Biostatistics 140 653 Case Study Amateur Boxing Neuropsychological
Biostatistics 140. 653 Case Study: Amateur Boxing & Neuropsychological Impairment July 14, 2011
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.
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
Scientific Question: Does boxing cause cerebral injury? • Hypothesized pathway: brain jarring
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
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 – Electrophysiologic Battery – Ataxia and Neurological Tests (Today: Block Design) • Covariates – Primary: – Secondary: number of bouts boxed age, race, education, Ravens IQ score, club, non-boxing concussion history, drug test result
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
Unlinking Effect evidence: Status versus Change
Unlinking Effect evidence: Status versus Change
Model Building • Suppose goal = capture both relationships: status and change – Considered, rejected: E[Yit|Xi] = 0+ 1 Xit • Y = blocks score; X=#bouts • i=people 1, …, n; t=times 1, 2 (…) Allows age-related – Way to think: status 1 & change 2 change Time 1: E[Y |X ] = + X i 1 i 0 1 i 1 between t 1 and t 2 Time 2: E[Yi 2|Xi] = 0+ 1 X + i 1 2(Xi 2 -Xi 1+) 3
Model Building E[Yi 1|Xi] = 0+ 1 Xi 1 E[Yi 2|Xi] = 0+ 1 Xi 1 + 2(Xi 2 -Xi 1) + 3 i. e. E[Yit|Xi 1, Xi 2] = 0+ 1 Xi 1 + 2(Xi 2 -Xi 1)*1{t=2} + 31{t=2} • Interpret • Zero out other 3 coefficients you can: Xi 1 = Xi 2 -Xi 1=0 • Then, time 2 mean = 0+ 3; time 1 mean = 0 • 3 = Mean change in block score among non-boxers thru time 2 • How to test for equal status, change relationships? • Test H 0: 2 = 1 f
Model Building • From now on: we’ll analyze relationship between change in blocks score (t 2 -t 1) and – baseline bout total – change in bout total – N=413 in the analysis • Why the baseline bout total? • Models potentially delayed effect
Exploratory Data Analysis blkdiff blbouts y=0 boutdiff
New model building goal • From now on: we’ll analyze relationship between change in blocks score (t 2 -t 1) and – baseline bout total – change in bout total • In real life: validation, errors-invariables (covariates) analysis
Exploratory Data Analysis Scatterplot: Blocks Change vs. BL Bouts
Exploratory Data Analysis Scatterplot: Blocks Change vs. BL Bouts . lowess blkdiff blbouts if blbouts < 75
Modeling options • Linear Y, X model OTHERS? Highly sensitive to • Polynomial Y, X model extreme points Obscure • Replace X by √X, etc. (transform) interpretation Wastes much exposure • Categorize X information; categories arbitrary? • Spline Y, X model
Spline Model Relationship: 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:
Spline Model Relationship: Change in Blocks, Bouts • Order - Number of polynomial terms underlying relationship – Plot up to 75 bouts appears fairly linear – Smooth after 75 bouts appears fairly linear - Order = 1 • (Population) Model: E[Yi 2 -Yi 1|Xi 1] = 0+ 1 Xi 1 + 2(Xi 1 -10)+ + 3(Xi 1 -35)+ + 4(Xi 1 -75)+
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)
Design Matrix
Regression model • regress blkdiff blboutspl 1 boutspl 2 boutspl 3 Source | SS df MS -------+---------------Model | 281. 256924 4 70. 314231 Residual | 14922. 6559 408 36. 575137 -------+---------------Total | 15203. 9128 412 36. 9027011 Number of obs F( 4, 408) Prob > F R-squared Adj R-squared Root MSE = = = 413 1. 92 0. 1058 0. 0185 0. 0089 6. 0477 ---------------------------------------blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------+--------------------------------per-bout 1. 84 diff in 0. 066 Blocks Change, Novice. 4234422 Boxers blbouts |. 2049663 Mean. 1111387 -. 0135095 boutspl 1 | -. 3300803. 145362 -2. 27 0. 024 -. 6158321 -. 0443284 boutspl 2 |. 1565677. 0787441 1. 99 0. 047. 0017729. 3113624 boutspl 3 | -. 033317. 0469676 -0. 71 0. 479 -. 1256457. 0590117 _cons | 1. 452344 Mean. 7033785 2. 06 0. 040. 0696462 2. 835043 Block Score Change, 0 Bouts ---------------------------------------Mean per-10 bout diff in Blocks Change, Novice Boxers? In each case, coefficient estimates the population mean! 2. 05 points
Regression model • regress blkdiff blboutspl 1 boutspl 2 boutspl 3 Source | SS df MS -------+---------------Model | 281. 256924 4 70. 314231 Residual | 14922. 6559 408 36. 575137 -------+---------------Total | 15203. 9128 412 36. 9027011 Number of obs F( 4, 408) Prob > F R-squared Adj R-squared Root MSE = = = 413 1. 92 0. 1058 0. 0185 0. 0089 6. 0477 ---------------------------------------blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------+--------------------------------blbouts |. 2049663. 1111387 1. 84 0. 066 -. 0135095. 4234422 boutspl 1 | -. 3300803. 145362 -2. 27 0. 024 -. 6158321 -. 0443284 boutspl 2 |. 1565677. 0787441 1. 99 0. 047. 0017729. 3113624 boutspl 3 | -. 033317. 0469676 -0. 71 0. 479 -. 1256457. 0590117 _cons | 1. 452344. 7033785 2. 06 0. 040. 0696462 2. 835043 --------------------------------------- Boxed t-test, CI tests H 0: 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
Regression model • regress blkdiff blboutspl 1 boutspl 2 Source | SS df MS -------+---------------Model | 262. 852541 3 87. 6175137 Residual | 14941. 0603 409 36. 5307098 -------+---------------Total | 15203. 9128 412 36. 9027011 Number of obs F( 3, 409) Prob > F R-squared Adj R-squared Root MSE = = = 413 2. 40 0. 0675 0. 0173 0. 0101 6. 0441 ---------------------------------------blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------+--------------------------------blbouts |. 1943893. 110067 1. 77 0. 078 -. 0219783. 4107569 boutspl 1 | -. 300474. 1391568 -2. 16 0. 031 -. 5740259 -. 0269222 boutspl 2 |. 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.
What is good, bad about the estimates? • The good – Accuracy (estimator is unbiased if correct mean model; SEs are accurate if correct A 1 -A 4) – Precision (estimator is BLUE) • The bad – Not terribly robust (may be influenced by isolated points)
The Estimated Relationship: Mean Block Score Change, Bouts Slope =. 19 -. 30 = -. 11 Slope =. 19 Slope ≈. 19 -. 30+. 11≈0
Estimated Relationship: Mean Block Score Change, Bouts On bout range < 75
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
Relationship between block score change and baseline block score
Regression Model Adjusting for Baseline Block Score, Age • regress blkdiff blboutspl 1 boutspl 2 boutspl 3 cenblock cenage Source | SS df MS -------+---------------Model | 1423. 72075 6 237. 286792 Residual | 13780. 1921 406 33. 9413598 -------+---------------Total | 15203. 9128 412 36. 9027011 Number of obs F( 6, 406) Prob > F R-squared Adj R-squared Root MSE = = = 413 6. 99 0. 0000 0. 0936 0. 0802 5. 8259 Little change in direct effects (here) from total (slide 22) ---------------------------------------blkdiff | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------+--------------------------------blbouts |. 1808688. 1071491 1. 69 0. 092 -. 0297675. 3915052 boutspl 1 | -. 2856816. 1402603 -2. 04 0. 042 -. 5614087 -. 0099546 boutspl 2 |. 1390732. 0759187 1. 83 0. 068 -. 0101697. 2883161 boutspl 3 | -. 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. gen cenage=blage-17; . gen cenblock=blblocks-25 If final (blue) spline term removed, RSS = 13802. 1648 ; SSreg = 1401. 74799
General F-testing Is 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 X 1) Save the RSS. . regress blkdiff blbouts cenblock cenage Source | SS df MS Model | 1254. 61956 3 418. 20652 Residual | 13949. 2933 409 34. 1058515 -------+---------------Total | 15203. 9128 412 36. 9027011 Number of obs Prob > F R-squared Adj R-squared Root MSE = = = 413 0. 0000 0. 0825 0. 0758 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 ---------------------------------------
General F-testing Is 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
General F-testing Is there evidence of nonlinearity in the Blocks change / Bouts relationship? • Sequential ANOVA table: Source SS df 5 1401. 7 Regression 3 1255 X 1 2 147= Splines|X 1 13949 -13802 Residual Total 13802 15204 (add) 411 412 and 147 must add to 1402 MS SS/df (all cases)
General F-testing Is 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 (2) – p = number of covariates in larger model (5) – RSSL/(n-p-1) = residual variance estimate (larger model)
General F-testing Is 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 F 2, 411(. 95) = 3. 02; is less – do not reject!
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
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