Implications of Longitudinal Data in Machine Learning for Medicine and Epidemiology

Transcription

1 Implications of Longitudinal Data in Machine Learning for Medicine and Epidemiology Billy Heung Wing Chang, Yanxian Chen, Mingguang He Zhongshan Ophthalmic Center, Sun Yat-sen University Biostatistics Seminar Dalla Lana School of Public Health Feb 3, 2015 Longitudinal Prediction Feb 3, / 33

2 Outline 1 Myopia and Myopia Prediction 2 Supervised Machine Learning and Prediction 3 Myopia Progression 4 Principal Component Analysis 5 Conclusion Longitudinal Prediction Feb 3, / 33

3 Myopia Commonly 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: Longitudinal Prediction Feb 3, / 33

4 Myopia Progression COMET (2013) IOVS 54: Emmetropic at early ages. Myopia onset during elementary school. Myopia stabilization during secondary school. Age of onset, age of stabilization, and progression rates varies. Longitudinal Prediction Feb 3, / 33

5 Risk Factors for Myopia Largely believed to be genetic in the past. Prevalence in certain countries on rapid rise recently. Lin, et al (2004) Ann Acad Med Singapore, 33, Education, near work, outdoor time. Longitudinal Prediction Feb 3, / 33

6 High Myopia An extreme level of myopia. SE < -6.0 D. Increased risk of blindness. Irreversible. Prevention. Longitudinal Prediction Feb 3, / 33

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

8 Prediction of Children At-Risk Given SE at early ages (10-13 years old). Predict the SE at age 15. Longitudinal Prediction Feb 3, / 33

9 Outline 1 Myopia and Myopia Prediction 2 Supervised Machine Learning and Prediction 3 Myopia Progression 4 Principal Component Analysis 5 Conclusion Longitudinal Prediction Feb 3, / 33

10 Supervised Machine Learning Construct a prediction model based on a training" sample of predictors and responses {x i, y i } N i=1, (x i, y i ) (X, Y ). At prediction time: input the test case x test = (x1 test, x2 test,...) into the fitted model to obtain the prediction y test. E.g. linear regression. E(Y X) = β0 + β 1 X 1 + β 2 X Training data {x i, y i } N i=1 to estimate ˆβ 0, ˆβ 1, ˆβ 2,... ŷ test = ˆβ 0 + ˆβ 1 x1 test + ˆβ 2 x2 test +... Longitudinal Prediction Feb 3, / 33

11 Criterion for a Good Prediction Model Generalization Ability: Can the model make accurate prediction for data unused for training? Can the model be applied for prediction in the future? Can the model be applied for other population? Longitudinal Prediction Feb 3, / 33

12 Existing Works Follow the above scheme: Training Data Prediction Model Prediction Issues of Generalization: Must use data from the past. Rely on population parameters. Also need Y = endpoint SE: unrealistic. Longitudinal Prediction Feb 3, / 33

13 Prediction using Longitudinal Data With longitudinal data, we can extrapolate using SE at early ages. Endpoint SE not needed for model building. But this naive approach ignores myopia stabilization. SE SE Age Age Longitudinal Prediction Feb 3, / 33

14 Change-point Model Myopia progression will stabilize during adolescence. Use a Change-point Regression Model to imitate stabilization. SE SE Age Change-Point Age Change-Point Longitudinal Prediction Feb 3, / 33

15 Mean-Matching for Change-point Selection Fit 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 that best matched the regression-predicted mean at the midpoint age. change-point SE SE Age mid-point Age mid-point Longitudinal Prediction Feb 3, / 33

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

17 Results: Prediction MSE for Twin Data One Follow up Age SE follow up, Naive Endpoint SE Predicted follow up, Change Point Endpoint SE Predicted follow up, LME Endpoint SE Predicted Two Follow up Age SE follow up, Naive Endpoint SE Predicted follow up, Change Point Endpoint SE Predicted follow up, LME Endpoint SE Predicted Longitudinal Prediction Feb 3, / 33

18 Results: Validation on Optometry Clinic Data, Prediction MSE follow up, Change point Endpoint SE Predicted follow up, LME Endpoint SE Predicted Longitudinal Prediction Feb 3, / 33

19 Brief Summary A simple change-point model for future SE prediction. Higher accuracy than linear mixed effects model. Potential reason: Change-point model accounts for myopia stabilization. Linear mixed effects model contains many population parameters. Lack generalization ability. Longitudinal Prediction Feb 3, / 33

20 Outline 1 Myopia and Myopia Prediction 2 Supervised Machine Learning and Prediction 3 Myopia Progression 4 Principal Component Analysis 5 Conclusion Longitudinal Prediction Feb 3, / 33

21 Analysis of Myopia Progression To study the various aspects of myopia progression. Progression rate, myopia onset, myopia stabilization. To identify factors associated to progression rate, onset and stabilization. Longitudinal Prediction Feb 3, / 33

22 Existing Appraoch for Progression Modelling Gompertz 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 do some analysis? COMET (2013) IOVS 54: Longitudinal Prediction Feb 3, / 33

23 Outline 1 Myopia and Myopia Prediction 2 Supervised Machine Learning and Prediction 3 Myopia Progression 4 Principal Component Analysis 5 Conclusion Longitudinal Prediction Feb 3, / 33

24 Principal Component Analysis (PCA) Let x = {x 1, x 2,..., x P } F, E(x) = 0 {x i } N i=1 i.i.d. samples from F 1 Find a unit vector v 1 such that var(x ˆ T v 1 ) is maximized. Step 1 Step 2 x x2 x x2 x1 x1 2 Find a unit vector v 2, v 2 v 1, such that ˆ var(x T v 2 ) is maximized. 3 Repeat if necessary for v 3, v 4, etc... z ij = x T i v j is the jth principal component scores for x i. Longitudinal Prediction Feb 3, / 33

25 Principal Component Analysis x x2 z x z1 Longitudinal Prediction Feb 3, / 33

26 PCA on Longitudinal Data What if PCA is applied to longitudinal data? It finds major trends hidden within the data. Revisit the Twin data set. 637 first born twins with without cataract surgery history or loss of 3 consecutive visits. Right-eye SE are used. Missing data are imputed using linear regression. Purpose: to identify major trends of myopia progression, and identify potential factors associated with those trends. Longitudinal Prediction Feb 3, / 33

27 PCA on the Twin Data Set PC 1 PC 2 PC 3 PC Loading PC Loading PC Loading follow up follow up follow up Longitudinal Prediction Feb 3, / 33

28 PC Scores > 0.5 vs. < -0.5 PC2 represents rate of myopia progression. PC3 with positive scores represents myopia stabilization. PC3 with negative scores represents myopia onset. Longitudinal Prediction Feb 3, / 33

29 Using the PC Scores as Responses in Regression The PC scores z ij = x T i v j are measures of the strength of the trends. To identify risk factors for each trend. Regress z ij = x T i v j onto the predictors. Longitudinal Prediction Feb 3, / 33

30 PCA scores and Risk Factors Longitudinal Prediction Feb 3, / 33

31 PCA scores and Risk Factors Longitudinal Prediction Feb 3, / 33

32 Outline 1 Myopia and Myopia Prediction 2 Supervised Machine Learning and Prediction 3 Myopia Progression 4 Principal Component Analysis 5 Conclusion Longitudinal Prediction Feb 3, / 33

33 Conclusion Change-point model with longitudinal data: a prediction method with good generalization ability. 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, / 33