## 3 Results
### Survival Analysis  
We used the follow-up data for the 3504 former NBA players, of whom 687 (19.1%) died before 15 April 2015, to study the time elapsed from the end of their NBA career until death. The unadjusted nonparametric estimation of the survival function (Figure 1) shows that the estimated probability of survival to 67 years of age is about 0.15. The estimated median survival time is 54.8 years (95% confidence interval, 95% CI = 53.7-55.9 years). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Total 1** & **Active 1** & **Former 1** & **Players Who Died 2** \\ \hline  & N = 3985 & N = 481 & N = 3504 & N = 687 \\ \hline
**Position** & & & & \\ Center & 431 (11.0\%) & 53 (11.3\%) & 378 (11.0\%) & 70 (18.52\%) \\ Center–Forward & 177 (4.53\%) & 11 (2.35\%) & 166 (4.83\%) & 51 (30.72\%) \\ Forward & 1122 (28.7\%) & 146 (31.1\%) & 976 (28.4\%) & 163 (16.7\%) \\ Forward–Center & 326 (8.34\%) & 32 (6.82\%) & 294 (8.55\%) & 84 (28.57\%) \\ Forward–Guard & 193 (4.94\%) & 20 (4.26\%) & 173 (5.03\%) & 50 (28.9\%) \\ Guard & 1342 (34.3\%) & 163 (34.8\%) & 1179 (34.3\%) & 178 (15.1\%) \\ Guard–Forward & 317 (8.11\%) & 44 (9.38\%) & 273 (7.94\%) & 77 (28.21\%) \\
**Ethnicity** & & & & \\ White & 1535 (38.7\%) & 112 (23.3\%) & 1423 (40.9\%) & 517 (36.33\%) \\ Mixed & 103 (2.60\%) & 47 (9.79\%) & 56 (1.61\%) & 1 (1.79\%) \\ African-American & 2324 (58.7\%) & 321 (66.9\%) & 2003 (57.5\%) & 165 (8.24\%) \\
**Place** & & & & \\ Non-USA & 360 (9.03\%) & 100 (20.8\%) & 260 (7.42\%) & 12 (4.62\%) \\ USA & 3625 (91.0\%) & 381 (79.2\%) & 3244 (92.6\%) & 675 (20.81\%) \\
**Left handed** & & & & \\ No & 3753 (94.2\%) & 439 (91.3\%) & 3314 (94.6\%) & 661 (19.95\%) \\ Yes & 232 (5.82\%) & 42 (8.73\%) & 190 (5.42\%) & 26 (3.78\%) \\
**Age–years-at debut (mean; SD)** & 23.4 (2.11) & 22.0 (1.93) & 23.6 (2.06) & 24.2 (2.34) \\
**Age–years-at end of the last NBA** & & & & \\ season (mean; SD) & 28.2 (4.36) & 27.4 (4.21) 3 & 28.3 (4.37) & 27.8 (3.56) \\
**Height–cm (mean; SD)** & 198 (9.32) & 201 (8.75) & 198 (9.34) & 194 (8.81) \\
**Weight–kg (mean; SD)** & 94.8 (12.0) & 100 (12.1) & 94.1 (11.8) & 198 (22.1) \\
**Number of NBA games (mean; SD)** & 277 (310) & 342 (294) 3 & 268 (311) & 183 (230) \\ \hline \hline \end{tabular}  
* Percentages represent proportions of all, active, and former players, respectively; 2 Percentages represent the number of players who died, as a proportion of all former players; 3 These measures are not comparable because the active players are still playing.  
\end{table} 
Table 1: Descriptive analysis of variables for active and former players, and players who died. Regarding age of death of NBA players, we analyzed data for all active and former players and computed an unadjusted nonparametric estimation of the survival function (Figure 2). The estimated median age at death was 81.3 years (95% CI = 80.2-82.5 years). The youngest NBA player to die was [PERSON], who was killed at the age of 24 years in an airplane crash. The oldest former NBA player was [PERSON], who died at the age of 99 years. Table 2 presents the proportional hazards models for both response variables of interest; these models include all variables that were statistically significantly associated with the survival times of NBA players. According to both models, the height of NBA players is related to survival time. The positive sign of the estimated parameters indicates that instantaneous risk increases with  
Figure 1: Estimated survival probabilities of former NBA players after their NBA career. The shaded area represents the 95% confidence bands, and the horizontal line represents survival probability of 0.5. Figure 2: Estimated survival probabilities as a function of age of active and former NBA players. The shaded area represents the 95% confidence bands, and the horizontal line represents survival probability of 0.5.  
increasing height.