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Tremor rating scales are the standard method for assessing tremor severity and clinical change due to treatment or disease progression. However, ratings and their changes are difficult to interpret without knowing the relationship between ratings and tremor amplitude (displacement or angular rotation), and the computation of percentage change in ratings relative to baseline is misleading because of the ordinal nature of these scales. For example, a reduction in tremor from rating 2 to rating 1 (0–4 scale) should not be interpreted as a 50% reduction in tremor amplitude, nor should a reduction in rating 4 to rating 3 be interpreted as a 25% reduction in tremor. Studies from several laboratories have found a logarithmic relationship between tremor ratings _{f}−T_{i})/T_{i}=10_{α(Rf−(Ri)}−1, where the subscripts

Modern transducers respond to energy from a physical system (i.e., stimulus) and produce an electrical signal (usually voltage) that is linearly proportional to the stimulus. Good transducers are not biased by the initial conditions. For example, a linear accelerometer can detect tremor fluctuations in inertial acceleration even though the transducer is subjected to the acceleration of gravity.

Weber found that the “just noticeable difference” or smallest discernible change _{0}. Fechner derived a mathematical relationship between human perception _{10}(

_{10}

The Weber–Fechner law predicts that tremor ratings

Values of slope α and intercept β in

_{n}_{4} for a 0–4 rating using

Tremor rating scales are now used in virtually all clinical treatment trials, and the Fahn–Tolosa–Marín Clinical Rating Scale has been used most commonly.

For example, suppose patients A and B have baseline right upper limb postural tremor ratings of 2 and 4, and both patients experience a 1‐point improvement with treatment. It has been common practice to express improvement as a percentage of the baseline score, and the percentage improvements for patients A and B would be 50% and 25%, respectively. However, the actual percentage change in tremor amplitude (as recorded with a linear motion transducer) is the same for both patients because the fractional or percentage change in tremor amplitude is given in

Thus, the fractional change in tremor amplitude _{f} – R_{i}_{i}

It is often assumed that the total score of a scale with

Similarly, the sum of all changes in the scale items is given in

The ratios _{f}_{i}

Note that 1/

In _{total}/N is simply the average change in N 0–n ratings, so

In the pivotal trial of focused ultrasound thalamotomy for essential tremor, a subscale of eight upper limb items (maximum total score 32 points) from parts A and B of the Fahn–Tolosa–Marín Clinical Rating Scale was used as the primary outcome measure. The percentage improvement in mean score was reported as 47% at 3 months, decreasing from 18.1±4.8 to 9.6±5.1 (mean arithmetic change of –8.5 points). Most patients and physicians would not be impressed with a 47% reduction in tremor amplitude after focused ultrasound thalamotomy or any other form of functional neurosurgery. However, this change in tremor rating cannot be interpreted as a 47% reduction in tremor amplitude. In fact, the percentage reduction in tremor amplitude is actually much greater than 47%. Assuming α = 0.5, the actual reduction in tremor amplitude can be estimated using

Subsequent analysis of the data from this study revealed that one of the eight scale items, rest tremor, was poorly correlated with the other items. Rest tremor was usually scored as 0, and test–retest reliability was very low.

This example illustrates the important requirement that items of a scale or subscale be strongly correlated when using

Many items of the Fahn–Tolosa–Marín Clinical Rating Scale_{10} that relates to the slope α_{4} of 0–4 scales according to

The range of tremor amplitudes for each rating is illustrated in graphical and tabular formats.

Given the relatively simple physical quantity being assessed (tremor), one could reasonably consider the use of a visual analog scale instead of ordinal ratings. There is no published estimate of the mathematical relationship between a visual analog scale and transducer measures, but the data from

Linear measures of tremor with motion transducers correlate very well with clinical ratings; however, the relationship is logarithmic, not linear. The logarithmic relationship between tremor amplitude and tremor ratings is predicted by the Weber–Fechner law of psychophysics. Fractional or percentage change in tremor ratings is misleading because it does not reflect the true fractional change in tremor amplitude. Arithmetic differences in clinical ratings should be reported in clinical trials, not fractional or percentage changes relative to baseline. The fractional or percentage change in tremor amplitude should be estimated using the Weber–Fechner relationship between tremor ratings and amplitude.