A Robust Recursive Partitioning Algorithm for Mining Multiple Populations

Transcription

1 A Robust Recursive Partitioning Algorithm for Mining Multiple Populations Jose Alvir 1 Javier Cabrera 2 Frank Caridi 1 Ha Nguyen 1 Pfizer Inc 1 & Rutgers University 2 Rutgers Biostatistics Day, 4/25/2008

2 The Challenge of Personalized Medicine Drugs do not work for everybody Certain drugs may work for certain individuals compared to other drugs Individuals may need more or less of a drug than other individuals

3 The Challenge of Personalized Medicine Shift from individuals to groups of individuals with similar characteristics Search for subgroups where response is maximal Classification techniques like CART are available

4 Pima Indians Diabetes Data Set 768 females at least 21 yrs old of Pima Indian heritage Variable Mean SD Number of times pregnant Plasma glucose concentration Diastolic blood pressure Triceps skin fold thickness Hour serum insulin Body Mass Index Diabetes pedigree function Age Diabetes 268/768

5 Classic Example of CART: Pima Indians & Diabetes 768 Pima Indian females, 21+ years old ; 268 tested positive to diabetes 8 predictors: PRG, PLASMA, BP, THICK, INSULIN, BODY, PEDIGREE, AGE PLASM A< AG E<28. 5 BO DY< BO DY< BO DY< PLASM A< PLASM A< PLASM A< AG E< PEDI G REE< BP<

6 ARF Activity Region Finder Identify High Activity Regions Find regions where concentration of success is highest, unlike other classification trees (e.g. CHAID, CART) that aim to predict response across the entire range Splitting a node when there is substantial evidence that the response is higher/lower in the child node (compared to the parent node) Written in R

7 Alvir J, Cabrera J, Caridi F, Nguyen H. Mining Clinical Trial Data. In Knowledge Discovery and Data Mining: Challenges and Realities with Real World Data, edited by Xingquan (Hill) Zhu and Ian Davidson, 2007

8 ARF applied to Pima Indian data DATASET n=768;p=35% PLASMA [155,199] n=122;p=80% PLASMA [128,152] n=153;p=49% BODY [29.9,45.7] n=92;p=88% AGE [29,56] n=199;p=35% BODY [30.3,67.1] n=99;p=64% PEDIGREE [0.344,1.394] n=55;p=96% PEDIGREE [0.439,1.057] n=38;p=82% Subset %Success n 1 PLASMA in [155,199] & BODY in [29.9,45.7] & PEDIGREE in [0.344,1.394] PLASMA in [128,152] & BODY in [30.3,67.1] & PEDIGREE in [0.439,1.057] PLASMA in [0,127] & AGE in [29,56]

9 Differences between CART & ARF trees Best node for the CART tree has 9 observations with 100% diabetes ARF tree has a node of 55 observations with 96% rate of diabetes The node from CART has a high probability of occurring by chance ARF tree produces sketches that summarize only important information and downplay less interesting information

10 Ziprasidone Placebo Controlled Trials 4- & 6-wk U.S. trials Protocol weeks N=195 Protocol weeks N=132 Protocol weeks N=299 Protocol weeks N= subjects on haloperidol excluded Total N = 951

11 Ziprasidone Data N by dose (mg./day) & Protocol # PBO

12 Ziprasidone Data Mining Variables Outcomes: Change in BPRS Total score Predictors: age, sex, race, protocol, dose, baseline clinical ratings (positive Sx, CGI-S, anergia, depressive Sx, AIMS), duration of illness in years, current smoking status

13 Patient Characteristics Total = 951 Male Race Smoker White Black Other N %

14 Data Definitions AIMS = mean of AIMS total/5 and TD severity BPRS total & Sx scores (positive, depression, anergia) absolute minimum is zero (items scored with minimum = 0 and not 1) Positive Sx score sum of conceptual disorganization, hallucinatory behavior, unusual thought content, suspiciousness Depression sum of anxiety, guilt feelings, depressive mood Anergia sum of blunted affect, emotional withdrawal, motor retardation Residual BPRS change Residual (observed minus predicted) LOCF BPRS total regressed on baseline BPRS

15 Patient Characteristics Mean S.D. Range BPRS change , 55 Residual change , 65 Baseline BPRS , 86 Age , 72 Duration of illness , 54 Baseline Positive Sx , 24 Baseline Depression , 17 Baseline CGI-S , 7 Baseline Anergia , 18 Baseline AIMS , 4

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18 The Challenge of Personalized Medicine revisited Can we identify subgroups for which the drug is more effective than placebo or other drugs? Are there subsets for which a low dose is better than placebo? Are there subsets for which a high dose is better than a low dose or vice versa?

19 Conventional tree methods can only answer these questions indirectly In conventional modelling: - The X space is defined by one sample - We estimate the conditional mean of a response variable given a set of predictors.

20 Comparative efficacy Subsets where: the drug is more effective than placebo or other drugs low dose is better than placebo high dose is better than a low dose or vice versa In these situations: -The X space is defined by two or more samples. -We estimate the conditional difference of means or in general a function of the conditional means. -We extend ARF to the differences between two or more means

21 47th Interscience Conference on Antimicrobial Agents and Chemotherapy Chicago,September 17-20, 2007 Symptom Resolution with Azithromycin Extended Release Versus Amoxicillin/Clavulanate in Patients with Acute Sinusitis in a General Practice Physician Environment J. F. Piccirillo 1, B. F. Marple 2, C. S. Roberts 3, J. R. Frytak 4, V. F. Schabert 5, J. C. Wegner 4, H. Bhattacharyya 3, S. P. Sanchez 3 1 Washington University School of Medicine, St Louis, MO 2 University of Texas Southwestern Medical Center, Dallas, TX 3 Pfizer Inc, New York, NY 4 i3 Innovus, Eden Prairie, MN 5 Integral Health Decisions Inc, Santa Barbara, CA

22 Sample Characteristics

23 Ziprasidone: 120 mg/160 mg Vs Placebo MULTIRESPONSE CART BASEDEP< 2.5 URATILL>=16.5 BASEPOS< n=37 n=57 BCGIS< n=86 DURATILL>= n=30 DURATILL< n=27 RACE=bde DURATILL>= n=62 ANERGIA>= n= n= n=26 n=94

24 y y y Ziprasidone: 120 mg/160 mg Vs Placebo TOP THREE SPLITS BASEDEP x DURATIL x BASEPOS x

25 Software These two ARF applications are being incorporated into PfarMineR, a suite of statistical methods for EDA and Data Mining ARF is available at: