilization.SESEAgeChange-PointAgeLongitudinal PredictionChange-PointFeb 3, 201514 / 33

Mean-Matching for Change-point SelectionFit regression using the available SE measures.Mean SE at midpoint age (14 years) was estimated.Fit change-point models using a range of change-points.Choose the change-point with the averaged prediction values thatbest matched the regression-predicted mean at the midpoint udinal PredictionFeb 3, 201515 / 33

Data SetTraining Data: Guangzhou Twin Eye Study.III1281 pairs of twins. First-born twins are considered for analysis.inclusion: 2nd follow-up SE before age 13. Endpoint age 15.72 subjects remains. Right-eye SE is used.Validation Data: Zhongshan Ophthalmic Center Optometry ClinicData.III1573 subjects.same inclusion criterion as above.56 subjects remains. Left-eye SE is used.Proposed methods compared with linear mixed effects model(LME).Longitudinal PredictionFeb 3, 201516 / 33

Results: Prediction MSE for Twin Data 1214Age160 2 40 6 4 22 follow up, Change Point2 follow up, LME 0 0 10 10 Endpoint SE 2 Endpoint SE 4 10 6 6 4 6 8 4 2Predicted0 2 6 2022 follow up, Naive SE0Two Follow up 4 2 Predicted 4Endpoint SE 0 6Age 216 414 Predicted12 Predicted 80 2Predicted 10 6 1 follow up, LME 8 1 follow up, Change Point 6 12 40Predicted 8 6 4 20 2SE 4 6 61 follow up, Naive2One Follow up 6 4 2Endpoint SE0 6 4 2Endpoint SELongitudinal Prediction0 6 4 20Endpoint SEFeb 3, 201517 / 33

Results: Validation on Optometry Clinic Data, Prediction MSE2 follow up, Change point 8 6 4 2 4 6Predicted 8 10 2 0 2Predicted 4 6 82 follow up, LME0 8Endpoint SE 6 4 20Endpoint SELongitudinal PredictionFeb 3, 201518 / 33

Brief SummaryA simple change-point model for future SE prediction.Higher accuracy than linear mixed effects model.Potential reason:IIChange-point model accounts for myopia stabilization.Linear mixed effects model contains many population parameters.Lack generalization ability.Longitudinal PredictionFeb 3, 201519 / 33

Outline1Myopia and Myopia Prediction2Supervised Machine Learning and Prediction3Myopia Progression4Principal Component Analysis5ConclusionLongitudinal PredictionFeb 3, 201520 / 33

Analysis of Myopia ProgressionTo study the various aspects of myopia progression.Progression rate, myopia onset, myopia stabilization.To identify factors associated to progression rate, onset andstabilization.Longitudinal PredictionFeb 3, 201521 / 33

Existing Appraoch for Progression ModellingGompertz model.A pre-defined model for modelling the entire progression.Require long term follow-up data. Lack-of-fit issues.Idea: perhaps with shorter-term follow-up data, we can still dosome analysis?COMET (2013) IOVS 54:7871-7883Longitudinal PredictionFeb 3, 201522 / 33

Outline1Myopia and Myopia Prediction2Supervised Machine Learning and Prediction3Myopia Progression4Principal Component Analysis5ConclusionLongitudinal PredictionFeb 3, 201523 / 33

Principal Component Analysis (PCA)Let x {x1 , x2 , . . . , xP } F , E(x) 0{xi }Ni 1 i.i.d. samples from Fˆ (xT v1 ) is maximized.Find a unit vector v1 such that var3Step 23Step 1 1x3 012 101233 2x123 1 2 1 2 0 x20 1 2 221x3 2 2 1012 10123x213x1ˆ (xT v2 ) is maximized.Find a unit vector v2 , v2 v1 , such that varRepeat if necessary for v3 , v4 , etc.zij xTi vj is the jth principal component scores for xi .Longitudinal PredictionFeb 3, 201524 / 33

2Principal Component Analysis 123 0z2 1 20 2 11 10123 x2 2 2 10x3123 2x1 1012z1Longitudinal PredictionFeb 3, 201525 / 33

PCA on Longitudinal DataWhat if PCA is applied to longitudinal data?It finds major trends hidden within the data.Revisit the Twin data set.III637 first born twins with without cataract surgery history or loss of 3consecutive visits.Right-eye SE are used.Missing data are imputed using linear regression.Purpose: to identify major trends of myopia progression, andidentify potential factors associated with those trends.Longitudinal PredictionFeb 3, 201526 / 33

PCA on the Twin Data Set1234follow up5670.60.4 0.4 0.20.0PC Loading0.20.4 0.4 0.20.0PC Loading0.20.40.20.0 0.2 0.4PC LoadingPC 30.6PC 20.6PC 1123456follow upLongitudinal Prediction71234567follow upFeb 3, 201527 / 33

PC Scores 0.5 vs. -0.5PC2 represents rate of myopia progression.PC3 with positive scores represents myopia stabilization.PC3 with negative scores represents myopia onset.Longitudinal PredictionFeb 3, 201528 / 33

Using the PC Scores as Responses in RegressionThe PC scores zij xTi vj are measures of the strength of thetrends.To identify risk factors for each trend. Regress zij xTi vj onto thepredictors.Longitudinal PredictionFeb 3, 201529 / 33

PCA scores and Risk FactorsLongitudinal PredictionFeb 3, 201530 / 33

PCA scores and Risk FactorsLongitudinal PredictionFeb 3, 201531 / 33

Outline1Myopia and Myopia Prediction2Supervised Machine Learning and Prediction3Myopia Progression4Principal Component Analysis5ConclusionLongitudinal PredictionFeb 3, 201532 / 33

ConclusionChange-point model with longitudinal data: a prediction methodwith good generalization ability.PCA: hypothesis-free approach to analyze longitudinal trends inmyopia progression.Hopefully, this presentation can suggest some ideas on howlongitudinal data can be used for prediction, and how dimensionreduction techniques can be used in longitudinal data analysis.Longitudinal PredictionFeb 3, 201533 / 33

PCA: hypothesis-free approach to analyze longitudinal trends in myopia progression. Hopefully, this presentation can suggest some ideas on how longitudinal data can be used for prediction, and how dimension reduction techniques can be used in longitudinal data analysis. Longitudinal Prediction Feb 3, 2015 33 / 33