T and Z scores

Z-scores: interpretation Z-scores: calculation T-scores: calculation Femoral neck is lower than total hip in men Converting T-scores to Z-scores Common misunderstandings

Z-scores

The bone density is measured in units of g/cm². Bone density naturally decreases with age, so the results also are expressed as z-scores which are the number of standard deviations below the average for a person of the same age, race and gender.

The Z-scores are related to percentiles, which are used by pediatricians to interpret the height of a child. If you know that a girl is 36 inches tall, you still don't know if she is normal. If you know that a boy is in the 30th percentile for height (z-score of -0.53), you know that he is normal but you don't know how tall he is. In some situations you need to know the absolute height, in others the percentile. This example is the closest one to interpretation of bone density. It is important to know both the absolute value (which relates to the strength of the bone) and the relative value (which relates to what is expected).

Calculation of z-scores

You need to have a table of reference values showing the mean (average) and standard deviation for the age, gender, race, skeletal site, and densitometer measurement units. I call this the "expected BMD". Then you use the formula:

Z = (BMD - expected BMD) / SD

Relationship between z-score and fracture risk

Epidemiologists measure bone density in a large population, then wait to see who fractures their bone. Using statistical models, they calculate the risk of fracture for each standard deviation below the mean for the age, race and gender. This also can be called the "gradient of risk" or the "relative risk". These risks depend on the population, skeletal site of measurement, technique of measurement, and type of fracture. For example, DEXA of the hip has a relative risk of about 2.5 for each standard deviation, therefore, a person with a z-score of -1 has 2.5 times the chance of a hip fracture compared to a woman with an average bone density. You still don't actually know what the fracture risk is unless you also know the risk of an average person, which depends on age, race, gender and other factors not related to the bone density. This topic is discussed in greater detail in the section about BMD and fracture risk.

T-scores

In the 1980's we measured bone density and reported z-scores. But when the bone density machines became commercial, the different companies could not agree on a standard measurement. A person would be about 6% higher on a Lunar machine than on a Hologic machine. To get around this difficulty, the T-score was invented. T-scores are not used (to my knowledge) in any other aspect of clinical medicine, and for 20 years they have caused trouble and confusion.

Just as height can be expressed in units of inches or centimeters, the bone density can be expressed in g/cm² or in T-score units.

Calculation of T-score

The T-score is a linear transformation of the bone density, and depends on the mean and standard deviation at peak bone mass. The original T-scores were calculated only for white women. For white men or black men and women, the T-scores can be calculated using the peak values specific for their race and gender (as done here), or they can be calculated using the peak values for the white women. Hispanic and Asian bone density results are similar to white values.

Consider these two equations. The first is for converting temperature from degrees Fahrenheit to degrees centigrade (as shown in the familiar thermometer on the top of this page). The second is for converting BMD to T-scores. It is the same kind of equation:

For example, here are transformations of total hip BMD measured by Hologic for white men and women. The white numbers show that average "temperature" for that age.

The values can also be plotted in coordinate graphic form, as shown here. The formula for T-score is the same as the equation for a straight line, y = mx + b .
Notice that when the T-score is zero (average peak bone mass) the bone density is highest in black men and lowest in white women. At very T-scores, however, the bone density is the same. This is due to differences in the standard deviations of the young populations.

T-score of femoral neck is lower than total hip in men

For older men, the T-score for the femoral neck will be lower than the T-score for the total hip. This graph shows the data from the NHANES study, using the young male values as the reference value. The graph shows the T-scores for average men. In other words, for all these points the Z-score is zero. For example, a 65-year old man with a T-score of -0.6 at the femoral neck would have the SAME risk of fracture as a 65-year old man with a T-score of the total hip of -1.06.

The graph shows the T-scores, calculated from young female reference values, for average men and women from a large meta-analysis (Johnell, ASBMR abstract 2005).

Converting T scores to Z-scores

You must know the age, gender and race and skeletal site and have a reference table, as shown below. Then the Z-score is the T-score of the person minus the reference T-score in the table. For example, if a 55 year old black woman had a T-score at the total hip of -2, her z-score would be -1.5.

Some common misunderstandings

1. The T-score can predict fracture risk better than the Z-score.

Neither one of these scores can predict the fracture risk unless you also know the age. Because the T-score and Z-score can be converted back and forth, you predict fractures equally with either one.

2. A measurement that gives lower T-scores has better ability to predict fractures

If a measurement has lower T-scores in older people, it could be due to a faster decline with aging (as in the case of QCT or femoral neck bone density). It also could be due to smaller standard deviations in the young population. The fracture rates go up steeply with age, so any test that is closely related to age will be able to predict that an older person has more fractures than a young person. But clinically we want to know whether the test can discriminate between those of the same age who will or won't fracture. So if a person has a QCT measurement 1SD lower than average for age (ie, Z-score of -1) her risk of fracture is quite similar to a person with DEXA Z-score of -1. The T-score of the QCT, however, will be much lower than of DEXA.

3. The risk of a hip fracture increases 2.5 times for every SD decrease in the
hip T-score, so the fracture risk is 2.5 times the T-score compared to an
average person the same age.

The standard deviations don't change very much with age, so the risk per SD will be the same using T-score or Z-score. The reference, however, should be to a person the same age with a T-score of zero, who would be above average and have a low fracture risk.

4. The T-score of the femoral neck is interchangeable with
the T-score at the total hip

This is approximately true for women, but not for men. The fracture risk per Z-score is similar for the femoral neck and the total hip, but the conversion formulas from the T-score at the total hip are not the same as those from the femoral neck.