# GPS and/or GDI? Part 2 – Scaling the result

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.