# What are the chances my wife has lupus?

*1.5 million people have lupus in America out of a population of 308 million. 90 percent are women. My wife is white, as is 63 percent of the country. Minorities are three times more likely to have lupus than whites.

My wife has been diagnosed with lupus, but the diagnosis may not be correct.

*20 percent of lupus patients have a parent or sibling with lupus. My wife does not.

• 70 percent of people with lupus have positive double-stranded anti-DNA test.
My wife does not.

*70 percent of lupus cases are systemic, which is what she is diagnosed with.

What is the probability she has lupus?

So, to be simple… What are the chances given the first set of stats, the 1.5 million out of 308 million and further reducing stats, that she would have lupus (one out of 9 million, etc)?

second question, can the probablity and odds be calculated from the percentages. There was a one in five chance a sibling or parent has it, plus a 70 percent chance she would have the double dna test, but didn’t. As we combine these percentages and figures, can it be deduced?

First, we know nothing about the tests that were performed. You can see that the answer must depend on the reliability of the tests by considering the extreme cases: If the test is utterly unreliable and its results bear almost no relation to the actual presence of the disease, then the probability is tiny, namely roughly the same as before the test. If the test is perfectly reliable and never fails, the probability is $1$. That’s a huge difference, and the only way to know where between those extremes the actual probability lies is from information about the reliability of the test, which we don’t have.
Second, all the correlating properties that you list (ethnicity, sex, relatives, …) may or may not be correlated among each other. That is, lupus might tend to be congenital in men but not in women or vice versa. Without knowing these correlations, one could only give bounds on the probability by making opposite extreme assumptions on the correlations. These bounds might be slightly more useful than the range “between tiny and $1$” due to the reliability issue, but to get a single probability you’d have to know these correlations or at least make reasonable assumptions about them.