If you change health insurance companies 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 doesn't 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 physician to send you an end-of-year bill. Otherwise, your old and new insurers will have to distribute the individual fees among themselves, which may lead to delayed settlement.
Treatment undergone during the change of year is liable to the old and new year's deductible rate. This is why it is generally not recommended to seek treatment if you can wait for the new year (especially when considering hospital stays).