Bias Adjustment: Local Control Analysis of Radon and Ozone

Transcription

1 Bias Adjustment: Local Control Analysis of Radon and Ozone S. Stanley Young Robert Obenchain Goran Krstic NCSU 19Oct2016

2 Abstract Bias Adjustment: Local control analysis of Radon and ozone S. Stanley Young, CGStat LLC Robert L. Obenchain, Risk Benefit Statistics LLC Goran Krstic, Fraser Health Authority Large (observational) data sets typically present research opportunities, but also problems that can lead to false claims. In Big Data, the standard error of an average effect estimate goes to zero as sample size increases, so even small biases can lead to declared (but false) claims. In addition, the average of treatment can be almost meaningless when there are interactions with confounders that create local variation in effect-sizes. Data miners need statistical methods that can deal simply and efficiently with these sources of bias. Here, we demonstrate use of a JMP add-in, Moving Median, and a new JMP platform, Local Control, for the analysis of two data sets. Our first case study illustrates reduction of bias in an environmental epidemiology data set. Our second study uses Local Control on a time series air quality example. By detecting interactions, data miners can produce more realistic and more relevant analyses that reduce the bias typically implied by the variety and heterogeneity of Big Data. 2

3 Collaborators S. Stanley Young Robert Obenchain Goran Krstic 3

4 Key Analysis Steps 4

5 Plan for Radon Data Set 1. Radon background 2. Local Control analysis strategy 3. Analysis of 2,881 US counties 4. Local Control LTD Results 5. Summary 5

6 Figure 1. Spatial distribution of obesity, lung cancer, radon and smoking. Obesity Lung Cancer Source: Ever Smoking 6

7 EPA cited meta analysis (1) 26 authors! 2004 Low Dose Linear But see Cohen. 7

8 EPA cited meta analysis (2) 16 authors 2005 Low Dose Linear But see Cohen. 8

9 Bernard L. Cohen: Low-dose radon is protective 1. Cohen BL. (1989) Expected indoor 222Rn levels in counties with very high and very low lung cancer rates. Health Physics 57, Cohen BL. (1995) Test of the linear-no threshold theory of radiation carcinogenesis for inhaled radon decay products. Health Physics 68, Cohen BL. (1997) Lung cancer rate vs. mean radon level in U.S. counties of various characteristics. Health Physics 72, Cohen BL. (2008) The linear no-threshold theory of radiation carcinogenesis should be rejected. J. Amer. Physicians and Surgeons 13,

10 Local Control Analysis Process Large observational data set A vs B comparison (or LR) The steps 0. Variable selection 1. Aggregate cluster, LTDs 2. Confirm randomization test 3. Explore sensitivity analysis 4. Reveal modeling, MLR, RP 10

11 Step 0: Select clustering variables Predict Lung Cancer Mortality, Step-wise regression 11

12 Variables selected for clustering. NB: Regression coefficient for radon is NEGATIVE. 12

13 Local Control Analysis Radon Most Typical micro-aggregation of 2,881 US Counties on 3 primary X-confounders 1. Age Over 65 % 2. Obesity % 3. Currently Smoke % Y-outcome = Lung Cancer Mortality. Binary Treatment Indicator: Radon High ( > 2.1 pci/l ) vs. Low 13

14 Local Control Add-In Russ Wolfinger/Bob Obenchain 14

15 Step 1: Clustering Within cluster statistics 1. Local Treatment Difference, LTD 2. Local Linear Regression (slope and intercept) 3. Local Survival Analysis (Failure times) 4. Etc. 15

16 Local Treatment Difference at the centroid of an informative cluster E[ (Y t=1) - (Y t=0) X ] Single df comparison Given X, local effect. Fair Treatment Comparison 16

17 Aggregate Cycle Observed LTD Distribution (49 Informative Clusters) 17

18 Step 2: Confirm clustering matters Random Distribution Observed Distribution Observed LTD Distribution 18

19 Step 2: Confirm Cycle Observed LTD empirical Cumulative Distribution Function (CDF) LTD-like Random Permutation CDF 19

20 Step 3: Explore Cycles Tried using Complete Linkage as well as Fast Ward Tried using of 3 out of 5 potential X-confounders for clustering: Age Over 65 % Obesity % Currently Smoke % Ever Smoke % Median Household Income ($1,000s) Tried using between 50 and 100 clusters. 20

21 Reveal Cycle Fitted Supervised Learning Models for predicting observed LTDs: JMP 12 Modeling Platform -> Partition option single Tree (7 terminal nodes) Bootstrap Forest Model Average of 100 Trees JMP Fit Model Platform Multi-Variable Regression (Degree at most 2) Tried using 6 potential X-confounders for predicting observed LTDs: Age Over 65 % Obesity % Currently Smoke % Ever Smoke % Median Household Income ($1,000s) Radon ( or Ln[Rn] ) Level (as either ordinal or continuous measures) 21

22 Tree (LTD)

23 Node Summary Node N AvDiff Log Parent Worth

24 Method Two (Bootstrap Forest), R^2 =

25 Regression Results Use LTD as y, Stepwise regression SLR R^2 =

26 Partial Correlations 26

27 Conclusions Radon 1. Low dose Radon is protective against lung cancer. 2. Cohen is supported. 3. EPA should make their data set public. 27

28 London, Ozone and Mortality 28

29 London Smog,

30 Singapore Haze

31 EPA and ozone Bad Good???? ppm 0.20 ppm Ozone Generators that are Sold as Air Cleaners Reviewed by EPA 31

32 LC London Ozone 0. Variable selection 1. Cluster to MLR within cluster 3. Append to intercept and slopes to data set 4. P-value plots 5. Histograms 6. RP on intercepts and slopes (lag 0. lag 1)

33 London Time Series Mortality and Ozone 33

34 Time Series Smoother Add-In Paul Fogel Paris 34

35 Smoothed Time Series Smoothed Subtract Moving Median

36 Step 0: Variable selection 36

37 Clustering 37

38 50 Clusters N

39 t-tests, Int, D_Ozone, D_Ozone-1 39

40 D Ozone and D Ozone -1 40

41 RP For slope of D_mort/D_Ozone LogWorth for each split is large, 11.1 to Heterogeneity. 41

42 Slope D_Ozone

43 RP for slope of D_Ozone-1 LogWorth for each split is large, 11.5 to Heterogeneity. 43

44 RP for slope of D_Ozone

45 Regression Analysis 45

46 Possible Ozone Effect 46

47 Summary of ozone Local Control Analysis 1. NB: Outlier time period was removed. 2. Variables were de-trended. 3. Any possible effect of ozone depends on other variables; ozone is not causal of deaths. 4. Slope is heterogeneous, RP; one size does not fit all. 47

48 Key Analysis Steps 48

49 Contact Information S. Stanley Young Robert Obenchain Goran Krstic Offering protection against unreliable claims! 49

50 References 50

51 51

52 Outlier temperature period 52

53 Hazmat/Radon 53