The combined effect of ever-rising healthcare spending AND ever-lengthening wait times is a complex form of misery that, if quantified, can help us work to improve our healthcare system. Here is my mathematical model to quantify this misery.
It is common knowledge that over the decades, our spending on healthcare has risen inexorably while at the same time the wait for receiving specialist treatment has also increased in tandem. Longer wait necessarily creates inferior outcomes for patients, and a lot of people are at pains to point out that the hope of increasing spending leading to better outcomes is belied by the actual performance of the healthcare system.
However (and this is a very unpleasant surprise to me) no effort appears to have been made to combine the effect of the financial and health costs that we are paying. I believe that devising a metric that gives us a quantitative measure of the cumulative misery can help us better understand the failings of our healthcare system. We can use this understanding to formulate policy measures that can help alleviate the misery.
In this article, I will attempt to create a mathematical model that uses the data on healthcare spending and wait times to yield a quantified measure of our misery.
My approach is as follows:
Take the annual healthcare spending and divide it by 12. This would yield the average healthcare spending per week.
Take the wait time (which is usually measured in terms of weeks).
Multiplying the two numbers would give us the amount of healthcare spending that took place between the two relevant points in time, i.e., the day when a patient was placed on a waiting list and the day when they received the prescribed treatment. For ease of reference, I will call this resulting number ‘the product’.
An increase in the product indicates a worsening of misery, and vice versa.
Finally, in order to avoid the extraordinary developments in the Covid era, I will use data from 2019, as I believe this will show how our healthcare system was faring before any unusual (non-routine) demand was made from it (in what we may call ‘normal times’).
Before I delve into the numbers, however, I will give you an analogy that I believe will clarify why I think this measure of misery is valid.
Suppose there is a society where every member has to contribute a quantity of water to a reservoir. The quantity required from each member is based on a collectively agreed formula. The water is then released along a pathway that leads to farms. Anyone who needs any produce from the farms has to line up on a bridge over the pathway of the water. They can see the water flowing underneath the bridge, and there is a mechanism to tell them how many cubic feet of water is passing.
Now suppose that as time passes, members are required to contribute an increasing amount of water to the reservoir. The measuring mechanism tells them how much the flow has increased, and how much greater quantity of water is passing underneath the bridge.
But at the same time, people arriving on the bridge for the produce that they need / have requested are receiving it later and later. Sometimes, it arrives when it is no longer of any use (in the healthcare context, this would be when the patient has either died while waiting, or their ailment has become untreatable due to the delay).
In any sane society, this would lead to an investigation for the reasons for the deterioration of their produce-supply system. Barring the few who can source their produce from other societies, everyone wound demand that the system be improved and restored to it prior level of efficacy.
I believe that waiting lists are an exclusive feature of the publicly funded healthcare system. I am assuming that when people pay for their medical treatment from personal means or via their insurance, they receive the required treatment without delay, and within the medically determined timeframe.
As a result, my model takes only the public funding on our healthcare system as input.
The earliest data for wait times that I am able to find is from 1993. Therefore, I will take corresponding figure for the amount of healthcare spending from that year.
I have sourced the following data for this mathematical model from the sources noted against each:
- Provincial & Territorial healthcare spending in 1993: $ 48.6 Billion, from a report by the government of Newfoundland & Labrador at this link. The report was issued in June 2000 and documented spending and other aspects of healthcare from 1977 to 1999. The data I have cited is at page #4.
- Federal healthcare transfers to province & territories in 1993: $ 6.0 Billion. Until 1996-97, federal grants to provinces & territories under the Established Funding Program (EFP) included funding for healthcare as well as education. The figure for EPF in 1993-94 was $ 8.22 Billion (see this link to the report by the Fraser Institute, issued in March 2007). It is not clear how much of this was for healthcare. In the NFLD government report mentioned at (1) above, page #5 contains a graph where the healthcare funding from the federal government in 1993 corresponds to approximately $ 6 billion on the Y-axis. I have taken the latter figure for my calculations.
- Total public funding for healthcare in 1993: $ 54.6 Billion, this is the total of (1) and (2) above.
- Average Weekly Healthcare Spending for 1993: $ 1.05 Billion.
- Total public funding for healthcare in 2019: $ 185.08 Billion. This 2019 report by the Canadian Institute for Health Information (CIHI) shows total healthcare spending in Canada in 2019 at $264.4 Billion (Page 6 of the report), out of which 30% is from non-public funds (viz., Out of Pocket, Private Insurance and Other Means); this detail is on Page 13 of the report. This ‘private funding’ comes to $ 79.32 Billion. The remaining $ 185.08 Billion is from Provincial & Territorial Governments and Other Public Sector.
- Average Weekly Healthcare Spending for 2019: $ 3.56 Billion.
- Waiting time in 1993: 9.3 weeks, from this report by the Fraser Institute.
- Waiting time in 2019: 20.9 weeks, from the same report as above.
I will now rechristen ‘the product’ as ‘Healthcare Deterioration Measurement’, or ‘HDM’ for short.
The formula is:
(Healthcare spending per week) x (wait time in weeks) = HDM
HDM For 1993: 1.05 x 9.3 = 9.765.
This means that during the time an average patient was on a waitlist in 1993, the publicly funded healthcare system managed to spend $ 9.77 Billion.
HDM For 2019: 3.56 x 20.9 = 74.404
This means that during the time an average patient was on a waitlist in 2019, the publicly funded healthcare system managed to spend $ 74.4 Billion.
In other words, the amount of ‘water’ flowing under the ‘bridge’, as people waited for the ‘produce’ that they needed, and that they had contributed ‘water’ to, went up by a factor of 7.62.
This represents a 662% drop in the return on their contribution of water.
Before we fly into premature rage, however, let us bear in mind that these numbers are not adjusted for inflation. Although there is school of thought that the government is a primary driver of inflation, and therefore figures affected by inflation are the result of their own misdeeds, I will cut them some slack here and proceed to adjust the above HDM comparison for inflation that took place between 1993 and 2019.
ADJUSTING FOR INFLATION
According to the Inflation Calculator at the Bank of Canada website (see this link), $ 100 in 1993 was worth $ 158.05 in 2019.
Thus, the inflation adjusted HDM for 2019 is:
(74.404) divided by (1.5805) = 47.076.
Compared to the 1993 HDM of 9.765, the inflation adjusted 2019 HDM is 382.1% higher (i.e., a factor of 4.821).
To reiterate, the combined misery of higher healthcare spending and longer wait lists was nearly 5 TIMES worse in 2019 than it was in 1993, in inflation adjusted terms.
But wait, we need to adjust for higher population as well. To use the jargon of economics, ‘everything else being equal’, higher population would automatically lengthen the wait times and thus lead to higher HDM. Of course, this is remediable by increasing the healthcare infrastructure or its delivery mechanism (what I call the ‘supply’ and ‘logistics’ of healthcare services). But strictly speaking, that would fall under the umbrella of policy measures that we deploy to arrest a rising HDM, so I am not including that effect here.
In a nutshell, what we need is a HDM that is adjusted for inflation as well as rise in population.
ADJUSTING FOR POPULATION
The population of Canada in 1993 was 28.68 million (see this link).
So, our factor to adjust for population is:
(37.59) divided by (28.68) = 1.311
What this means is that if the population in 2019 had been the same as in 1993, the HDM number for 2019 would have been lower by a factor of 1.311, and our HDM for 2019 would have been (47.076) divided by (1.311) = 35.91.
The HDM for our base year (1993) is 9.765.
Therefore, the net result is that between 1993 and 2019, HDM adjusted for both inflation and population went up from 9.765 to 35.91, which can also be expressed as follows:
(35.91) divided by (9.765) = 3.677.
Conclusion: After adjusting for both inflation and population, our medical misery as reflected in HDM increased by 267.7% between 1993 and 2019. The combined effect of higher taxes to pay for increased healthcare spending and later availability of needed medical treatment made our lives roughly four times worse in a span of 26 years (or roughly one generation).
We can create a line graph to show the year-to-year changes in HDM, in raw numbers of HDM.
It is desirable, in my view, to convert the HDM measure into an index. Treating the base year 1993 as a value of 100, we can then derive the corresponding index value for any year from the HDM of that year. I would call this HDMI (Healthcare Deterioration Measurement Index). In our example, the HDMI for 2019 would be 367.7.
The two graphs for the exercise that I have done in this article are given below (please note that the lines in the graphs are straight because I have taken data for only two years; with more than two years in the graph, the line would form an angle at each data point. I am emphasizing this in order to clarify that the lines on my graphs do not imply a linear (= identical from year to year) increase in the HDM & HDMI that I have calculated).
I hope that being a highly educated society, we will be able to incorporate such a tool in our policy making on healthcare. Ideally, I would want to see a negative value for HDM (meaning a reduction in the misery faced by Canadian patients), and so a declining value for HDMI from year to year, all the way to 100, where it was in 1993, and hopefully further below.
If we, as voters, take this up with our elected representatives at both the federal and provincial level, we can make that happen.