If you change your health insurance provider for the following year and are currently undergoing medical treatment, you must take note of the treatment date. Your previous insurer must provide coverage for all treatment before the year's end, even if the bill does not arrive until the next year. If treatment must be continued in the following year, you can minimise administration costs for insurers if you ask your doctor to send you an end-of-year bill. Otherwise, your old and new insurers will have to distribute the individual items of the invoice among themselves, which may lead to delayed settlement.
Treatment undergone around the turn of the year is liable to the old and the new year's deductible. This is why it is generally not recommended to seek treatment then if you can wait for the new year (especially when considering hospital stays).