I'm not talking about your interpretation as to whether "overtreatment" is a concern, but rather your interpretation of how the professionals chose to deal with overtreatment. This is what you said:
"The guideline is based on the expectation of over-treatment. And the solution put forth is to skip the test, but is that a rational approach to the problem? If a certain percentage of the women getting the test will test positive and be overtreated, there's little to be gained by deferring the error for a year. It's true that fewer women per year will be harmed, simply because there will be half as many tests, and presumably if a woman who has HPV but the ability to get over it unaided happens to go through the entire process in a non-testing year, she'll dodge the harm, but if she gets it at any other time, there's no reason here to expect she won't be over-treated just the same as before, because the cause of the harm is not really being addressed. In the meantime, a person who has something more serious will lose a year of early detection.
I understand the balance problem, I think, but a person is not a population, and a plan that reduces the number of persons harmed in a given period may look good, but if it does not also reduce the likelihood of an individual being harmed, it's a hollow victory."
You ask whether this is a rational approach, and of course, it would not be. If screening intervals affected both groups equally - those who would benefit and those who would not - then to choose simply on the basis of making the population numbers look good at the expense of individuals would be unreasonable. If you are willing to assume that the professionals who made these recommendations are unreasonable, then it wouldn't occur to you that perhaps the assumption ("screening intervals affect both groups equally") was wrong. If you are not willing to assume that the professionals are unreasonable, then it would occur to you to consider whether your assumption is wrong.
The reason that intervals can be lengthened in response to over-treatment is because lengthening those intervals preferentially affects those who would not benefit from screening in the first place. It changes how the dice are loaded.
Changing the underlying case prevalence by decreasing false positives without decreasing true-positives or increasing false-negatives is one way to improve decision-making.
Linda