Thoughts on “Primary care capitation payments in the UK. An observational study.”

August 23, 2011

I read an interesting paper the other day.

BMC Health Serv Res. 2010 Jun 8;10:156. Primary care capitation payments in the UK. An observational study.

The authors described a study of capitation payments in the UK. While it is entirely appropriate to seek case-mix adjustments that better reflect differences between sub-populations covered under capitation payments and the total population, case mix adjustments are insufficient to correct capitation payments for the entire population.

Case mix adjustments, while needed when there is a “cost bias” attributable to different demographic characteristics, such as the fact that the population of Wales is apparently older, and sicker, than the entire population covered by the NHS, and on whose experience the capitation payments are based, these correctable case mix related “cost biases” are a small piece of the flaws in using capitation.

Unfortunately, one of the problems with risk adjusted, case-mix compensating mechanisms is that there is no incentive whatsoever for health care providers who should get negative case mix adjustments to request such modifications. In essence, all the providers in Lake Wobegon think they receive capitation payments that are at, or below, adequate levels. No provider in Lake Wobegon ever thinks their capitation payment is excessive.

The authors have some keen insights but leapfrogged a bit. They saw an aberrant consequence of capitation payment schemes but have not fully accounted for the true causes of the “revenue to cost” gaps that necessarily arise under capitation. If I were solely a health care provider I would, at best, be in their position as well.

My advantage in all this is that I am a mathematician and statistician and I spent close to a decade in the actuarial field (Insurance Services Office, NY, NY; Liberty Mutual Insurance Company, Boston, MA; General Accident Insurance Company, Philadelphia, PA; and Reliance Insurance Company, Philadelphia, PA).

Even having done insurance and reinsurance rate making and reserving and financial reporting for most of a decade, it took more than a decade away from insurance and reinsurance to see that most of what I thought was true about insurance operations was hopelessly muddled by the incorrect assumptions in insurance rate making and reserving theory.

Actuaries as it turns out, are far more concerned about getting their company’s rate filings approved than they are concerned about educating regulators and the public about how insurance really works.

Insurance makes less and less sense the more you view it the way rate making, reserving, and financial reporting actuaries view it. On the other hand, it makes perfect sense when viewed as a statistician or financial analyst might view it, focusing on: Profits, Losses, Insolvency risk, and Maximum sustainable benefit levels.

If actuaries were not enmeshed in roles as their employer’s advocates, they might concentrate more on educating regulators and the public about how insurance really works. But their roles as company/client advocates are far easier to fulfill when the public, politicians, and regulators are misinformed.

Explaining the flaws in capitation, as it turns out, is both more and less difficult than I imagined 14 years ago. Central to this problem is that the explanation is a bit more sophisticated than most potential beneficiaries can comfortably digest, and and the human tendency, is to err conservatively – rejecting things we do not understand.

It is far safer, and easier to question the proponent of a new theory, especially a counter-intuitive theory, than to risk ridicule by accepting a theory that may prove unworthy. The best alternative is recognizing our inability to follow such arguments and commit to acquiring the additional skills we need to fairly appraise the theory. I won’t hold my breath.

Perhaps this teaser will encourage some people to look at my papers on “Professional Caregiver Insurance Risk”. (See my CV at

CV for Thomas Cox PhD, RN.

for a list of publications and presentations.) The mathematics behind Professional Caregiver Insurance Risk is undeniably correct. Still, many who read this material and are unable to evaluate the mathematics ask for empirical data that will “show” what I already know is a mathematical tautology: Capitation, no matter what it is called, is a deficient and inefficient mechanism for paying for health care services. Looking at empirical data is befuddling and boring for someone who understands the mathematics. Isolated sets of data support both extremes in the debate over capitation: Proponents and Critics, as detailed below.

The Wales Problem

The problem with isolated data is that in any accounting cycle there are predictable, though random, outcomes. During any financial cycles, Wales might indeed exhibit an excess of costs over revenues for three reasons: 1) A “Cost bias” that might be compensated for by a case mix adjustment scheme, and 2) An increase in cost variability unrelated to the case mix adjustable “Cost bias” that is solely dependent on small portfolio size compared to the NHS, 3) A combination of both of these effects, a clearly bias in costs and a very poor year as an insurer.

The next cycle, the “Cost bias” will continue in Wales if not case mix corrected. But the increased cost variability is likely to manifest in some other locality becoming the next “worst” outlier, not Wales. Wales may still receive inadequate “Cost bias” adjustments but another locality may have a greater discrepancy between costs and revenues than Wales because its patients are sicker than average that year.

Worse still, if Wales has an aberrantly low cost year next year, it may appear that the capitation payment for Wales should actually be lower, not higher, the following year, even though the population remains older and sicker than for the rest of the UK.

An Influenza Epidemic

One might imagine an influenza epidemic effecting office workers rather than factory workers because, we might assume, factories may have more fresh air than offices. The providers serving predominantly office workers will have unusually high costs, treating much higher numbers of office workers for influenza related conditions. Providers serving primarily factory workers will have much lower than average costs that year.

When viewed retrospectively the providers serving office workers have excessive costs, compared to revenues, which may appear to be a new case-mix problem. It is not a new case mix problem. It is a cost variability problem. These providers do not require a case mix adjustment – their misfortunes are solely the result of a bad year as insurers. The amount they were paid, per capita, is adequate for thir expected costs, but it does not adequately compensate for their roles as insurers for their patients, at least not this past year.

During each year, as the authors correctly note, there are over-paid providers and under-paid providers. Case mix adjustments certainly make a difference and actuarially adequate, but not redundant payments, ought to adjust for discernible case mix effects, such as the older and sicker population in Wales.

The problem is that while efficient case-mix adjustments can be made for the Wales’ demographics, it is mathematically impossible to efficiently compensate providers for their insurance risk management activities that are really responsible for the shortfalls in revenues for most under-paid providers during each accounting cycle.

At cycle end, one can always go back and look at the extremes and correctly note that some providers were paid inefficiently excessive amounts for the services provided. Others, of course, were inadequately compensated. The key is that we know this will occur (though we cannot specify which providers will be inadequately or excessively compensated each year) based on the mathematical theory.

This must happen in every accounting cycle, whenever the NHS, or any American health care finance entities, transfer insurance risks to smaller entities, through capitation payments schemes. The increased “variability” in costs in small portfolios of insurance risks – unlike the “Cost biases” that case-mix adjustments correct, cannot be efficiently compensated for by any level of sustainable and efficient capitation payments.

As disadvantaged providers cite instances of inadequate revenues as just cause for requesting increased revenues, budget cutters at the national level look at data for excessive payments as just cause for further reducing provider payments. What is needed, and what Professional Caregiver Insurance Risk provides, is a theory that encompasses both outcome extremes, and which explains why capitation mechanisms are always inefficient and unsustainable methods of financing health care services. at any level below that of a large, very efficient, risk retaining insurer.

When insurance risks are managed at the level of the NHS, what would have been excessive and inadequate payments for different providers/trusts, cancel each other out. This is why the NHS, functioning as risk manager, is a more efficient insurer than health providers/trust that manage sub-portfolios of the NHS’s insurance risks.

Insurance risk transfers are only efficient if the entity accepting the risks is larger, after the transfer, than the entity ceding the insurance risks. While this may not conform to the average person’s intuition – it is absolutely the case when you understand that risk management through insurance (and the mathematical theory it is based on) is all about coming close to average costs each year. Efficient insurers’ costs do not deviate far from average population costs, while inefficient insurers’ costs deviate dramatically, from average costs, each year.

Whenever insurance risks are transferred to smaller entities, none of them know, at the beginning of their accounting cycle, whether they will have excessive, or inadequate, resources at the end of the accounting cycle. To deal with this essential uncertainty, ALL risk assuming providers should reduce the level of benefits they plan to provide, below the average level represented by their fixed capitation payments, lest THEY be one of the providers whose revenues will prove inadequate because they had exceptionally high demand for services during the accounting cycle.

Maximum Sustainable Benefits

It is not appropriate to close one’s doors on 1 December 20X1 because you have used up all your resources during the first 11 months of the 20X1 funding cycle. The Maximum Sustainable Benefit (MSB) tells us how much providers/trusts managing sub-portfolios of insurance risks ought to reduce planned service capacity, compared to the levels they could sustain when the NHS (Or in the US, when an insurer, managed care organization, or the Medicare/Medicaid program) manages the same collection of risks, so that they are as able to provide identical care for identical symptoms at the beginning and the end of each risk assumption accounting cycle, as the NHS could if it simply retained these insurance risks.

While one might think that the Maximum Sustainable Benefit is a fixed amount – it is actually contingent on other factors: Profitability goals; Loss avoidance preferences, and Insolvency aversive-ness. Each such contingency results in different levels of maximum sustainable benefits because the variations in costs are non-linear stochastic processes, not a fixed determinate processes.

The most damaging inefficiency is not measured by the few providers who have excessive revenues at the end of the accounting cycle, nor by the few providers that have inadequate revenues at the end of the accounting cycle, it is measured by the reduced levels of care available from ALL providers, that affect ALL patients, throughout each financial cycle.

So, for example, we might at first glance conclude that the most inefficiently compensated providers are of two sorts:

5% of all providers receive the most excessive and inefficient payments for the accounting cycle.

5% of all providers receive the most inadequate and inefficient payments for the accounting cycle.

We might think that the funding inefficiencies are isolated and only one type of inefficiency actually harms both patients and providers: Underpayments to providers. These authors correctly noted this under-payment problem for a specific locality – Wales.

So the inefficiencies appear to affect, at worst, 10% of providers and their patients and only 5% of providers and patients appear likely to provide/receive inadequate care. This might even be considered to be a tolerable level of inefficiency compared with the presumed inefficiencies in what was essentially the old fee for service provider reimbursement system.

But the inefficiencies induced when insurance risks are transferred from large capable entities to much smaller entities actually affect 100% of providers and 100% of patients and at levels far greater than the levels suggested by the case-mix adjustments appropriate for the older and sicker Welsh demographics.

My papers in The Journal of Healthcare Risk Management and JONA’S Healthcare Law, Ethics, and Regulation (See my CV at

CV for Thomas Cox PhD, RN.

for a list of publications and presentations.) spell out how one might approach calculating these far greater inefficiencies by calculating Maximum Sustainable Benefits any risk bearing entity can provide, throughout the financial period.

While most researchers see isolated effects, such as the case mix adjustable inadequacy for Wales so that Welsh providers will receive adequate service revenues and maintain adequate service capacities for the Welsh population, the flaws in transferring insurance risks from large, capable, and efficient insurers such as the NHS, or American insurers and governmental programs such as Medicare and Medicaid, to smaller, less efficient entities such as individual providers or trusts, lead to situations in which ALL providers should reduce benefits by as much as 50-95%, depending on their size, relative to the NHS.

From a practical standpoint, the authors should go back, as they did and assess case-mix adequacy retrospectively after every accounting cycle. They should also attempt to advocate for case mix adjustments to reflect disparate Welsh epidemiology and demography. But there will always be outliers with the greatest under-payments and the greatest over-payments in every cycle in which capitation mechanisms are used because capitation is an extraordinarily inefficient health care service mechanism.

To adequately compensate ALL providers for their insurance risk management services, the NHS ought to be paying each provider substantially more than any case-mix adjusted system would suggest, and well beyond the levels that a sustainable and efficient national health insurance program would cost if the risks were managed at the national level. The only savings that come from capitation payment mechanisms are because providers, squeezed by their exposure to higher costs than revenues, systematically reduce the level of care they provide to their patients. Capitation mechanisms are logically and mathematically inconsistent with efficient health care (finance) systems.

The problem with adjusting capitation payments with case mix adjustments to correct “cost bias” in actual service costs for well defined differences in population health demographics is that these adjustments do not correct for the increased variability in costs that small portfolio size and inefficient insurance operations cause.

The authors leapfrogged a bit, skirting the issue of inefficient insurance risk management, which is fine. It is often impossible to convince seemingly excessively compensated providers that even their over-payments are actually inadequate for their dual services as clinicians and insurers.

Disadvantaged providers are almost always more likely to see a problem than those who receive over-payment. But neither set of providers tends to see that the real problem is a bit different and far more insidious than anything amenable to correction using case mix adjustments.

The reason it is harder to explain this to over-paid providers is that they like being overpaid. If their case mix correction should be negative they are thrilled because this suggests continuing over-payments. The problem is that the over-payments are likely still a random effect due to random, rather than systematic lower than expected costs. These providers are still likely to be inadequately compensated for their clinical AND risk management services.

Bureaucrats, on the other hand, are a real problem. As underpaid providers, not overpaid providers tend to look for positive case mix adjustments, bureaucrats look for data on over-paid providers, with the opposite intent: Cutting health care payments to providers because they see providers who are being over-paid providers and they believe this is sufficient to make further reductions in provider reimbursement.

The problem with case-mix adjustments is that they can be made after each accounting cycle: Providers with excessive revenues might have negative case mix adjustments for next year, reflecting the reduced costs, and/or excessive revenues, for patient care last year. There are two problems with this.

First, when the national entity wants to reduce costs, or at least restrain the growth in costs, it wants to spend less, not more, on provider payments. This pits provider against provider for a non-increasing pool of funds. This increases competition between providers for the wrong reasons.

Rather than working collaboratively to produce healthier populations, providers are competing for the same funds. A win for one provider becomes a loss for another. Surgeons want more money for operating rooms and surgical interventions while family practitioners want more money for prevention services and out-patient care.

The second, and more serious problem, is that transferring insurance risks to providers results in knee jerk reactions to the most recent years costs, leading to wildly erratic financial outcomes for providers. A provider that was accurately compensated last year, but which had lower than expected costs, should get a cut in its capitation payments. The reduced payments would be even more inadequate for an average year, so the provider is likely to suffer a big loss the following year.

On the other hand, a provider with unusually high costs last year, gets an increase in its capitation payments that far exceed its needs. It is paid excessively more than necessary in the second year.

It is one of the great 21st century paradoxes that these wild fluctuations in year to year payments and costs are precisely the effects true insurance mechanisms are intended to eliminate.

The piece these authors leapfrogged is the most critical for understanding health provider’s inefficient insurance operations.

Until I read the NHS White Paper (See “Equity and excellence: Liberating the NHS” at

Equity and excellence: Liberating the NHS

I thought the NHS was somewhat more immune to the US’s health care finance flaws. After reading the White Paper, I realized that both health care finance systems are nearly indistinguishable in their mismanagement of insurance risks.

Understanding Risk and Insurance: A Progressive’s Guide To National Health Insurance

August 20, 2011

I wrote this piece for one of those endless numbers of progressive websites – Figure they may not publish it so I thought I would put it here,


Progressives invoke lofty social goals to support a national health insurance program. They want to correct disparities in access to care, cover the uninsured, promote health and well being, and they cede arguments about waste and inefficiency to mainstream and conservative adversaries.

This is incorrect as well as inappropriate. The real reason for a national health insurance program is that it is the most mathematically efficient way to manage health care service costs.


Risk is uncertainty. None of us know whether our health costs will be $0 or $1,000,000 next year. We do not know whether we will live or die, be injured, or ill next year. If we knew, there would be no risk related to our future health care costs. Risk exists because we do not know how much we need to pay for health care next year.

Risk Management Through Insurance

Very few people can afford to set aside sufficient funds to cover their future health care costs. Not knowing our future costs means we should all set aside large amounts to cover even modest costs, such as $50,000 or $100,000.

But, insurance reduces these costs. By joining together we can pay modest premiums, say $3-4,000 per person rather than $50,000, $100,000, or more because an efficient insurer can charge a little more than the average cost to provide insurance. This fact is based on the Central Limit Theorem, the workhorse from statistics and probability theory. The CLT is why insurance works for health, general liability and homeowners and private passenger automobile insurance.

The larger the insurance company, the closer to the average its loss ratio will be, the more stable its operating results, and the more efficiently it turns dollars into health services.

This is what everyone knows!

How To Destroy An Efficient Insurance System

Our current health care finance system is not efficient. There are two major reasons. Most people either believe, or are unwilling to challenge, the idea that more competition in insurance markets, meaning many more small insurers, will operate more efficiently than a single large insurer, or a small number of very large insurers. Wrong.

But that is the smaller problem. We have far too many small, very inefficient insurers, but we create even more inefficiency by transferring health insurance risks to health care providers. I call these insurance risk transfers “Professional Caregiver Insurance Risk.”

There are many insurance risk transferring health care finance mechanisms: Capitation, episode based care, Diagnosis Related Groups payment schemes, The Medicare/Medicaid managed care programs and Prospective Payment Systems, and many other profit/risk sharing agreements between third party payers and health care providers.

Professional Caregiver Insurance Risk

When health care providers accept insurance risks the insurance risks do not disappear into the aether. Risk assuming health care providers become even smaller, less efficient insurers than the insurers transferring the risks! The Central Limit Theorem works both ways. If large insurers are more efficient risk managers than small insurers, the corollary is: Small insurers are less efficient than large insurers.

Serving as their patient’s undisclosed health insurers is an obvious ethical conflict. But it is far worse. The annual operating results of inefficient insurers are very different than the annual operating results of efficient insurers. We can compare operating results by portfolio size. All we need to do is make some assumptions about a large, fairly efficient insurer.

A Paradigm Insurer

Suppose a Paradigm Insurer (PI) insures 1,000,000 people each year. Because it is an insurer its future operating results are uncertain. The measure of this uncertainty, the variation in its loss ratios from year to year, when insuring policyholders from the same population is measured by its standard error.

We assume that PI’s average loss ratio is $0.75 per premium dollar, and it has non-health related expenses of $0.15 per dollar of premium. We assume the year to year variation in its loss ratio, its “standard error” is $0.05 per dollar of premium.

There are two remaining components of insurer’s premiums. We assume PI charges a profit margin of $0.05 per dollar of premium and a Risk Premium, a charge for its risk management services, of $0.05 per dollar of premium.

Without belaboring the statistics, PI has an even chance (Probability 0.5000) of earning profits of at least 10% at loss ratios less than 0.7500, probability 0.8413 of profits of at least 5% at loss ratios less than 0.8000, and PI’s probability is 0.9772 of profits of at least 0% at loss ratios less than 0.8500. PI has a modest probability (0.0013) of losing 5% or more for the year and virtually no chance of losses greater than 10%.

The Flaw In Transferring Risks To Health Care Providers

All insurers selecting policyholders from the same population, have the same probability (0.5000) of profits of 10% or more. This is not true for other outcomes. While PI’s standard error is 0.0500, the standard error for an insurer insuring 100 times as many people would be 0.0050 and this larger insurer’s probability of earning profits higher than 9% is 0.9772.

But insurers 1/100th as large as PI, have standard errors 0.5000 and probabilities of losses greater than 0% 0.4207. This is what efficiency means in insurance. Large insurers are less likely to incur high losses, more likely to earn modest profits, are less likely to become insolvent, and can offer higher benefits to their policyholders than smaller, less efficient insurers.

Progressives need to focus on educating the public about how insurance works to shift the terms of the debate and claim the high moral and financial ground that a national health insurer is the most efficient insurer possible, not cede this ground to moderates and conservatives.

Thomas Cox PhD, RN, MSW, MS is a statistician, registered nurse, certified social worker, chartered property casualty underwriter, and licensed health care risk manager and author of “Standard Errors: Our failing health care (finance) systems and how to fix them”.

Standard Errors: Our failing health care (finance) systems and how to fix them

May 17, 2011

Get a free copy of the Sampler version of my book:

Standard Errors: Our failing health care (finance) systems and how to fix them

Latest paper in the Journal of Healthcare Risk Management

April 28, 2011

Just had my latest paper published in the Journal of Healthcare Risk Management:

Cox, T. (2011), Exposing the true risks of capitation financed healthcare. Journal of Healthcare Risk Management, 30: 34–41. doi: 10.1002/jhrm.20066

The key points:

Small insurers are inefficient insurers: They have lower probabilities of achieving modest profit goals, higher probabilities of incurring operating losses, and higher probabilities of insolvency than larger insurers when both randomly select policyholders from the same populations.

Small insurers also have to cut benefits to match larger insurer’s probabilities of achieving modest profit goals, avoiding operating losses, and avoiding insolvency.

Despite this, and the obvious impact it has on service quality and quantity, almost every proposal for trimming health care costs assumes that putting health care providers into roles as their patients’ insurers is some sort of panacea.

Pandora’s Box would be a more fitting analogy.

MadAsHellDoctors for a single payer health care finance system

March 23, 2011

Thomas Cox PhD RN
March 21, 2011 at 8:23 pm

I tried to post this on the Mad As Hell Doctors website in support of a single payer health care finance system, but they don’t seem to like it… It is awaiting moderation…

The missing detail is what I call “Professional Caregiver Insurance Risk.”

Small insurers are terribly inefficient risk managers. Their loss ratios vary far more than loss ratios of large insurers. That is important! It is the reason insurance works.

Soooo, when you have lots of small insurers or you transfer insurance risks to health care providers through managed care, capitation, DRGs or PPS, health care providers become our insurers.

But inefficient insurers have lower probabilities of earning profits, higher probabilities of incurring operating losses, and higher probabilities of insolvency than larger, more efficient insurers.

So small insurers and insurance risk assuming providers have to reduce benefits to cope with their inefficiencies as insurers.

Why do we need a single payer system?


Its about math… The arguments agains SP are political double speak and Voodoo economics.

Hello world!

March 9, 2010