An Overview of the Running Performance of Athletes with Lower-Limb Amputation at the Paralympic Games 2004 – 2012

This paper analyses the performances of lower-limb amputees in the 100, 200 and 400 m running events from the 2004, 2008 and 2012 Paralympic Games. In this paper, four hypotheses are pursued. In the first, it investigates whether the running performance of lower-limb amputees over three consecutive Paralympic Games has changed. In the second, it asks whether a bi-lateral amputee has a competitive advantage over a uni-lateral amputee. In the third, the effect of blade classification has been considered and we attempt to see whether amputees in various classifications have different level of performance. Finally, it is considered whether the final round of competition obtains different levels of performance in comparison to the qualification heats. Based on the outcomes of these investigations, it is proposed that future amputee-based running events should be undertaken with separate and not combined events for the T42, T43 and T44 classifications at the Paralympic Games.


Introduction
Athletes who possess some level of disability have participated in competitive sports for over a century.However it was not until after the Second World War that the first formalised sports event for the disabled people took place.This was initially based in Stoke Mandeville in the UK and eventually directly influenced what has subsequently become known as the Paralympic Games from 1960 [1].These games currently take place every four years [2] at the same venue as the Olympic Games.Athletics forms a key part of the Paralympic Games programme and attracts the largest number of spectators [3].Structured competition involving running with a lower-limb amputation has taken place consistently since 1976 [4].
If an amputee with a lower-limb amputation wishes to compete in running competition within the Paralympic Games, they are assessed for their physical functionality [5] and then typically allocated into one of three race classifications [6].These event classifications are defined as: T42: a single (uni-lateral) above knee (trans-femoral) amputee or athlete with other impairments that is comparable to a single above knee amputation.
T43: double (bi-lateral) below knee (trans-tibial) amputees and other athletes with impairments that are comparable to a double below knee amputation.
T44: an athlete with a below knee lower limb impairment/s that meets minimum disability criteria for: lower limb deficiency; impaired lower limb; impaired lower limb muscle power; or leg length difference.
It should be noted that during the Paralympic Games that have been analysed in this study, the T43 category has been combined with the T44 category in the male running events.This has been mainly been due to the low participation numbers in the T43 category.The governing body has traditionally decided to combine this classification with the T44 category.This combined category is still referred to as 'T44' as it comprises more of these types of athletes.
Competing when using running specific lower-limb prostheses has not been without some level of controversy.For example, in 2008 it was proposed that a lower-limb bi-lateral amputee could have a performance advantage when compared to their able-bodied equivalent due to some level of performance enhancement from their prostheses [7].Additionally, due to fundamental functional differences, it was proposed that the T43 and T44 should be separated in competition-despite this not currently being the case [4].As a result, the aim of this paper is to address and reinforce some of the issues that may surround the diversity of athletes that will compete in the typical classifications at the Paralympic Games in recent editions.Four hypotheses are posed: (1) The performance of athletes with an amputation within the current format of athlete classification has changed from 2004 to 2012.(2) The number of prosthetic limbs being used by an athlete has an impact on race results when running specific prostheses are used.(3) The athletes in different classifications will have the same level of performance.(4) The final round of running competition at the Paralympic Games in each classification has the same level of performance as their qualification rounds.

Methodology
The race results from the 100, 200 and 400 m form the basis of a statistical analysis of the 2012 (London), 2008 (Beijing) and the 2004 (Athens) Paralympics Games.These results are located within the public domain and are extracted from the official website of the sport's governing body [8].This data includes the name, ranking and country of representation, as well as the performance of each athlete.The number of prosthetic lower-limbs that each athlete may have used was derived from the athlete's biography and/or online photographic evidence [8].The raw data is included in Appendix 1 and 2. While Appendix 1, gives some detailed information for 2012 results, the Appendix 2, represents the information for 2004 and 2008 Paralympic Games in the running event.
As the main purpose of this report is about identifying the differences between two or more groups, the ANOVA test was used as the best statistical tool to address the four hypotheses.The homogeneity test (whether different groups have the same level of variation between them or not) and normality are the two key assumptions when using the ANOVA test [9].After creating the data sets for each research question, both the normality and homogeneity tests were undertaken.If both of these two key assumptions were satisfied within and between groups, the ANOVA test was then used in order to address each research hypotheses.If any of these assumptions were not then satisfied, the Kruskal-Wallis test was used instead of ANOVA.The Kruska-Wallis test is a non-parametric test which is not sensitive to normality [10].

Hypothesis 1: The Performance of Athletes with an Amputation within the Current Format of Athlete Classification Has Changed from 2004 to 2012.
The answer to this question is primarily addressed in Table 1.In Table 1, the first column ("category") clarifies which specific category analysis was undertaken.The second column ("N") represents the whole sample size and the numbers in parentheses represent the sample size in each year (2004, 2008 and 2012).The third and fourth columns illustrate the p value of homogeneity and normality tests in each group.The fifth and sixed columns represent the results of p value for ANOVA or Kruskal-Wallis test (where relevant).In Table 1, the p value of the ANOVA and Kruskal-Wallis tests are all above 5%.Therefore, we can conclude that with adopting a 95% confidence interval, no statistical difference was identified between these three groups (2004, 2008 and 2012).This means that the posed hypothesis was incorrect and based upon the statistical analysis here, it is proposed that the running performance of the amputees from 2004 till 2012 did not change significantly.

Hypothesis 2: The Number of Prosthetic Limbs Being Used by an Athlete Has an Impact on Race Results
The race-based data was categorized in three different groups.The first group comprises amputees who use just one prosthetic limb.The second group contains amputees who use two prosthetic limbs and the third comprises those who run without prosthetic limbs at all (but due to their functionality, compete in the same classification).In order to detect any differences in the mean completion time of the event, either the ANOVA or the Kruskal-Wallis Test were then applied as appropriate.
In Table 2, the Kruskal-Wallis test did not identify any significant difference regarding the effect of the number of blades with a 5% significance level in either the 100 or 200 m.However, in the 400 and 200 m T44 event, the test identified a significant difference between three groups at a 5% significance level.Alternatively, this finding could also be interpreted as when the distance of the competition gets longer (400 m), the number of prostheses used ultimately affects the results of the event.In order to answer which group in particular has any advantage when compared to other groups, further analysis is required.In order to address this issue, the Tukey post hoc test was applied.Tables 3 and 4 represents the results of this test for 400 m and 200 m-T44.As the sample size in the group possessing no prosthetic limbs is so small (2), we cannot make any robust conclusions from it and instead focus on the results of the other groups.In Table 5 it is demonstrated that there is a statistically significant difference between the results of people who run with 1 blade or 2 blades (p = 0.00).Based on the descriptive data for these two groups (22.7 s for 2 blade and 24.27 s for 1 blades), it is proposed that those who are bi-lateral lower-limb amputees have a competitive advantage compared to those who are uni-lateral.It is worth noting that although the normality test in this category was calculated as negative (and that we cannot use post hoc test in this case), at least applying that test gives an indication as to where any difference is.The results of the Tukey post hoc Test indicate a statistically significant difference between the groups who use two blades when compared to the two other groups.By considering the mean time of the race completion by these groups (50.86 s for 2 prostheses, 54.51 s for 1 prostheses and 54.14 s for no prostheses) it is proposed that historically, when racing over 400 m, runners who have used two prosthetic lower-limbs may have had an advantage compared to other groups who had only one (or none).
The results of this analysis supports the posed hypotheses and indicates that, from a statistical perspective, bi-lateral amputees participating in the T44 events in either the 200 m and the 400 m distances, demonstrate better running performance when compared to other types of T44 participants (such as the T43 classification).This finding is supported by published research when evaluating such athletes physiologically [11] or as a mechanical system [12].In a study commissioned by the sport's governing body (the IAAF), a bilateral amputee world record holder utilized 25% less energy compared to able-bodied athletes when running at the same speed over the 400 m distance [11].It was also proposed that when a sinusoidal input is matched to an energy storage and return prostheses, it can make the prostheses susceptible to resonance.Theoretically, if this impulse could be synchronised with the frequency of a humans running effort, it could result in the storage (and then recovery) of a substantial amount of energy in the system therefore offering a degree of performance enhancement [13].

Hypothesis 3: Athletes Racing in Different Classifications Will Have the Same Level of Performance
The length of any amputated residual limb (such as above-knee or below-knee) could be considered as a factor which could affect the results of competition in running exercise.As it was mentioned earlier, in order to have a fair competition in Paralympic games, athletes are placed in different classifications based upon their functionality.This section of the paper compares the results of athletes who participate in the T42 category with those who participate in the T44 classification.The results are illustrated in Tables 5 and 6.
As in all cases p value is below 5%, there is a statistically significant difference between the T42 and T44 classifications.The descriptive analysis related to these two classifications is shown in Table 6.It is proposed that the posed hypothesis was correct and that the T44 category may have had an advantage in running-based competition when compared to T42.

Hypothesis 4: The Final Round of Running Competition at the Paralympic Games in Each Classification Has the Same Level of Performance as Their Qualification Rounds
During each Paralympic Games, athletes qualify for a final round based upon successful qualification from a heat or semi-final which had preceded it.However, it is not known how much effort an athlete applies in their heat to ensure qualification for the final.The data of each race classification type is separated into two groups.The first group is the data related to the qualification round and the second group is related to the final round.After the normality and homogeneity tests have been calculated, the p value of Kruskal-Wallis or ANOVA are then also calculated to see whether any difference exists between these rounds.The results of this are shown in Table 7.In all six categories (except the 100 m-T44), the P value of the Kruskal-Wallis test or ANOVA is above 5%.As a result it is proposed that when adopting a 95% confidence interval, the posed hypothesis was correct as these two tests did not identify any significant difference between the qualification rounds and the final rounds performances.This means that although the result in the final is paramount, there is generally no different in the relative result of the same athletes in the qualification rounds.However, due to the limitations of the design of current athletics tracks comprising typically 8-12 lanes, the existing process of qualification is warranted (despite the end result being similar) if overall participation levels of each qualification in the sport are intended to be maximised by the sport's governing body.

Conclusions
A statistical analysis of the results from three consecutive Paralympic Games from 2004 to 2012 do not show any significant change in the general performance of athletes.It was identified that the performance of athletes in the qualification heat did not change substantially when the same athletes ran again in the final.The statistical analyses in this research suggested that athletes with below-knee amputation consistently outperformed those with above-knee amputation.Finally, the results in this study demonstrate that in long running competition, bi-lateral lower-limb amputees have an advantage compared to uni-lateral lower-limb amputees.On the basis of the statistical analyses in this study, it is proposed that future Paralympic Games should be undertaken with separate events for the T42, T43 and T44 classifications and not hold combined events as they have done in the past.

Table 1 .
A comparison on the performance of amputees in 100 m in 2004, 2008, and 2012.

Table 2 .
The effect of number of blades.

Table 4 .
Table 4 represents the results of Tukey Post Hoc Test for 400 m competition.Tukey post hoc test for 400 m.

Table 5 .
Effect of classification.

Table 7 .
Effect of final round.