The data we used was taken from a Central Bureau of Statistics file which linked information on households from two surveys. The first survey, which was conducted in 2009, gathered socio-demographic and health information. The second survey, carried out in 2010, gathered both individual and household information regarding incomes. Of the 8,713 households (28,968 individuals) who responded to the health survey, 7,175 (24,595) – aver 80% - were matched with information from the income survey. The main reason for non-match was the dynamics of households’ formation: individuals change households and the match has no comparative meaning. Naturally, the rate of non-match is higher in the 20-40 age group. The linked data constitute a unique source of information, including health, use of health services as well as income data.
We were interested in evaluating how different variables – and in particular income - impact the length of time Israelis need to wait for medical care. We focus, restricted by the way the questions were asked, on scheduled (at the time of the interview) surgeries and on MRIs which were taken during the year prior to the interview.
Out of 28,968 individuals in the health survey, 559 (2%) underwent a MRI in the previous year. 82 of the 559 were conducted during hospitalization. We focused on the remaining 477 individuals whose MRI was not c while being hospitalized. For 460 individuals data on waiting times and incomes were available. They include publicly and privately financed MRIs.
The actual length of the wait for the MRI was divided (in the interview) into four ordered categories: less than one month, one to three months, three to six months and six to twelve (the maximal wait was less than 1 year).
Out of 28,968 individuals in the health survey, 295 (1%) had a scheduled surgery at the time of the interview. Because only 18 of the 295 surgeries were to be carried out outside of a hospital, we focused on the remaining 278 individuals whose surgeries - publicly or privately financed - were to be carried out in a hospital.
Because the surgeries that the survey referred to were surgeries scheduled in the future (as opposed to MRIs that were already carried out in the past year), the survey broke the wait into two periods: from the time the individual was registered to the surgery until the date of the survey and from the date of the survey until the scheduled date of the surgery. Of the 278 cases where the individual was waiting for a surgery in a hospital, in 91 cases a specific date for the surgery was not reported. The answer reported was “as recommended by the doctor”. After excluding these cases and an additional five cases in which the individual did not know the length of the wait, we remained with 182 surgeries scheduled to be done in a hospital whose length of wait and income were known.
Both periods had the same four options as in MRIs (up to a month, 1-3 months, 3-6 months and 6-12 months). Expected waiting time for surgery was defined of the sum of two waiting periods. Because there were relatively few inpatients and nine separate (but sometimes overlapping) waiting categories, we combined categories and were left with four ordered categories; (1) expected wait is less than 2 months, (2) 2-3 months, (3) expected wait is 4-5 months, and (4) 6-12 months.
We also had information regarding the type of surgery to be conducted (8 categories: eye, e.n.t., heart, stomach or digestive system, gynecology or urinary tract, orthopedic, blood vessels and other). Because of the small numbers of surgical patients, we chose to use the pooled data, disregarding the type of surgery.
The focal variable income was indicated by the household’s monthly net income per standardized adult (in thousands IS). Health was measured by the number of chronic sicknesses (out of ten: high blood pressure, heart attack, other heart diseases, stroke, diabetes, asthma, chronic lung disease, chronic disease in the digestive system, cancerous disease and depression or anxieties) reported by the individual.
The additional covariates were: place of MRI (hospital or community), age (in 20 age groups, from 0 to 85+), sex, ownership of voluntary health insurance (yes vs. no), public finance only of the MRI / the surgery (yes, possibly with some copayment vs. any private finance), peripheral status (peripheral vs. intermediate or center), origin (Israel and former USSR vs. all other, including Arabs) and level of education (12+ vs. up to 12 years of schooling).
In order to evaluate the income’s and other variables’ effects on the length of the wait for an MRI we ran an Ordered Probit regression with the length of wait measured by the 4-level scale as the dependent variable and income and all the variables mentioned above as explanatory variables. An indicator whether the MRI was taken in an outpatient clinic or in the community was introduced as well.
We ran an Ordered Probit regression on the expected 4-level waiting time variable for surgeries using the same set of explanatory variables as we did with MRIs excluding place of MRI.
Accounting for the selectivity of MRI/surgeries users
The above analysis is conditional on having been registered for a MRI or surgery. The effects of the independent variables on waiting time might be biased since the need for a MRI or surgery is not random and may be correlated with these independent variables. In the second part of the analysis we used the Heckman Selection Model to account for such correlation. The Heckman model specifies a 2 equation model: first, a Probit model for the probability of needing a MRI or surgery, and the second equation specifies the waiting time (Ordered Probit). The first equation applies to the entire sample and the second – to the selected sample of those needing a surgery, but the (non-zero) correlation between the two equations is accounted for. For MRI, the identifying variable was voluntary insurance ownership. Voluntary insurance ownership affects the use of services, but once using public finance only - or having made any private finance - of the procedure is held constant, it does not expect to exercise an effect on waiting time. For surgeries, education served as the identifying variable. The effect of education on the use of services is well known. Its effect on expected waiting time, controlling for income, is assumed to be small, since while higher education is correlated with better navigation of the medical bureaucracy, this applies more (at least in Israel) to the stage of getting a referral for the procedure.
The model was estimated using maximum likelihood. In all runs, since the coefficients of the Ordered Probit models have no clear meaning, we present the marginal effects of the independent variables on the probabilities to belong to the specific waiting time categories. The Additional file 1 presents the cut points and their 95%CIs. These cut points divide the normal distribution into segments which are assumed to underlay the waiting categories.