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Hi Marilyn. How long have you been married?
The year is not as important as the duration of your marriage. Some STDs can be carried into a marriage from a previous relationship. This would not be an issue after 36 years as symptoms would have arisen already. That said, if you and your husband have been completely monogamous over the course of those 36 years, there is no risk of STD. If you now marry someone else, you could pick up an STD from him (from his prior relationships). Using condoms consistently greatly reduces the chances of transmision of all STDs but does not eliminate the risk completely. If you have your new partner tested for all STDs and he comes back disease-free, then you can "start fresh" so to speak regarding STDs. In other words, if you both stay completely monogamous after negative testing, you do not need to worry about contracting an STD.
The tests are getting better (earlier detection) and more reliable every few years. The sensitivities depend on what one is testing for and the type of test used eg. PCR, western blot, EIA, culture, etc). In general, sensitivities run in the 85 -99% range. Positive tests are often confirmed with secondary testing. Negative results can also be confirmed by re-testing.