Estimated Bounds of Joint Probabilities of the Highest Level of American Football Played and CTE Status, Conditional on Death, VA-BU-CLF Brain Bank, 2008–2019
| Joint Probabilitiesa . | Lower Bound . | Upper Bound . |
|---|---|---|
| |$P(D+,E1\ |\mathrm{Death})$| | |$\displaystyle\frac{22}{447,081}$| | |$\displaystyle\frac{433,012}{447,081}$| |
| |$P(D+,E2\ |\mathrm{Death})$| | |$\displaystyle\frac{47}{447,081}$| | |$\displaystyle\frac{12,476}{447,081}$| |
| |$P(D+,E3\ |\mathrm{Death})$| | |$\displaystyle\frac{166}{447,081}$| | |$\displaystyle\frac{1,538}{447,081}$| |
| |$P(D-,E1\ |\ \mathrm{Death})$| | |$\displaystyle\frac{29}{447,081}$| | |$\displaystyle\frac{433,019}{447,081}$| |
| |$P(D-,E2\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{12,442}{447,081}$| |
| |$P(D-,E3\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{1,345}{447,081}$| |
| Joint Probabilitiesa . | Lower Bound . | Upper Bound . |
|---|---|---|
| |$P(D+,E1\ |\mathrm{Death})$| | |$\displaystyle\frac{22}{447,081}$| | |$\displaystyle\frac{433,012}{447,081}$| |
| |$P(D+,E2\ |\mathrm{Death})$| | |$\displaystyle\frac{47}{447,081}$| | |$\displaystyle\frac{12,476}{447,081}$| |
| |$P(D+,E3\ |\mathrm{Death})$| | |$\displaystyle\frac{166}{447,081}$| | |$\displaystyle\frac{1,538}{447,081}$| |
| |$P(D-,E1\ |\ \mathrm{Death})$| | |$\displaystyle\frac{29}{447,081}$| | |$\displaystyle\frac{433,019}{447,081}$| |
| |$P(D-,E2\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{12,442}{447,081}$| |
| |$P(D-,E3\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{1,345}{447,081}$| |
Abbreviations: CTE, chronic traumatic encephalopathy; VA-BU-CLF, Veterans Affairs–Boston University–Concussion Legacy Foundation.
a P(D+, E1|Death) denotes the joint probability of CTE diagnosis and having played high school football; P(D+, E2|Death) denotes the joint probability of CTE diagnosis and having played college football; and P(D+, E3|Death) denotes the joint probability of CTE diagnosis and having played professional football. P(D−, E1|Death) denotes the joint probability of no CTE diagnosis and having played high school football; P(D−, E2|Death) denotes the joint probability of no CTE diagnosis and having played college football; and P(D−, E3|Death) denotes the joint probability of no CTE diagnosis and having played professional football.
Estimated Bounds of Joint Probabilities of the Highest Level of American Football Played and CTE Status, Conditional on Death, VA-BU-CLF Brain Bank, 2008–2019
| Joint Probabilitiesa . | Lower Bound . | Upper Bound . |
|---|---|---|
| |$P(D+,E1\ |\mathrm{Death})$| | |$\displaystyle\frac{22}{447,081}$| | |$\displaystyle\frac{433,012}{447,081}$| |
| |$P(D+,E2\ |\mathrm{Death})$| | |$\displaystyle\frac{47}{447,081}$| | |$\displaystyle\frac{12,476}{447,081}$| |
| |$P(D+,E3\ |\mathrm{Death})$| | |$\displaystyle\frac{166}{447,081}$| | |$\displaystyle\frac{1,538}{447,081}$| |
| |$P(D-,E1\ |\ \mathrm{Death})$| | |$\displaystyle\frac{29}{447,081}$| | |$\displaystyle\frac{433,019}{447,081}$| |
| |$P(D-,E2\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{12,442}{447,081}$| |
| |$P(D-,E3\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{1,345}{447,081}$| |
| Joint Probabilitiesa . | Lower Bound . | Upper Bound . |
|---|---|---|
| |$P(D+,E1\ |\mathrm{Death})$| | |$\displaystyle\frac{22}{447,081}$| | |$\displaystyle\frac{433,012}{447,081}$| |
| |$P(D+,E2\ |\mathrm{Death})$| | |$\displaystyle\frac{47}{447,081}$| | |$\displaystyle\frac{12,476}{447,081}$| |
| |$P(D+,E3\ |\mathrm{Death})$| | |$\displaystyle\frac{166}{447,081}$| | |$\displaystyle\frac{1,538}{447,081}$| |
| |$P(D-,E1\ |\ \mathrm{Death})$| | |$\displaystyle\frac{29}{447,081}$| | |$\displaystyle\frac{433,019}{447,081}$| |
| |$P(D-,E2\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{12,442}{447,081}$| |
| |$P(D-,E3\ |\ \mathrm{Death})$| | |$\displaystyle\frac{13}{447,081}$| | |$\displaystyle\frac{1,345}{447,081}$| |
Abbreviations: CTE, chronic traumatic encephalopathy; VA-BU-CLF, Veterans Affairs–Boston University–Concussion Legacy Foundation.
a P(D+, E1|Death) denotes the joint probability of CTE diagnosis and having played high school football; P(D+, E2|Death) denotes the joint probability of CTE diagnosis and having played college football; and P(D+, E3|Death) denotes the joint probability of CTE diagnosis and having played professional football. P(D−, E1|Death) denotes the joint probability of no CTE diagnosis and having played high school football; P(D−, E2|Death) denotes the joint probability of no CTE diagnosis and having played college football; and P(D−, E3|Death) denotes the joint probability of no CTE diagnosis and having played professional football.
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