Table 7.

Estimated Relationship Between Highest Level of American Football Played and Diagnosis of CTE, After Adjustment for Selection Bias, When CTE Is Conditioned on Death (Sensitivity Analyses) Among Brain Donors From the VA-BU-CLF Brain Bank, 2008–2019

Highest Level of Play a	Selection-Bias–Adjusted Estimate b
	Mean RR	95% SI	Median RR
Collegec
Upwards	2.33	1.28, 5.17	2.01
Downwards	1.97	0.58, 4.87	1.72
No relationship between probabilities	2.11	0.58, 5.50	1.77
Initially randomly selecting a probability	2.25	0.84, 5.50	1.93
Professionalc
Upwards	2.43	1.51, 4.33	2.25
Downwards	2.20	0.99,4.21	2.05
No relationship between probabilities	2.24	1.05, 4.30	2.07
Initially randomly selecting a probability	2.38	1.26, 4.52	2.19

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

^a Sampling schemes were implemented as follows: 1) by first sampling the smallest conditional selection probability in the imposed inequality and iterating upwards; 2) by first sampling the largest conditional selection probability in the imposed inequality and iterating downwards; 3) by assuming no hierarchical relationship between the conditional selection probabilities and drawing each from the prespecified bounds, independently of all other probabilities; and 4) by first randomly selecting a conditional selection probability and then sampling according to its plausible bounds, and then sampling the remaining conditional selection probabilities in order to maintain the inequality.

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

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