Data

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.

MRI

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).

Surgeries

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.

Independent variables

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).

Statistical strategy

Surgeries

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.

MRI

87% owned voluntary private insurance, and the share of MRI users whose MRI was completely financed publicly was 82%. These two variables are significantly related (p = 0.004). While all those who did not own voluntary insurance had their MRI financed completely publicly, 21% of those who owned voluntary insurance had public finance only of their MRI. Among those who had public finance only, 3% owned voluntary insurance. Both voluntary insurance ownership and having a public finance only are significantly related to income (positively at p = 0 and negatively p = 0.06 respectively). After some experimentation with the estimation of the models, we decided to include the variable indicating public finance only in the waiting time equation and voluntary insurance ownership in the use of MRI equation.

From Table 4 panel B it is clear that advanced age and worse health are positively related to the likelihood of having a MRI. Controlling for age and the number of chronic sicknesses, income has a significant positive effect and so does ownership of voluntary insurance. In other words, while rich persons are more likely to undergo a MRI, controlling for age and sickness, their waiting time is similar to that of poor persons.

Surgeries

We first tried to see whether having a missing value on the expected waiting time due to “the date of the surgery was determined by the recommendation of the doctor” is random. It turned out that this group includes more women than in the valid sample (66% vs. 44%); has a lower mean income (IS3,316 vs. IS 3,996); is sicker (1.5 chronic conditions on average vs. 1) and is less educated (78% with less than 12 years of schooling vs. 64% in the valid sample). Consequently, the working sample is somewhat medically and socio-economically stronger than the population waiting for surgeries.

Table 1 panel B presents the variables’ means among persons who are on the waiting list for an inpatient surgery. The mean expected waiting time is 3.5 months (median = 2.5 months). 44% of the population were women, mean age was 12 (of 20 age groups), namely, 45-49, and mean income per standardized adult was IS3,996. The mean number of chronic conditions was one. 23% of the population resided in a peripheral location, and 48% were of Israeli born or former USSR origin. 48% had more than 12 years of schooling.

81% owned voluntary private insurance, and the share whose surgery is to be financed from public money only was 69%, less than the 82% found among users of MRI. Among those who owned voluntary insurance, 36% had any private finance in their future surgery. The corresponding rate among MRI users was 21%. Furthermore, among those who had no voluntary insurance, 15% had some out of pocket finance of their prospective surgery. Among those who had any private finance of their surgery, 90% owned voluntary insurance. Rich persons are more likely to own voluntary insurance (p = 0) and to make any private finance (p = 0.005). As with waiting for MRI, after some experimentation with the estimation of the models, we decided to include the variable indicating public finance only in the waiting time equation and voluntary insurance ownership in the being on the waiting list for surgery equation.

Table 2 panel B shows that 31% have an expected waiting time of less than a month. The remaining 69% are distributed uniformly across the waiting time categories of 2-3, 4-5 and 6+. Waiting time for orthopedic surgeries – the biggest single type of surgery – is somewhat longer, while that for eye surgeries – the second biggest type – is distributed in a similar way to its distribution among all persons on waiting lists for surgeries.

Table 6 panel B presents the marginal effects of the personal characteristics on the probability to have a surgery scheduled. While income has no effect, all the other covariates exercise significant marginal effects: women are more likely to be on the waiting list for a surgery than men; older persons – than young ones; those with voluntary health insurance - than those without; sick persons – than healthy persons; in the periphery – than in the center; and persons with higher education – less than persons with lower education.