Mortality risk factors among National Football League players: An analysis using player career data.

In general, National Football League (NFL) players tend to live longer than the general population. However, little information exists about the long-term mortality risk in this population. Frequent, yet mild, head trauma may be associated with early mortality in this group of elite athletes. Therefore, career playing statistics can be used as a proxy for frequent head trauma. Using data from Pro Football Reference, we analyzed the association between age-at-death, position, and NFL seasons-played among 6,408 NFL players that were deceased as of July 1, 2018. The linear regression model allowing for a healthy worker effect demonstrated the best fit statistics (F-statistic = 9.95, p-value = 0.0016). The overall association of age-at-death and seasons-played is positive beginning at the 10.75 and 10.64 seasons-played point in our two models that feature seasons-played and seasons-played squared as explanatory variables. Previous research that does not account for the healthy worker effect may not adequately describe mortality risk among NFL players.


Invited Reviewers
Any reports and responses or comments on the article can be found at the end of the article.

Introduction
Very little information exists about mortality and long-term health outcomes among National Football League (NFL) players. Elite football players tend to have a lower overall mortality rate than the general population, often attributed to routine physical activity 1,2 . However, this occupational group cannot be directly compared to the general population 3 . Several studies in small numbers of NFL players have found an association between traumatic brain injuries with depression, suicide, dementia, and chronic traumatic encephalopathy [4][5][6] . There is mounting evidence that even sub-clinical head impacts, especially when they occur frequently, can also lead to these adverse health outcomes 7,8 . However, these relationships are difficult to study systematically due to few cases, challenges with diagnostics, and long lag time from the injury to symptom onset. Yet, there exists a rich repository of data surrounding NFL career playing statistics 9 . We hypothesize that certain player career attributes, including position-of-play and seasons-played, are likely to be strong predictors for mortality from repeated, yet mild, head trauma.
Here, we study the association between mortality and NFL seasons-played, while controlling for playing position.

Methods
Data was collected from Pro Football Reference, a free online database maintained by Sports Reference LLC that includes playing statistics from every player in NFL history, over 25,000 in total, with meticulously recorded data beginning in 1922 9 . Variables of interest include birthdate, death date, position, height, weight, and seasons-played. This data is freely and publicly available from Pro Football Reference 9 . Individuals with any missing data were eliminated, leaving 24,740 players. Category 3: offensive and defensive linemen: 3,118 dead/9,097 players (34%).

Statistical analysis
Expected age-at-death was calculated from the 2017 National Vital Statistics Report 12 using average years of life remaining at 20 years of age for the decade of the 20th year plus 20. Age-at-death residuals were calculated as observed age-at-death minus expected age-at-death. This analysis was completed in Stata Version 14 13 , and data was visualized using R 3.6.1 14 .
Associations were assessed using linear regression models with a quadratic term for seasons-played. Specifically, we use (position) fixed-effect ordinary least squares modeling to determine whether associations exist between age-at-death residual, number of NFL seasons-played (squared), and position category fixed effects. In these models, we seek to assess whether career duration exposure relates significantly to age-at-death residual conditional on position-of-play. The survivorship bias turning point was calculated using standard differential calculus techniques (i.e., calculating the minimum point of a best fit surface).

Position Category Fixed Effects Model
Age at Death Residual i,t = β 0 + β 1 Number of Seasons Played i,t + ε i,t + β 2 Number of Seasons Played 2 i,t + ε i,t + β 3 Position Category i + ε i,t Table 1 indicates substantial demographic sample variation between players of different position categories in height, weight, BMI, and age-at-death. Certain healthy or durable players can play an increased number of seasons without a corresponding reduction in expected age-at-death as compared to players of shorter career duration 3 .

Results and discussion
The Seasons-played Squared and Position Category Fixed Effects models specify a quadratic term for number of NFL seasonsplayed. For both models, the coefficient for this variable is significant and improves the model's explanatory power according to an Anova F-test for difference in overall model significance (F-statistic = 9.95, p-value = 0.0016; F-statistic=10.98, p-value<0.001) ( Table 2). We calculate that overall association of age-at-death residual and seasons-played is positive beginning at 10.75 and 10.63 seasons-played for the Seasons-played Squared and Position Category Fixed Effects model, respectively. This demonstrates a survivorship effect within the NFL population, where certain players are not as prone to playrelated mortality risk. We define this effect within the NFL population as a longitudinal survivorship bias where certain

Amendments from Version 2
The replicated data for this study is no longer available online. However, the original data is freely available from the primary data source, which is cited in the paper. This version of the paper has been updated to include all steps necessary to calculate the derived data from the primary data source.   players' ability to play diminishes over time such that the players are removed from the cohort. For these deceased players, the survivorship bias is sufficiently strong to dominate an observed mortality risk, where the survivorship effect drives the negative relationship between seasons-played and age-at-death residual for those playing fewer than 10.75 (10.63) seasons. The survivorship bias and the mortality risk hold conditional upon position category control variables, as found in previous literature 11 . However, dividing players into three position categories may not sufficiently capture the differing on-field exposures that may contribute to mortality.

Policy implications
This study suggests that NFL career duration is typically a risk factor for early mortality. However, player characteristics leading to extreme career survivorship are also important and can act to countervail the risk exposures from NFL seasons played. Injury histories of players with a relatively short NFL career may be particularly important toward recommending modifications to game play that are conducive to mitigating these early mortality risk factors. We also find variation in early mortality risk by position category. Again, rule changes that serve to mitigate risks (e.g., head impact) at particularly vulnerable positions may lead to marked long term improvements in player health.

Conclusion
This paper finds evidence of both player health risk (in terms of age-at-death residual) for increasing NFL seasons played and a survivorship bias among NFL players. For Category I and II players, the latter risk dominates the former for NFL players with sufficient career survivorship. This effect holds conditional upon position-of-play control variables. Previous research not accounting for this survivorship bias/healthy worker effect may not adequately describe mortality risk among NFL players.

Future work
As this study only used publicly available data, we only analyzed all-cause mortality as cause of death is not included in the database. Both cause of death and quality of life throughout life are very important to the study of the hazards associated with football. We are pursuing additional research to examine the association of on-field playing characteristics with mortality and cause of death among NFL players.

Ethics
This study was determined by the Syracuse University Institutional Review Board to not be human subjects research and therefore, not to require review and oversight. The authors recognize that what they may have found is a "longitudinal survivorship effect" within a worker cohort, not a "healthy worker effect," and they now use the former term more often than the latter. However, the first time either term appears is in the Abstract, where "healthy worker effect" alone is used. Because so many articles in the football-risk literature fail to appreciate the HWE, it's important that this one-which does "get it"-uses the term correctly.
I may not have been completely clear in my prior review about my concerns with respect to outliers. The authors have justified their use of players with an extremely long number of seasons played as a statistical matter (although their response to reviews claims they have added a statement about the limitations of using all data, which they haven't really done…). But my concern was/is about how the outliers with respect to the number of seasons may not in fact be outliers with respect to the number of games played, and thus that the entire analysis using seasons may be sub-optimal. I merely note that the five players with the greatest number of seasons (Tittle, Baugh, Blanda, Unitas, and Morrall) may well not have played any more games than players in the middle of the distribution, because they were backup QBs for part of their careers. So a second analysis using games rather than seasons as the main independent variable could be very illuminating.

2.
I agree that the authors have examined all-cause mortality, but that's why it's slightly confusing that they invoke "frequent head trauma" in the abstract and use three keywords relating to concussion and CTE. I look forward to their future research where cause-of-death and quality-of-life data may be marshaled to firm up the connection between seasons (games) played, head trauma, and those causes of death and morbidity that are plausibly related to head trauma.

3.
The new "policy implications" paragraph is welcome, but it does not mention the single most important point, one that the authors put in their response to reviews: "To make the game safer, we must identify which players are at an elevated risk." This is the policy implication of a survivorship effect. As a policy analyst, I would personally go on to say that we need not only to identify those players but craft policies (rule changes, medical monitoring, protective equipment, etc.) that can reduce these players' risks without discriminating against them needlessly because of their "susceptibility." The football literature is already replete with confused and tautologous statements about how CTE only occurs "among those who are sensitive."

4.
Competing Interests: No competing interests were disclosed.
Reviewer Expertise: quantitative risk assessment; epidemiology; regulatory policy

If applicable, is the statistical analysis and its interpretation appropriate? Yes
Are all the source data underlying the results available to ensure full reproducibility? Yes

Are the conclusions drawn adequately supported by the results? Yes
In this context, a true HWE occurs when reach the mistaken conclusion that X is not riskier than not-X (as in "football players don't die more often of cancer than general population"), or even that X is safer than not-X, but what's really happening is that being in class X shows you were less likely to have the risk than general to begin with. This is important to find and point out, because then  635-644 4 ). Heterogeneity-dynamics means that you may need to adjust the slope of an observed dose-response function to account for the fact that there are 2 or more subpopulations within the subpopulation-everyone can have an individual positive association between seasons and risk, but the group may have a flat (null) slope simply because those who played the most seasons were not "lucky" but more immune.
The difference between a finding of an HWE between football and the general public, versus the finding of two of more differentially-susceptible subgroups within the NFL population, is far from merely semantic, because the practical implications of the two situations are so different. Finding an HWE allows the researcher to correct for it, either by discarding a flawed analysis in favor of an apples-to-apples comparison, or by taking the existing analysis and trying to re-estimate the odds ratio (see, for example, Joffe, 2012 5 ). Even without correction, researchers who appreciate the pitfalls of the HWE can simply say that it leads to false negatives preferentially: comparing, for example, the cognitive performance of 60-year-old retired NFL players against the general population of that age would tend to divert attention away from the consequences of repeated head trauma (RHT) simply because the general population includes many persons who were never fit enough to work, let alone work in this taxing occupation.
But finding a negative-then-positive relationship between length of (NFL) career and age at death, because the cohort under study has, by definition, more fit persons remaining as more and more of the cohort dies early, may have no empirical or policy implications whatsoever. The authors say nothing about how we might even identify who among incoming NFL players might "benefit" from longer careers and whose dose-response is the most steeply negative-if we could, and IF we had the means and the will to discourage the latter group from choosing this occupation, THEN perhaps we could make use of the "finding" that some players are not at risk to the extent that others are (there is an extensive literature about the gap between identifying a powerful interindividual risk factor in a working population-these are usually genetic factors, such as "slow acetylators" who are more at risk from certain occupational chemicals-and the wisdom of trying to exclude these people from the workplace. Generally, policy analysts prefer interventions that can make the workplace safe for everyone who participates-imagine a policy of not allowing people with hemophilia to become carpenters, as opposed to OSHA regulations that mandate guards on saws so that no one will be cut by them).
So this article, at most, finds an "expected curiosity"-that once you have had a long career, you probably are revealing to an epidemiologist that you have been more "immune" to the harmful effects of that career than the average person-and then says nothing about how we could use the finding to adjust scientific conclusions or policy responses. By invoking the HWE throughout the paper, the authors are not only using the wrong term, but inviting statistical corrections or policy responses that have already been made or that would not respond to what they may have actually found.
But all the foregoing assumes that the authors have actually found evidence of a "resistant subpopulation" within the NFL cohort, and I'm not sure that's the case. The authors don't mention alternative explanations for the slight upslope in Figures 1a and 1b, including: (1) reverse causation-if a significant number of players died on the field or soon after sustaining footballrelated injuries early in their careers, then of course the remaining population would not have "negative death residuals" that large; and (2) effect modification-similarly, if physical inactivity leads to earlier death, then players who sustained career-ending injuries early on would die earlier than others.
More problematic is the use of rote statistics without also applying "common sense" to the finding. How robust, in particular, is the slight upslope obtained by regression to the presence of outliers?
The interactive Figures show that the five players with the longest careers were Sammy Baugh, Johnny Unitas, George Blanda, Earl Morrall, and YA Tittle. Some of these (Morrall) I believe played long careers but were backups much of the time, so an index based on number of games rather than seasons might have shown something different. It would be important to explore what happens to the upslope if outliers were trimmed-I say this in part because visual exploration of the Figures does not present a compelling "common sense" picture of a positive slope among the longer careers; I believe the numbers, but the visual impression, especially excluding outliers, is one of a rather FLAT dose-response that one might be convinced is slightly negative and then very slightly positive. Similarly, I accept (p. 3) that the quadratic model fits slightly better than the linear one, but the authors don't let on how well the linear model fit in the first place. Could they be "finding" something more sophisticated simply by over-fitting? Also, I dispute that the fixed-effects model is correct, with respect to the kinds of effects (CTE, dementia) the authors clearly are trying to shed light on. The three categories they use seem out-of-place here: other studies have shown that the three positions with the greatest cumulative amount of RHT (instances times g-forces) are tight ends, quarterbacks, and defensive linemen, and yet these are in three different categories in this model! Finally, the authors focus on mortality, which is fine, but completely ignore quality of life. Just consider the case of Earl Morrall, who lived to age 79 (death residual of > 10) but who reportedly had Stage 4 CTE and a reduced QOL. Someone who comes away from the paper concluding that "once you play 11 seasons, you may live longer than your cohort" may not realize that age at death is not the most relevant outcome… In summary, the authors should replace "HWE" with "interindividual variability in susceptibility," explore the implications of THAT analysis, consider how robust their analyses of statistical significance actually are, and ground this paper in terms of the other more ambitious studies that have already explored the relationship between better indices of lifetime intensity of play and mortality/morbidity (especially Montenigro et al., 2017 6 ). They might also consider this recent paper by Mez et al. 7 and explore if and how their quadratic model might better explain (or be contradicted by) these prior findings.
we will frame the HWE as a longitudinal survivorship effect where people are removed from the cohort. We agree there are heterogeneity dynamics at work and will term this as a "survivorship effect" throughout. We thank the reviewer for suggestions regarding the policy implications and will clarify our policy section accordingly. To make the game safer, we must identify which players are at an elevated risk.
While the reviewer has valid points about outliers, we would prefer to keep them in our analysis. To address outliers, we specified robust standard errors to measure risk factors for mortality in a manner consistent with valid derivation of t-statistics. We disagree with the reviewer and prefer to keep outliers in the dataset. We did not eliminate the outliers so as not to introduce selection bias. Furthermore, this a complete census of the players and we calculated population parameters, not sample statistics; therefore, we prefer to keep all players in the analysis. We will be more clear in the revised draft that we are analyzing the population of NFL players. As such, there is no need to worry about outliers that have an unrepresentative influence vis-à-vis the underlying population. However, we will add in a statement in the limitations about our choice to keep the outliers.
We agree that quality of life and cause of death are important considerations. Here, we analyze all-cause mortality, not CTE specific mortality. Therefore, the papers the reviewer suggested may not be appropriate because we have all deaths in this population, not a selected sub-sample. While in our future research, we hope to focus on quality of life and cause-specific mortality, that is not possible with this data. We will add in statements about these limitations and future directions.

Competing Interests:
No competing interests were disclosed.
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