If a test is said to be 99% accurate what they are referring to is the probability of the test coming back positive if you do have the disease. What you are interested in is the probability of having the disease if your test comes back positive; these are not the same thing. With all things that are not 100% accurate there is a chance of a false positive, being told you are positive when you are not, and a false negative being told you are negative when you're not.
Let's assume the disease is fairly rare and only occurs in only 2% of a population. For a population of the size of Canada, 24 million, that means 480,000 people have it and 23,520,000 don't. Since our test is 99% accurate that means that of the people that are positive 475,200 will come back positive and only 4,800 will be be told they are not, ie a false negative. At the same time, of the people that are not positive 23,284,400 will be told they don't have the disease and 235,200 will be told they do.
This leaves percetage of people that are positive out of the number that are tested positive is 67%. Since the disease is so rare the number of false positives is almost half as much as the number of people who actually have the disease, this makes telling a false positive from a real one very difficult. The rarer the disease the worse this effect. In many cases a test like this is used to screen patients since although it may scare a few people, very few sick people slip through the system. From there they can perform more expensive accurate tests to determine the results for sure.
