What happens if you missed an appointment due to an unforeseeable/uncontrollable event that resulted in great delay such as ’chefetz hashud’ and/or major traffic accident that prevented you from driving your car any further. If you were to call at the last moment to your doctor or anyone else you scheduled an appointment letting them know of your situation would that resolve you of any obligation to compensate them for the missed appointment.
In a case where the patient could not make it to the appointment due to circumstances beyond his control, he is exempt from payment (see Shulchan Aruch and Rama Choshen Mishpat 333, 2 & 334, 1). Many Halachic authorities posit that the obligation to pay a doctor for the loss caused by the patient not showing up for his appointment is according to the rule of "Dina D'garmi" (liability for damage caused indirectly). In a case where the patient could not make it to the appointment due to circumstances beyond his control, he is exempt from paying, because according to all opinions "Garmi" in such a case is exempt (see Shach Choshen Mishpat 386, 1. and see more about this in Mishpat Ha'poalim, employer-employee laws and relationship by Rabbi Yosef Rosner ZT"L Chapter 11, sources and notes 1). Nevertheless it is not clear from the case specified that it was beyond your control. Perhaps you should have left early enough taking into account possible setbacks along the way. In a case of an appointment cancellation not due to circumstances beyond his control, the law is as follows: In a country or a medical facility which have clear rules and regulations if and how much to pay in the event of cancellation of appointment, everything is in accordance with the common commercial practice. If there is no clear regulation on this issue, it depends: If the doctor accepted another patient in your place you do not have to pay him at all as he had no loss. If the doctor did not accept another patient in your place, you must pay him as you have caused him a loss. The amount to be paid to the doctor depends: If the work of the doctor in this case is very easy, such as a checkup etc. then he would not agree to be idle of his work and reduce a lot of his pay, therefore one must pay him almost the full amount and not as an unemployed laborer (a discounted rate that takes into consideration that people prefer having time off). But if the doctor's work entails technical labor such as a surgical activity or a dentist etc. then one can deduct more, as applicable. He may then be able to deduct half the pay as an unemployed laborer. Generally if a person knows he cannot get to the doctor on time for his appointment, he should inform the doctor's office as soon as possible, as the doctor may be able to accept another patient. It is also recommended to compromise with the doctor regarding the compensation for the appointment cancellation as it is difficult to know and to estimate whether he suffered a loss or not. (Shulchan Aruch Choshen Mishpat beginning of 333 and in Taz ibid. Mishpat Ha'poalim, employer-employee laws and relationship by Rabbi Yosef Rosner ZT"L 15, 6. & sources and notes 22. Pitchei Choshen Hilchot Sechirut 10, 2 & note 2).