Bone density and fracture risk

steoporosis, most simply and elegantly defined as “too little bone in the bone”, is generally the result of progressive bone loss which, for all practical purposes, starts at menopause in women and at about the age of 50 years in men. Because women have a lower bone organ density than men and then lose bone more rapidly, and also because women live longer, osteoporotic fractures, particularly at the hip, affect more women than men in Western countries — there are 20 000 hip fractures per year in Australia, with women outnumbering men by a ratio of two to one. The immediate cost of osteoporosis in Australia has been estimated at nearly $2 billion per year, with a further $5–6 billion in indirect costs. Doctors are in a difficult position when it comes to managing osteoporosis and preventing fractures. As with most disorders, they need to know the risk of an event such as fracture before reaching a treatment decision. They know that bone mineral density (BMD), measured by dual energy x-ray absorptiometry (DXA), is a major determinant of fracture risk, and they may have read that the risk goes up by a factor of 1.5–2 for every standard deviation fall in BMD (which is actually incorrect, as shown below), but they have no means of converting this information into absolute numbers. This is partly because of long-standing confusion between odds and risk, exemplified by the fact that the relative risks quoted in the literature are generally odds ratios or hazard ratios. The difference between odds and risk, well understood by professional statisticians, is not well understood by most clinicians. If 30 women out of 100 develop a fracture over a given period, the fracture risk is 30/100 or 0.30, but the fracture odds are 30/70 or 0.43 — a very different figure. At low levels of risk, say below 0.10, the difference between odds and risk is very small (one in 10 is close to one to nine) and can legitimately be ignored. However, as the risk increases, or the period over which it is calculated is extended, odds rise in a multiplicative fashion with fall in BMD, but risk does not. Odds have no upper limit, whereas risk can never rise above unity or rise by a multiplicative factor. A recent article sought to dispel this confusion by explaining the difference between fracture odds and fracture risk by reference to published data. A follow-up article, based on a prospective study carried out in Perth, contained a graph representing true fracture risk as a function of age and BMD in women without prevalent fracture. For those who would like to calculate the 6-year risk, the formula is: