Risk of horses falling in the Grand National.
Supplementary information
The Grand National course is approximately two and a quarter miles (18 furlongs)
long, the Grand National race comprising almost two complete circuits of this course
(figure 2). The thirty obstacles jumped during the race vary in construction and are
unique to this particular course. Some of the more challenging fences are individually
named. We classified fences into seven different categories: Plain fences (no ditch in
front), open ditch (ditch in front), first fence, water jump, Becher’s Brook (ditch on
landing side), canal turn (sharp turn immediately after plain fence) and The Chair
(high fence with big ditch in front). Traditional use of survival analysis measures time
to a defined outcome1. In this study we used arrival of a horse at each of the 30
obstacles on the course as the unit of measurement, sampling point 31 being the
finishing line. Kaplan-Meier plots2 were created to illustrate the cumulative
probability of horses reaching each obstacle for different exposure variables. The
probability of falling/unseating at fences of different types was evaluated using a
generalised linear mixed model, allowing for year as a random effect, on a dataset of
jumping efforts at each fence type. A further analysis was performed with jumping
efforts re-categorised as first or second circuit. The model results were broadly
similar, with odds ratios always in the same direction.
Univariable analysis of putative explanatory variables revealed twelve
variables that showed some evidence of association with non-completion. These were:
age, age at which horse first steeplechased, official handicap rating, starting price
(average odds offered by bookmakers of the horse winning), highest ever steeplechase
rating, previous course experience by the horse, previous completion of the course by
the horse, previous course experience by the jockey, previous falls on the course by
the horse, interval since last race, number of runners, and ground condition (going).
Two Cox proportional hazards models were generated, one with non-completion as
the outcome, one with falling/unseating as the outcome. A random effect (frailty) term
was included in each model to allow for clustering within races in different years3. A
second Cox proportional hazards model was developed with falling or unseating
(involuntary separation of horse and jockey due to a jumping error) as the outcome of
interest. We considered the potential effects of informative censoring on the risk of
falling and concluded that it was unlikely to be related to other, identified covariates.
Model diagnostics were performed. Schoenfeld residual plots for the noncompletion model showed some evidence of non-proportionality4 for the starting price
multiplier variable (chi-squared test for non-linearity P = 0.004). However, the
observed slight increase in hazard during the second half of the race was unlikely to
be important. The model for falling/unseating demonstrated no significant variation in
coefficients with time. Scaled changes in the regression coefficient for each
observation (delta-betas) indicated that for the non-completion model three
observations had values in the region of 0.4 indicating high leverage. All three
observations were for horses completing the race in heavy going (a relatively rare
outcome). Re-running the model excluding each of the three observations resulted in
minor changes to coefficients. For the falling/unseating model all delta-beta values
were less than 0.25, indicating that individual observations had relatively little
influence on the model parameters. Deviance residual plots for both models
demonstrated little evidence of poorly predicted subjects.
Chris Proudman, Gina Pinchbeck, Peter Clegg, Nigel French.
Epidemiology Group, Faculty of Veterinary Science, University of Liverpool,
Leahurst, Neston, Wirral CH64 7TE, UK.
e-mail c.j.proudman@liverpool.ac.uk
1. Cox, D.R. Regression models and life-tables (with discussion). J. Royal Stat.
Soc. 34, 187-220 (1972).
2. Kaplan, E.L. & Meier, P. Non-parametric estimation from incomplete
observations. J. Am. Statist. Soc. 53, 457-481 (1958).
3. Wood, J.L.N., Eastment, J., Lakhani, K.H., Harkins, L. and Rogers, K. (2001).
Modelling a retrospective study of death on racecourses. Proceedings of the
Society for Veterinary Epidemiology and Preventive Medicine, pp 115-126.
4. Therneau, T. M. & Grambsh, P.M. Modeling Survival Data (Springer, New
York, 2000).
Figure 2 Layout of the Grand National course with each obstacle numbered.