## 3 Results
### Survival Analysis
In addition, when comparing African-American players to white players, the estimated adjusted hazard ratio is 1.4 for both models, indicating higher instantaneous risk among African-American players. The increase in LE in recent decades is reflected in the negative sign of the parameter estimate for the variables for year of players' last (Model I) and first NBA seasons (Model II). The positive sign of the parameter estimate of the age variable at end of their NBA career (Model I) is expected because it reflects the fact that average survival time is longer the younger the player was when he finishes his career. However, it does not imply that this variable is related to age at death. Further NBA career-related variables, such as number of NBA games, which could have been included in Model I, were not statistically significant. The analysis of the Schoenfeld residuals by means of R's cox.zph function revealed that the proportional hazards assumption holds reasonably well. In the case of Model I, the \(p\)-value corresponding to the null hypothesis of proportional hazards was 0.061, and in the case of the Model II, it was 0.548. Model II models the age at death of NBA players and can be used to estimate the median survival time based on the variables included in the model, which can be interpreted as the players' LE. Table 3 shows the estimations (95% CI) for African-American and white NBA players of 2 m tall for different NBA debut years. It can be observed that the estimated LE of NBA players increased steadily throughout the last decades and that in 2010, it was 89 years for white NBA players and 85.8 years for African-American players. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method I Variables** & **Estimate** & **SE** & **HR (95\% CI)** & \(p\)**-Value** \\ \hline Height & 0.02 & 0.005 & 1.02 (1.01–1.03) & \textless{}0.001 \\ Age at end of NBA career & 0.09 & 0.011 & 1.10 (1.07–1.12) & \textless{}0.001 \\ Year of last NBA season & \(-\)0.02 & 0.005 & 0.98 (0.97–0.99) & \textless{}0.001 \\ Ethnicity (African-Americans vs. White) & 0.35 & 0.113 & 1.41 (1.13–1.76) & \textless{}0.001 \\ \hline
**Model II Variables** & **Estimate** & **SE** & **HR (95\% CI)** & \(p\)**-Value** \\ \hline Height & 0.02 & 0.005 & 1.02 (1.01–1.03) & \textless{}0.001 \\ Year of first NBA season & \(-\)0.02 & 0.005 & 0.98 (0.97–0.99) & \textless{}0.001 \\ Ethnicity (African-Americans vs. White) & 0.31 & 0.109 & 1.37 (1.11–1.69) & 0.002 \\ \hline \hline \end{tabular} SE: Standard error; HR: Hazard ratio.  
\end{table} 
Table 2: Cox regression models to analyze factors associated with mortality among NBA players during the period 1946–2015. The response variable in Model I is the time elapsed from the end of the NBA career until death. The response variable in Model II is age at death. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ethnicity** & **Height (cm)** & **Year** & **Median Age (Life Expectancy)** & **CI 95\% LI** & **CI 95\% LS** \\ \hline White & 200 & 1950 & 79.6 & 78.6 & 81.0 \\ African-American & 200 & 1950 & 76.6 & 74.2 & 79.2 \\ White & 200 & 1960 & 81.0 & 79.7 & 82.6 \\ African-American & 200 & 1960 & 78.5 & 76.5 & 80.0 \\ White & 200 & 1970 & 82.8 & 80.6 & 85.1 \\ African-American & 200 & 1970 & 79.6 & 78.4 & 81.5 \\ White & 200 & 1980 & 84.3 & 81.7 & 87.8 \\ African-American & 200 & 1980 & 81.0 & 79.2 & 84.0 \\ White & 200 & 1990 & 85.9 & 82.6 & 91.2 \\ African-American & 200 & 1990 & 82.6 & 79.9 & 86.4 \\ White & 200 & 2000 & 87.4 & 83.7 & 94.3 \\ African-American & 200 & 2000 & 84.3 & 80.6 & 89.7 \\ White & 200 & 2010 & 89.0 & 84.5 & – \\ African-American & 200 & 2010 & 85.8 & 81.7 & 92.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimated median ages (and 95% confidence intervals) at death among NBA players of 2 m in height as a function of ethnicity and year of first NBA season.