In the last two posts I’ve looked at the differences between the GDI (Schwartz & Rozumalski, 2008) and GPS (Baker et al., 2009). The broad conclusion is that they are very minor. Much less important than I thought when we published the GPS paper in 2009. The derivation of the GPS is much simpler than that of the GDI and this is what I really like about it (but takes no less time to calculate once you’ve got the software). I prefer the way the GPS is scaled but now accept that this is simply personal preference and the requirement to log transform data before performing statistical tests is clumsy (and I suspect is being ignored in many applications). On balance we should probably have published an alternative derivation of the GDI rather than proposing an alternative index.

The other issue, of course, is the Movement Analysis Profile. This is an obvious and extremely useful extension of the GPS. There are technical reasons why an equivalent doesn’t flow from the derivation of the GDI. If we’d published an alternative derivation of the GDI in 2009 as opposed to a different index, however,  then it would have been the easiest thing in the world to define similarly scaled variables for the different joints and different planes. We’d then have a MAP that was equivalent to the GDI.

In conclusion what we should have done in 2009 was to propose an alternative derivation of the GDI and extended that to develop a MAP_GDI. Hindsight is a wonderful thing – we didn’t. We’re thus stuck with two indices that are very much the same but different. Some research groups have understood the subtleties of the differences and opted for one or the other for a good reason. Others may have tossed a coin. Other groups have chosen to report both.  There is an argument that we should try and roll back the clock by proposing MAP_GDI now but I don’t know what stomach there is for even more new indices in the community. It might be interested see what comments this post prompts from you. Should we try and tidy this up by doing what we should have done in 2009 or will this just cause even more confusion?

What is clear is that there is little point any study reporting the results of both GPS and GDI (they are too similar for this to be useful). There is absolutely no point performing statistical tests on both because they should give identical results (as long as the log transform is applied to the GPS). People should choose which they prefer and report that. Mike and I have submitted a joint paper to GCMAS next year which includes the formulae required to convert one index to the other.

Perhaps even more important – research should not focus solely on either measure. Whilst the indices provide a simple number that describes how different the kinematics are from normal there is a lot more to walking than looking like everyone else. Gait speed is an extremely important measure of gait function and how this depends on cadence and step length provides basic clinical insight. Simply taking the rather poorly defined “self-selected” walking speed used in most gait analysis tests may be the easiest measure of speed but it is not necessarily the best. Endurance is also important and the 6-minute walk test that is becoming standard in other areas of exercise physiology is combines elements of speed and endurance that have considerable face validity. In many cases it is also important to assess dependence on walking aids (as in the FMS, Graham, Harvey, Rodda, Nattrass, & Pirpiris, 2004) and orthoses. Whilst GDI and GPS greatly enhance our ability to characterise gait kinematics they should not be used to the exclusion of other measures.

Graham, H. K., Harvey, A., Rodda, J., Nattrass, G. R., & Pirpiris, M. (2004). The Functional Mobility Scale (FMS). J Pediatr Orthop, 24(5), 514-520.

Schwartz, M. H., & Rozumalski, A. (2008). The gait deviation index: A new comprehensive index of gait pathology. Gait Posture, 28(3), 351-357.

Baker, R., McGinley, J. L., Schwartz, M. H., Beynon, S., Rozumalski, A., Graham, H. K., & Tirosh, O. (2009). The gait profile score and movement analysis profile. Gait Posture, 30(3), 265-269.

In the last post we looked at the different mathematical approaches that the GDI (Schwartz & Rozumalski, 2008) and GPS (Baker et al., 2009) use to derive the underlying measure of difference. These result in the scatter of data about the trend line in the graph below. In this post we’re going to look at the difference in scaling between the two measures which explains the characteristic shape of this curve.  There are two major differences.

First is the logarithmic transform. When you look at the distribution of the GPS across either a GMFCS category (Wood & Rosenbaum, 2000)) or FAQ level (Novacheck, Stout, & Tervo, 2000) you find a skewed distribution.  The figure below illustrates this for GMFCS II kids. It is clear that the data is not normally distributed and should be log transformed before subjecting to any parametric statistical tests. I’ve got a hunch that the skewing in the data is telling us something useful and would prefer to leave the index as it is (but recommend the transform as an additional step before performing the stats). Mike is less convinced and thinks incorporating the log transform in the derivation of the index is a lot tidier.

It is this log transform that gives the curve in the first figure its characteristic shape. The graph is steeper to the left which means that GPS will tend to record proportionally greater changes between people with more abnormal gait patterns than the GDI. It is flatter to the right meaning that this will be reversed in people with less abnormal gait patterns. Having said this most patients have a GDI of between 50 and 80 (GPS between 8° and 20°) and the relationship is reasonably linear within this range.

The second difference in the scaling is the way the GDI is transformed so that a normal score is 100 and for each standard deviation away from this the score drops by 10 points. It is this that leads to the quite different magnitudes of the two indices. Again there is logic to both approaches. Scoring this way gives a number that can be interpreted without any understanding of the underlying measure. On the other hand some people who do understand that the measure derives from angular measurements might be interested in the actually size of this which is lost in the GDI.

After several years’ experience using the GPS I’ve become less convinced of the usefulness of this. The averaging of the deviations over the gait cycle and different joint angles tends to make the absolute value of the score less meaningful. Having said this it is often appropriately sobering to find that differences that appear highly significant can represent average changes of just a couple of degrees.

In summary there is little to choose between the two scaling options. I used to think there were strong reasons for preferring the GPS scaling but the older I get the more I see this as essentially a matter to personal preference. The GDI was published first and maybe that should give it the edge.

 

Schwartz, M. H., & Rozumalski, A. (2008). The gait deviation index: A new comprehensive index of gait pathology. Gait Posture, 28(3), 351-357.

Baker, R., McGinley, J. L., Schwartz, M. H., Beynon, S., Rozumalski, A., Graham, H. K., & Tirosh, O. (2009). The gait profile score and movement analysis profile. Gait Posture, 30(3), 265-269.

Wood, E., & Rosenbaum, P. (2000). The gross motor function classification system for cerebral palsy: a study of reliability and stability over time. [Research Support, Non-U.S. Gov’t]. Dev Med Child Neurol, 42(5), 292-296.

Novacheck, T. F., Stout, J. L., & Tervo, R. (2000). Reliability and validity of the Gillette Functional Assessment Questionnaire as an outcome measure in children with walking disabilities. Journal of Pediatric Orthopaedics, 20(1), 75-81.

A check on Scopus shows that our original article on the GPS (Baker et al., 2009)  has now been cited 33 times and Mike’s paper on the GDI 53  times (Schwartz & Rozumalski, 2008). 20 of these cite both papers – although I haven’t had the time to look to see whether both indices were used.  So should we use one or the other or both?

There are basically two differences – doing the maths and scaling the result. I’ll break this blog into two parts in the hope that this makes things clearer.

Computing the GDI is based on an analysis of a very large dataset including examples of all the different gait patterns you are likely to come across. From this a number of gait features are identified. The first feature represents the average gait trace amongst the whole population (not just people without pathology). All the other features represent different deviations from that average. You can represent any individual’s gait pattern as a combination of the different features. Mike showed that just using the 15 most common features allowed you to get very close to any given measured gait pattern. This actually means that any individual’s entire kinematic gait pattern can be represented by just 15 numbers which is kind of cool and could save a huge amount of computer storage. Having gone through this process you can take the root mean square (RMS) difference of the 15 numbers that represent your patient and those that represent healthy individuals with no gait pathology of a measure of how different your abnormal your patient’s gait is.

The GPS is just computed as the root mean square difference of the individual’s kinematic data from the “normal” reference data across relevant kinematic variables and the whole gait cycle. It can be visualised as representing the total area contained between the traces representing your patient and those for the reference dataset (see Figure below). Clearly the larger the difference between the traces, the bigger this area becomes.

This sounds radically different to the GDI but Mike did some work (which has been lodged as an electronic appendix to the GPS article) which shows that actually the two are very nearly identical and would be exactly the same if the GDI analysis was extended to include all 459 features and not just the first 15. This subtle difference leads to the scatter on the graph of GPS plotted against GDI (reproduced from the GPS article below). You can see from this that the differences are certainly small and probably random. There doesn’t seem any particular reason to claim that one is superior to the other.

Now that Mike has done all the hard work in the feature analysis the computation of the GDI isn’t much more complicated than that of the GPS and there are a number of spreadsheets in circulation that allow the calculation of one or the other or both. The main advantage of the on which the GDI is based is the data compression but this isn’t particularly relevant if all you want to do is calculate a gait index. The derivation of the GPS is more straight forward and easier to explain and understand. Following Ockham’s razor that the simplest explanation is generally the best, then the GPS maths probably wins out.

The advantages of the GPS derivation are perhaps clearest if analogous indices are to be produced for other variables. Deriving an equivalent of the GDI would require data from a population big enough to contain examples of all possible different gait patterns. Deriving an equivalent of the GPS only requires a population big enough to establish the average pattern for the healthy population reasonably accurately.

 

Baker, R., McGinley, J. L., Schwartz, M. H., Beynon, S., Rozumalski, A., Graham, H. K., & Tirosh, O. (2009). The gait profile score and movement analysis profile. Gait Posture, 30(3), 265-269.

Schwartz, M. H., & Rozumalski, A. (2008). The gait deviation index: A new comprehensive index of gait pathology. Gait Posture, 28(3), 351-357.