In bone densitometry the T-Score expresses, in units of standard deviations, the difference between the patient's bone density and the mean bone density of a young normal population. The statistical significance of the difference may be assessed using the above table. For older persons, the T-Score will invariably be negative, and often statistically significant. The clinical significance of the T-Score relates to its use as an indicator of fracture risk.

The Z-Score expresses, in units of standard deviations, the difference between the patient's bone density and the mean bone density of an age-matched population. The statistical significance of the difference may be assessed using the above table. Statistically significant losses here may indicate a clinical problem.

Changes over Time and their Statistical Significance
One of the most important functions of bone densitometry is to assess changes in bone density over periods of time. Basically this problem is one of comparing rates of bone loss or gain. It can be shown that if the rate of loss (or gain) is determined from two measurements of bone density taken over a time interval T, the Z statistic associated with the comparison of this rate with a reference value is:

At the 95% confidence level, Z=1.96, so the rate of bone loss which would be considered statistically significant is given by

where P is the precision of the bone densitometer measurements.

If we take the reference rate of bone loss to be zero, the precision to be 1.5%, and the time interval to be one year this means that a rate of bone loss of at least 4.16% per annum will be required in order to be statistically significant at the 95% confidence level. Note that if the measurements are taken at a shorter time interval, a larger rate of loss will be needed if we are to be confident about the statistical significance of the result. The time taken to obtain a statistically significant difference at the 95% confidence level can be simply derived from the above equations as follows

This quite clearly shows that the smaller the difference in bone loss rate we wish to detect, the longer we have to wait between measurements. The way in which an increased interval between measurements improves the precision with which the rate of bone loss can be determined is illustrated graphically in Figure 3.

Figure 3. Graphical illustration of the effect of increased time interval between
measurements on the precision of bone loss determinations.

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