I think the average time it takes to reach health facility, availability of key facilities and supplies at health facility, and behaviour of staff towards patients at micro level. At macro level, per capital allocation of funds at district/sub-district level, spatial distribution of health facilities. In situations where supply side such a doctor-population ratio and other parameters are lagging behind, access can not be improved by focusing on demand side interventions such as promotion of insurance. There is too much focus on demand side interventions to improve access without giving proper thought to supply side of health care.
Please go through the attached published research on detection and measurement of deprivation in health care especially at the level of primary health care catering deprived and needy patients from a community.
You might want to consider the argument that access to health care should not be measured through the utilization of health services. To put it simply, access happens before the patient enter the health system and when the patient already entered the health system and use health services then that is utilization. Access is different from utilization, although I understand that other authors consider utilization as a proxy of access.
See attached article by McIntyre et al. 2009. We tried to use this concept in our policy study on PhilHealth. Hope this helps.
I like the McIntyre paper attached to the previous answer. It gives a framework for understanding the multiple dimensions of assessing access. One, however, that needs mentioning and emphasis is getting information directly from the patient. It is one thing to determine the relationship between location of patients and health care facilities and another to ask patients if they have trouble getting to the nearest health care facility. Poorer people may have significant problems with transportation, getting time off from work if the facilities are open only during normal "business hours," etc. Another approach is to determine, by asking people, if they have had to use emergency facilities in the last 1 or 2 years. There is a relationship between the degree to which people have access to primary care and their having less need to seek emergency care. Etc.
The above responses give you plenty to look at. I might add that you could also conduct a provider survey as to what measures they have taken and did that increase accessibility. For example at Great Ormond Street Hospital years ago introduced free transport..taxiis within London and or rail passes for clinic visitors. Analogously NYU hospitals introduced subsidized carer residential or Texas Heart deal with a hotel chain or pediatric cancer carer assistance at Ronald McDonald houses. Many initiatives are narrow focused, small and anecdotally have intended impact in increasing accessibility. A literature search might find statistical data and analysis. But a fresh study, perhaps addressing shifts in locus of service provisions (I. E. inpatient to outpatient, outpatient to telemedicibe, episodic to maintenance) could be very relevant and timely.