Biostatistics 140.653 Case Study : Amateur Boxing & Neuropsychological Impairment

1. Biostatistics 140.653Case Study: Amateur Boxing & Neuropsychological Impairment July 14, 2011

2. Acknowledgments • Funding • National Institutes of Health • United States Olympic Foundation • Collaborators • Walter “Buzz” Stewart • Charlie Hall, Scott Zeger, David Simon • References • Stewart WF et al., A prospective study of CNS function in US amateur boxers, Am J Epidemiol 1994; 139: 573-88. • Bandeen-Roche K et al., Modelling disease progression in terms of exposure history, Statist Med 1999; 18:2899-2916.

3. Introduction (Imagine: 1989 news photo of Larry Holmes pounding the face of James “Bonecrusher” Smith) • Well publicized: Boxing may cause neurological harm • ~ 1986: IOC explores eliminating boxing (for golf?) • Olympic boxing is amateur: different from pro • Research study initiated: NIH / USABF collaboration

4. Scientific Question:Does boxing cause cerebral injury? • Hypothesized pathway: brain jarring

5. Scientific Question:Does boxing cause cerebral injury? • Injury model • Mild, transient • Focal axonal damage, re-growth • No measurable long-term injury • Cell disruption sufficient to cause hemorrhage • Progressive axonal death • Measurable long-term injury

6. Brief Study Design • "Full" Boxing club sample • NY, DC, Cleveland, St. Louis, Louisiana, Houston • N = 593 boxers • One baseline and three follow-up exams “per boxer”; 1988-1994 • N=493 with a first follow up • Outcomes • 17 neuropsychological tests (Today: Block Design) • Electrophysiologic Battery • Ataxia and Neurological Tests • Covariates • Primary: number of bouts boxed • Secondary: age, race, education, Ravens IQ score, club, non-boxing concussion history, drug test result

7. Step 1:Formulate model • Question: Do blocks scores tend to decrease as # of bouts increases? • Critique an approach: “Pool” all four rounds of data, and regress bouts (Y) on blocks score (X) • Wrong direction: Should be blocks (Y) on bouts (X) • Independence assumption violated: Multiple measures on same person; also clustering within clubs • Weak causal content: Fails to use within-person change

8. UnlinkingEffect evidence: Status versus Change

9. UnlinkingEffect evidence: Status versus Change

10. Model Building • Suppose goal = capture both relationships: status and change • Considered, rejected: E[Yit|Xi] = 0+ 1Xit • Y = blocks score; X=#bouts • i=people 1,…,n; t=times 1, 2 (…) • Way to think: status 1 & change 2 Allows age-related change between t1 and t2 Time 1: E[Yi1|Xi] = 0+ 1Xi1 Time 2: E[Yi2|Xi] = 0+ 1Xi1 + 2(Xi2-Xi1) + 3

11. Model Building E[Yi1|Xi] = 0+ 1Xi1 E[Yi2|Xi] = 0+ 1Xi1 +2(Xi2-Xi1) + 3 i.e. E[Yit|Xi1,Xi2] = 0+ 1Xi1 +2(Xi2-Xi1)*1{t=2} + 31{t=2} • Interpret 3 • How to test for equal status, change relationships? f • Zero out other coefficients you can: Xi1 = Xi2-Xi1=0 • Then, time 2 mean = 0+ 3; time 1 mean = 0 • 3 = Mean change in block score among non-boxers thru time 2 • Test H0: 2 = 1

12. Model Building • From now on: we’ll analyze relationship between change in blocks score(t2-t1) and • baselinebout total • change in bout total • N=413 in the analysis • Why the baseline bout total? • Models potentially delayed effect

13. Exploratory Data Analysis blkdiff blbouts boutdiff y=0

14. New model building goal • From now on: we’ll analyze relationship between change in blocks score(t2-t1) and • baselinebout total • change in bout total • In real life: validation, errors-in-variables (covariates) analysis

15. Exploratory Data AnalysisScatterplot: Blocks Change vs. BL Bouts

16. Exploratory Data AnalysisScatterplot: Blocks Change vs. BL Bouts .lowess blkdiff blbouts if blbouts < 75

17. Modeling options • Linear Y, X model OTHERS? Highly sensitive to extreme points • Polynomial Y, X model • Replace X by √X, etc. (transform) • Categorize X • Spline Y, X model Obscure interpretation Wastes much exposure information; categories arbitrary?

18. Spline ModelRelationship: Change in Blocks, Bouts • Choice of knots • Novice versus Open divisions: 10 bouts • Median of remaining bouts: 35 • Histogram suggests a cut at around 75:

19. Spline ModelRelationship: Change in Blocks, Bouts • Order • Plot up to 75 bouts appears fairly linear • Smooth after 75 bouts appears fairly linear • (Population) Model: E[Yi2-Yi1|Xi1] = 0+ 1Xi1 +2(Xi1-10)+ + 3(Xi1-35)++4(Xi1-75)+ - Number of polynomial terms underlying relationship - Order = 1

20. Aside • Suppose X = (0,1,5,11,14,30,36,55,78,102) • What is the design matrix for the model on the previous slide? (Posted version of slides will include answer)

21. Design Matrix

22. Regression model • regress blkdiff blbouts boutspl1 boutspl2 boutspl3 Source | SS df MS Number of obs = 413 -------------+------------------------------ F( 4, 408) = 1.92 Model | 281.256924 4 70.314231 Prob > F = 0.1058 Residual | 14922.6559 408 36.575137 R-squared = 0.0185 -------------+------------------------------ Adj R-squared = 0.0089 Total | 15203.9128 412 36.9027011 Root MSE = 6.0477 ------------------------------------------------------------------------------ blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- blbouts | .2049663 .1111387 1.84 0.066 -.0135095 .4234422 boutspl1 | -.3300803 .145362 -2.27 0.024 -.6158321 -.0443284 boutspl2 | .1565677 .0787441 1.99 0.047 .0017729 .3113624 boutspl3 | -.033317 .0469676 -0.71 0.479 -.1256457 .0590117 _cons | 1.452344 .7033785 2.06 0.040 .0696462 2.835043 ------------------------------------------------------------------------------ Mean per-bout diff in Blocks Change, Novice Boxers Mean Block Score Change, 0 Bouts Mean per-10 bout diff in Blocks Change, Novice Boxers? 2.05 points In each case, coefficient estimates the population mean!

23. Regression model • regress blkdiff blbouts boutspl1 boutspl2 boutspl3 Source | SS df MS Number of obs = 413 -------------+------------------------------ F( 4, 408) = 1.92 Model | 281.256924 4 70.314231 Prob > F = 0.1058 Residual | 14922.6559 408 36.575137 R-squared = 0.0185 -------------+------------------------------ Adj R-squared = 0.0089 Total | 15203.9128 412 36.9027011 Root MSE = 6.0477 ------------------------------------------------------------------------------ blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- blbouts | .2049663 .1111387 1.84 0.066 -.0135095 .4234422 boutspl1 | -.3300803 .145362 -2.27 0.024 -.6158321 -.0443284 boutspl2 | .1565677 .0787441 1.99 0.047 .0017729 .3113624 boutspl3 | -.033317 .0469676 -0.71 0.479 -.1256457 .0590117 _cons | 1.452344 .7033785 2.06 0.040 .0696462 2.835043 ------------------------------------------------------------------------------ Boxed t-test, CI tests H0: 4=0, i.e. no difference in per-bout difference in mean serial test performance change, above 75 bouts versus on range of 35-75 bouts

24. Regression model • regress blkdiff blbouts boutspl1 boutspl2 Source | SS df MS Number of obs = 413 -------------+------------------------------ F( 3, 409) = 2.40 Model | 262.852541 3 87.6175137 Prob > F = 0.0675 Residual | 14941.0603 409 36.5307098 R-squared = 0.0173 -------------+------------------------------ Adj R-squared = 0.0101 Total | 15203.9128 412 36.9027011 Root MSE = 6.0441 ------------------------------------------------------------------------------ blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- blbouts | .1943893 .110067 1.77 0.078 -.0219783 .4107569 boutspl1 | -.300474 .1391568 -2.16 0.031 -.5740259 -.0269222 boutspl2 | .1117487 .0469677 2.38 0.018 .0194205 .2040768 _cons | 1.480605 .7018227 2.11 0.035 .1009757 2.860235 ------------------------------------------------------------------------------ Notice that effect attenuates a little bit, but standard error decreases, and t statistic increases.

25. What is good, bad about the estimates? • The good • Accuracy (estimator is unbiased if correct mean model; SEs are accurate if correct A1-A4) • Precision (estimator is BLUE) • The bad • Not terribly robust (may be influenced by isolated points)

26. The Estimated Relationship:Mean Block Score Change, Bouts Slope = .19-.30 = -.11 Slope = .19 Slope ≈ .19-.30+.11≈0

27. Estimated Relationship:Mean Block Score Change, Bouts On bout range < 75

28. Comments • Odd finding: Apparent benefit of novice boxing, and loss of benefit (back to nominal) in early open boxing • Checked for influence: Little • Are we being misled by relationships with other variables? • Age • BL blocks design score

29. Relationship between block score change and baseline block score

30. Regression ModelAdjusting for Baseline Block Score, Age • regress blkdiff blbouts boutspl1 boutspl2 boutspl3 cenblock cenage Source | SS df MS Number of obs = 413 -------------+------------------------------ F( 6, 406) = 6.99 Model | 1423.72075 6 237.286792 Prob > F = 0.0000 Residual | 13780.1921 406 33.9413598 R-squared = 0.0936 -------------+------------------------------ Adj R-squared = 0.0802 Total | 15203.9128 412 36.9027011 Root MSE = 5.8259 ------------------------------------------------------------------------------ blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- blbouts | .1808688 .1071491 1.69 0.092 -.0297675 .3915052 boutspl1 | -.2856816 .1402603 -2.04 0.042 -.5614087 -.0099546 boutspl2 | .1390732 .0759187 1.83 0.068 -.0101697 .2883161 boutspl3 | -.0364184 .0452629 -0.80 0.422 -.1253974 .0525606 cenblock | -.1591111 .0324602 -4.90 0.000 -.2229221 -.0953 cenage | -.2683838 .1223957 -2.19 0.029 -.5089922 -.0277754 Little change in direct effects (here) from total (slide 22) . gen cenage=blage-17; . gen cenblock=blblocks-25 If final (blue) spline term removed, RSS = 13802.1648 ; SSreg = 1401.74799

31. General F-testingIs there evidence of nonlinearity in the Blocks change / Bouts relationship? • Step 1: Fit model with age, baseline blocks score, baseline bouts only. (Call these variables X1) Save the RSS. . regress blkdiff blbouts cenblock cenage Source | SS df MS Number of obs = 413 Model | 1254.61956 3 418.20652 Prob > F = 0.0000 Residual | 13949.2933 409 34.1058515 R-squared = 0.0825 -------------+------------------------------ Adj R-squared = 0.0758 Total | 15203.9128 412 36.9027011 Root MSE = 5.84 ------------------------------------------------------------------------------ blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- blbouts | -.0037381 .0065357 -0.57 0.568 -.0165858 .0091096 cenblock | -.1628229 .0324808 -5.01 0.000 -.2266731 -.0989727 cenage | -.2787612 .1224796 -2.28 0.023 -.5195294 -.0379931 _cons | 1.89059 .3536493 5.35 0.000 1.195393 2.585787 ------------------------------------------------------------------------------

32. General F-testingIs there evidence of nonlinearity in the Blocks change / Bouts relationship? • Step 2: Fit model with age, baseline blocks score, baseline bouts, and spline terms for 10, 35 bouts • Done on slide 29. Save RSSL = 13802

33. General F-testingIs there evidence of nonlinearity in the Blocks change / Bouts relationship? • Sequential ANOVA table: Source SS df MS Regression X1 Splines|X1 Residual Total 5 3 2 411 412 1401.7 SS/df (all cases) 1255 147= 13949-13802 13802 15204 (add) and 147 must add to 1402

34. General F-testingIs there evidence of nonlinearity in the Blocks change / Bouts relationship? • Step 3: F-test • [(RSSS-RSSL)/(pj)]/[RSSL/(n-p-1)] • pj = # extra parameters in larger vs. smaller model • p = number of covariates in larger model • RSSL/(n-p-1) = residual variance estimate (larger model) (2) (5)

35. General F-testingIs there evidence of nonlinearity in the Blocks change / Bouts relationship? • Step 3: F-test • [(RSSS-RSSL)/(pj)]/[RSSL/(n-p-1)] = [(13949-13802)/2]/[13802/411] = [147/2]/[13802/411] = 73.5/33.6 = 2.19 Compare to F2,411(.95) = 3.02; is less – do not reject!

36. Summary • Little evidence of relationship between boxing exposure and subsequent longitudinal decline or improvement in visuo-spatial ability as measured by the Blocks score • More work to elucidate longitudinal relationship between exposure accrual and changes in ability is needed