Table 8 Open in new tab Estimated...

	Selection-Bias–Adjusted Estimate When CTE Is Not Conditioned on Death^a
College^c
Upwards	1.46	0.60, 3.55	1.23	2.92	1.20, 7.11	2.46	4.38	1.81, 10.66	3.69
Downwards	1.24	0.32, 3.38	1.03	2.48	0.63, 6.75	2.06	3.72	0.95, 10.13	3.09
No relationship between probabilities	1.33	0.32, 3.75	1.07	2.65	0.63, 7.51	2.13	3.98	0.95, 11.26	3.21
Initially randomly selecting a probability	1.41	0.44, 3.73	1.17	2.83	0.88, 7.46	2.34	4.24	1.32, 11.19	3.51
Professional^c
Upwards	1.76	0.87, 3.55	1.58	3.51	1.74, 7.09	3.17	5.27	2.61, 10.64	4.75
Downwards	1.59	0.62, 3.43	1.42	3.17	1.25, 6.87	2.85	4.76	1.87, 10.30	4.27
No relationship between probabilities	1.62	0.64, 3.50	1.45	3.23	1.29, 7.00	2.89	4.85	1.93, 10.50	4.34
Initially randomly selecting a probability	1.72	0.75, 3.66	1.54	3.44	1.51, 7.32	3.07	5.15	2.26, 10.98	4.61

Selection-Bias–Adjusted Estimate When CTE Is Not Conditioned on Death^a

Highest Level of Play

0.50^b

1.00^b

1.50^b

Mean RR

95% SI

Median RR

Mean RR

95% SI

Median RR

Mean RR

95% SI

Median RR

College^c

Upwards

1.46

0.60, 3.55

1.23

2.92

1.20, 7.11

2.46

4.38

1.81, 10.66

3.69

Downwards

1.24

0.32, 3.38

1.03

2.48

0.63, 6.75

2.06

3.72

0.95, 10.13

3.09

No relationship between probabilities

1.33

0.32, 3.75

1.07

2.65

0.63, 7.51

2.13

3.98

0.95, 11.26

3.21

Initially randomly selecting a probability

1.41

0.44, 3.73

1.17

2.83

0.88, 7.46

2.34

4.24

1.32, 11.19

3.51

Professional^c

Upwards

1.76

0.87, 3.55

1.58

3.51

1.74, 7.09

3.17

5.27

2.61, 10.64

4.75

Downwards

1.59

0.62, 3.43

1.42

3.17

1.25, 6.87

2.85

4.76

1.87, 10.30

4.27

No relationship between probabilities

1.62

0.64, 3.50

1.45

3.23

1.29, 7.00

2.89

4.85

1.93, 10.50

4.34

Initially randomly selecting a probability

1.72

0.75, 3.66

1.54

3.44

1.51, 7.32

3.07

5.15

2.26, 10.98

4.61

	Selection-Bias–Adjusted Estimate When CTE Is Not Conditioned on Death^a
College^c
Upwards	1.46	0.60, 3.55	1.23	2.92	1.20, 7.11	2.46	4.38	1.81, 10.66	3.69
Downwards	1.24	0.32, 3.38	1.03	2.48	0.63, 6.75	2.06	3.72	0.95, 10.13	3.09
No relationship between probabilities	1.33	0.32, 3.75	1.07	2.65	0.63, 7.51	2.13	3.98	0.95, 11.26	3.21
Initially randomly selecting a probability	1.41	0.44, 3.73	1.17	2.83	0.88, 7.46	2.34	4.24	1.32, 11.19	3.51
Professional^c
Upwards	1.76	0.87, 3.55	1.58	3.51	1.74, 7.09	3.17	5.27	2.61, 10.64	4.75
Downwards	1.59	0.62, 3.43	1.42	3.17	1.25, 6.87	2.85	4.76	1.87, 10.30	4.27
No relationship between probabilities	1.62	0.64, 3.50	1.45	3.23	1.29, 7.00	2.89	4.85	1.93, 10.50	4.34
Initially randomly selecting a probability	1.72	0.75, 3.66	1.54	3.44	1.51, 7.32	3.07	5.15	2.26, 10.98	4.61

Table 8

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Estimated Relationship Between Highest Level of American Football Played and Diagnosis of CTE, After Adjustment for Selection Bias, When CTE Is Not Conditioned on Death (Sensitivity Analyses) Among Brain Donors From the VA-BU-CLF Brain Bank, 2008–2019

	Selection-Bias–Adjusted Estimate When CTE Is Not Conditioned on Death^a
Highest Level of Play	0.50^b			1.00^b			1.50^b
	Mean RR	95% SI	Median RR	Mean RR	95% SI	Median RR	Mean RR	95% SI	Median RR
College^c
Upwards	1.46	0.60, 3.55	1.23	2.92	1.20, 7.11	2.46	4.38	1.81, 10.66	3.69
Downwards	1.24	0.32, 3.38	1.03	2.48	0.63, 6.75	2.06	3.72	0.95, 10.13	3.09
No relationship between probabilities	1.33	0.32, 3.75	1.07	2.65	0.63, 7.51	2.13	3.98	0.95, 11.26	3.21
Initially randomly selecting a probability	1.41	0.44, 3.73	1.17	2.83	0.88, 7.46	2.34	4.24	1.32, 11.19	3.51
Professional^c
Upwards	1.76	0.87, 3.55	1.58	3.51	1.74, 7.09	3.17	5.27	2.61, 10.64	4.75
Downwards	1.59	0.62, 3.43	1.42	3.17	1.25, 6.87	2.85	4.76	1.87, 10.30	4.27
No relationship between probabilities	1.62	0.64, 3.50	1.45	3.23	1.29, 7.00	2.89	4.85	1.93, 10.50	4.34
Initially randomly selecting a probability	1.72	0.75, 3.66	1.54	3.44	1.51, 7.32	3.07	5.15	2.26, 10.98	4.61

	Selection-Bias–Adjusted Estimate When CTE Is Not Conditioned on Death^a
Highest Level of Play	0.50^b			1.00^b			1.50^b
	Mean RR	95% SI	Median RR	Mean RR	95% SI	Median RR	Mean RR	95% SI	Median RR
College^c
Upwards	1.46	0.60, 3.55	1.23	2.92	1.20, 7.11	2.46	4.38	1.81, 10.66	3.69
Downwards	1.24	0.32, 3.38	1.03	2.48	0.63, 6.75	2.06	3.72	0.95, 10.13	3.09
No relationship between probabilities	1.33	0.32, 3.75	1.07	2.65	0.63, 7.51	2.13	3.98	0.95, 11.26	3.21
Initially randomly selecting a probability	1.41	0.44, 3.73	1.17	2.83	0.88, 7.46	2.34	4.24	1.32, 11.19	3.51
Professional^c
Upwards	1.76	0.87, 3.55	1.58	3.51	1.74, 7.09	3.17	5.27	2.61, 10.64	4.75
Downwards	1.59	0.62, 3.43	1.42	3.17	1.25, 6.87	2.85	4.76	1.87, 10.30	4.27
No relationship between probabilities	1.62	0.64, 3.50	1.45	3.23	1.29, 7.00	2.89	4.85	1.93, 10.50	4.34
Initially randomly selecting a probability	1.72	0.75, 3.66	1.54	3.44	1.51, 7.32	3.07	5.15	2.26, 10.98	4.61

Abbreviations: CTE, chronic traumatic encephalopathy; RR, risk ratio; SI, simulation interval; VA-BU-CLF, Veterans Affairs–Boston University–Concussion Legacy Foundation.

^a The adjusted RR estimate is the mean (and median) of the sampling distribution; the 95% SI was constructed from the 2.5th and 97.5th percentiles of the sampling distribution.

^b |$\frac{P(\mathrm{Death}|E+)\kern0.50em }{P(\mathrm{Death}|E-)}$|_.

^c Referent: high school (RR = 1).

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