# Should medical professional liability insurance be experience rated?

Should Medical Professional Liability Insurance Be Experience Rated?

Introduction

In a recent article in this Journal, Nye and Hofflander (1988) corroborate earlier work by Rolph (1981) and demonstrate that the probability of incurring a medical malpractice claim is not constant for all physicians within a given specialty, but is instead highly skewed, with some physicians accounting for disproportionate numbers of such claims. Based on these findings, both articles argue in favor of experience rating based on prior claims experience for medical malpractice insurance.

This study reexamines the evidence concerning experience rating of medical malpractice insurance using a similar statistical approach as in Nye and Hofflander, and Rolph, but on a larger, more complete, and more recent data set.(1) As in these previous studies, clear evidence is presented that physicians do indeed differ significantly in their probabilities of experiencing malpractice claims, and that conditional means for physicians with different numbers of claims incurred during the previous five years vary substantially.

This study extends earlier research by consideration of the financial implications of experience rating from an individual physician's point of view. Doing so highlights two points important for assessing the desirability of experience rating. The first is that although rating based on prior claims experience does improve the correlation between premiums and expected claims costs, it remains a highly imperfect tool for doing so. Expected premiums for physicians with different underlying risks move only slightly towards the actuarially fair rates within five years.

The second point is that using prior claims for experience rating introduces serious financial risk for many providers. The research literature to date (Nye and Hofflander, 1988; Rolph, 1981) implies that premiums should reflect Bayesian conditional means. As shown in this article, for many provider specialties, even low-risk physicians face significant risk of large premium increases if premiums are set using conditional means using Bayes' law. A single paid claim implies that premiums increase by a factor of four or more in more than half of all physician specialties examined. This introduces serious inequities in the pricing of insurance to physicians with identical underlying risks.

At present, past claims experience plays a very limited role in rate setting. Medical malpractice liability insurers now set premiums on the basis of the physician specialty and in some cases, tasks performed within that specialty (such as making a distinction between major and minor surgery), and geographic location. Physicians working less than full time generally pay lower rates. None of these factors depends on the physicians' prior claims experience. In a few cases, however, malpractice liability policies include surcharges related to past instances of malpractice. Limited experience rating has emerged in New York and Massachusetts - two states where rates are heavily regulated.

Data

Since 1975, insurers and self-insured hospitals in New York have been required to submit data on malpractice claims to the New York State Insurance Department. As part of a larger study (New York Department of Health, 1988), the New York State Department of Health assembled a data set consisting of the 9,268 malpractice claims closed against New York physicians between 1980 and 1983. Slightly less than half of these claims resulted in payment to the patient. Table 1 contains a summary of the 4,305 paid claims in the data. Over the four years patients received a total of $343,143,671 in compensation for their injuries.

Dollar awards for malpractice liability are highly skewed. Of the claims closed with payment, 11 percent resulted in awards in excess of $200,000. This 11 percent of paid claims consumed 53.8 percent of the total indemnification. In this analysis (as in the research by Nye and Hofflander, 1988 and Rolph, 1981) large and small paid claims are treated identically for purposes of experience rating. In principle, information on the size of the award should be used in an experience-rating formula. This form of experience rating could not be pursued with access only to aggregate information about claims. An important area for further research is the feasibility and desirability of taking into account the size as well as the frequency of paid claims.

From the third column of Table 1, which shows the percentage of physicians with at least one paid claim, it is clear that paid claims are not evenly distributed across physician specialties. For general practitioners, 29.2 percent experienced at least one claim over the four-year period, versus only 1.2 percent of psychiatrists, or 4.9 percent of pediatricians. Clearly, physician specialties should be treated separately for purposes of experience rating.

Table 1 also indicates that the occurrence of multiple claims differs markedly across provider specialties. Orthopedic surgeons accounted for 5 percent of physicians but 26 percent of all physicians with more than four paid claims between 1980 and 1983. Obstetricians, general surgeons, and otolaryngologists are also over represented in the multiple paid claims pool. Hence, Table 1 also provides evidence that the dispersion of claim rates among physicians differs across physician specialties. The next section develops a model which reflects differences in average claim rates both across provider specialties and across physicians in the same specialty. [Tabular Data Omitted]

A Statistical Model of Paid Claim Incidence

A model of the incidence of medical malpractice claims identical to that found in Nye and Hofflander, and Rolph is used in this study. The model assumes that the number of claims experienced by an individual physician is Poisson distributed with a constant probability of a claim throughout the sample period. Moreover, it also assumes that individual physician Poisson probabilities are not constant across all physicians, but are themselves distributed according to a gamma distribution, with parameters [alpha] (a shaping parameter) and [beta] (a scaling parameter). Small values of [alpha] correspond to a wide dispersion in Poisson probabilities, while the ratio [alpha]/[beta] corresponds to the expected claims rate across all physicians.

Using the frequency distribution of claims for each specialty shown in Table 1, the maximum likelihood values of parameters [alpha] and [beta] for each specialty was first estimated.(2) For one specialty, general practitioners, estimates of gamma distribution parameters were unobtainable, since the distribution of claims appears to be inconsistent with the gamma distribution.(3) Results for general practitioners are not presented in the remainder of this article.

Next the null hypothesis of no differences in the underlying claims rate within a physician specialty was tested using a likelihood ratio (LR) test of the negative binomial distribution versus the Poisson distribution at their respective maximum likelihood values. The results of this test are shown in Table 2. For all specialties except anesthesiology the null hypothesis of no differences in the underlying claims rate could be rejected at the 5 percent significance level. Since failure to reject the null hypothesis for anesthesiology may be due to imprecision in the estimates of [alpha] rather than the absence of any differences, results are reported for that specialty as well as the others.

To illustrate what is implied by the estimated gamma distribution parameters for individual physicians that are at low, moderate, and high risk of experiencing a paid claim, the expected claims rate for the 10th, 50th, and 90th percentile physicians were calculated for each specialty.(4) The results are contrasted with the mean claims rate for each specialty in Table 2.

The magnitude of the differences in underlying claims rates for different physicians in the same specialty is striking. For ten of the 17 specialties, the low-risk physicians (10th percentile) have a one-year expected claims rate of less than one in 10,000. In contrast, in all but five of the physician specialties, high-risk physicians (90th percentile) have one-year expected claims rates of at least one in 20. The specialties showing the smallest dispersion, as measured by the ratio of the 90th to 10th percentile physician are anesthesiology, general surgery, neurosurgery, and obstetrics/gynecology.

The results in Table 2 indicate that a low-risk, 10th percentile physician and a high-risk, 90th percentile physician do indeed experience vastly different claims rates. How well will experience rating based on the number of paid claims over a period of five prior years reflect these differences? The first step in examining the impact of experience rating on individual physicians is to generate the experience-rated premium structure. Following Nye and Hofflander, and Rolph, estimated gamma distribution parameters can be used to calculate the experience-rated premiums appropriate for physicians with different numbers of observed claims over a five-year base period. The conditional means needed for the calculation can conveniently be calculated using the Bayesian updating formula for a gamma distribution. If the one period prior distribution of claims before experience is taken into account is gamma distributed with parameters ([alpha],[beta]), then after N periods in which X claims are experienced, the posterior distribution is gamma distributed with parameters ([alpha] + X, [beta] + N) (Rolph, 1981). The mean of this posterior distribution is ([alpha] + X)/([beta] + N); this formula was used to calculate the conditional means in Table 3. [Tabular Data Omitted]

Table 3 confirms the result in Nye and Hofflander, that for most specialties conditional means differ substantially according to the number of prior claims experienced. For all specialties but anesthesiology (for the hypothesis that all risks are identical cannot be rejected) and general surgery, the conditional mean claims rate more than doubles as soon as the first paid claim is experienced. The largest proportional change in the conditional mean occurs for psychiatrists, where the conditional mean changes by a factor of 19.8. In eight other specialties, the conditional mean increases by a factor of four or more once the physician experiences at least one paid claim. The fact that experience rating according to conditional means implies such large changes in premiums is of central importance and will be considered further below. [Tabular Data Omitted]

Experience Rating for Low, Median, and High-Risk Physicians

From Table 3, it is clear that experience rating will make a difference in the premium paid by physicians with different number of paid claims. A related issue is the difference experience rating will make to physicians of different inherent risks (due to type of patient seen, volume of practice, medical skills, or other factors). This issue is addressed by examining the likely impact of experience rating for physicians at the 10th, 50th, and 90th percentile of the gamma distribution of rate of claims for three large specialties with different patterns of paid claims: internal medicine, obstetrics/gynecology, and orthopedic surgery.(5) We assume that five years of data are available for setting premiums. This seems about as long a period as it is reasonable to assume that the underlying probabilities for physicians remain constant.

In order to forecast the impact of experience rating on a physician with a certain risk of a paid claim, the probability that a physician will have zero, one, two, three, etc. claims over the five year period is estimated. The difference in these probabilities is responsible for the differential impact of experience rating on physicians of different risks. Any physician in a specialty, given one paid claim, would pay the same rate with experience rating. Low-risk physicians will in general benefit from experience rating because they are less likely to incur a paid claim.

The results for internal medicine are first discussed in detail and then the findings for the other two specialties are contrasted. Applying the Poisson distribution to the rates shown in Table 2, we calculated the probability distribution that a 10th percentile specialist in internal medicine has zero, 1,2,3, etc. paid claims over five years. From Table 2 the rate of claims for one year is zero to four decimal places. Applying this small positive rate for five periods implies that the probability the 10th percentile internist has no claims over five years is .9999 (see Table 4). [Tabular Data Omitted]

The internist at the 90th percentile is much more likely to run into trouble with malpractice. The high-risk internist has one claim with a 19 percent probability, and more than one claim with a two percent probability. It is still notable, however, that almost eighty percent of the time, the internist at the 90th percentile looks, for purposes of experience rating, as skilled as can be - that is, has no paid claims. The median-risk internist has less than a two percent chance of having one paid claim, and a very small chance of having more than one.

Table 5 summarizes the average financial impact of experience rating on the low, median, and high-risk physicians. In terms of financial impact, a .9999 chance of having no claims after five years for an internist at the 10th percentile means a .9999 chance of paying the rate corresponding to .0126 from Table 3. In other words, the low-risk internist is extremely likely to pay the best rate.

The internist at the 50th percentile also generally benefits from experience rating. This median-risk internist can expect to save 19 percent on liability premiums because of experience rating. However, the median internist bears more risk than the internist at the 10th percentile. There is a two percent chance that the median-risk internist will have a paid claim and pay premiums three and a half times greater than the nonexperience rated amount.

Experience rating can be seen to have two effects on the premium fairness. Experience rating improves the fairness of the insurance system for groups of physicians with different degrees of risk; however, it worsens fairness for individual physicians facing the same risk. In terms of groups of physicians, experience rating lowers expected liability premiums for internists below the average rate and increases them for those above the average rate. However, although the gains for some physicians can be substantial, even after five years, experience rating does not move the pricing very close to the actuarially fair premiums. As Table 5 shows, for example, the median internist can expect to pay a premium still four times too high in relation to his or her true rate. [Tabular Data Omitted]

On the other hand, for physicians facing the same true risk of a paid claim, experience rating introduces inequities: some physicians pay too little and some too much. For example, the 2 percent of the median-risk internists who have a claim will be paying too much in premiums. Even the 20 percent of the 90th percentile internists who pay the rate corresponding to one claim in five years are paying a rate (.0605) above their actuarially fair rate (.0496).

It is important to keep in mind that full experience rating using conditional means would imply that a paid claim has an impact on premiums for several years. If records were used for experience rating for five years, a physician in internal medicine with one paid claim would pay a rate proportional to .0605 (from Table 3) for five years(6) instead of proportional to .0126 (with no claims and experience rating) or, with no experience rating, a rate proportional to .0166. If the nonexperience rated premium of .0166 corresponds to $8,800 (the 1988 premium for an internist in New York State outside of New York City and Long Island), and premiums under an experience - rated system are proportional to the conditional means, the premiums after one paid claim would rise from $6,700 to $32,100, and involve an annual penalty of the difference, about $25,000.(7) Over five years, then, the penalty to a physician for the one paid claim would amount to $125,000.

Experience rating will never appeal to the 90th percentile physicians, and probably will always appeal to the 10 percentile physicians. It may be most interesting to ask about experience rating from the median-risk physicians' point of view. For the 50th percentile physician, are the potential gains from experience rating worth the potential costs?

The median-risk internist can be viewed as facing a choice between two lotteries. If the experience-rated lottery is chosen, the internist pays $8,800 with probability .9841, $32,000 with probability .0156, and $57,400 with probability .0001. Although, the expected cost of the experience-rated lottery is $1,700 less than a lottery without experience rating, it is not obvious that a risk averse physician would prefer experience rating.

Two observations can be made on this situation. The first is that if the physician has the option of introducing some experience rating, adjusting a fraction of the premium on the basis of experience, the median physician would desire some of the premium to be experience rated. Initially, the risk costs introduced by uncertainty would be small in relation to reductions in expected premiums introduced by experience rating. Second, the median physician will tend to favor experience rating the greater the expected gains. Expected gains to the median physician will be larger in specialties where malpractice risk is concentrated in the upper tail of the distribution. The median physician in a specialty with a few "bad apples" will favor experience rating. In seven of the specialties listed in Table 2, the mean claims per year exceeds the median claim rate by a factor of five or more. These are specialties where experience rating is more likely to appeal to the majority of physicians.

Obstetricians provide an interesting contrast to internists, since the occurrence of a paid claim is much more common for obstetricians. The unconditional mean is .0798 per year compared to .0166 for internists. Obstetricians at all risk levels, as shown in the middle portion of Table 4, are more likely to have a paid claim in five years. The probability of having no paid claims for five years is 96 percent for low-risk, 76 percent for median-risk, and only 40 percent for high-risk obstetricians. This increased probability of incurring a paid claim more than offsets the more gradual increase in conditional means shown in Table 3. Hence, experience rating imposes greater financial risk on obstetricians than on internists in the current sample.

Malpractice premiums for obstetricians in upstate New York for 1988, as set by the largest insurer in the state, Medical Liability Mutual Insurance Company are $42,600. Assuming that this corresponds to the unconditional mean of .0798 for obstetricians and that premiums in an experience-rated system are proportional to the conditional means, one paid claim in an experience rated system increases the obstetricians' premium from about $30,000 (with no claims in five years) to $61,500 (with one claim in five years). Over a five-year period, this one claim would increase the obstetrician's liability premiums by more than $150,000, a major financial risk for an individual physician.

Orthopedic surgery is an interesting specialty because of the great differences in risk between the low and high-risk practitioners. As can be seen from Table 2, the low-risk orthopedic surgeon (in the 10th percentile of the gamma distribution) is virtually risk free, while the high-risk orthopedic surgeon has an annual rate of .1565, one of the highest for any specialty. In such a circumstance, a claim for malpractice, because it serves as a strong indicator that this physician is at a high-risk, will be associated with a large increase in the conditional mean, as shown in Table 3.

The expected experience of the physicians of different inherent risk differs markedly, as is evident from the last section of Table 4. Orthopedic surgeons in the 90th percentile are highly likely to have one or multiple claims paid in five years, while the low-risk orthopedic surgeons are unlikely to have any. The expected impact of experience rating is very large. Both low and median-risk orthopedic surgeons can expect to gain significantly, but the high-risk physicians in this specialty can expect a very large increase in premiums. For any of the 4 percent of the high-risk specialists who have three or more claims, the malpractice premium will be six times higher than it would be under no experience rating.

One paid claim appears to be more costly in orthopedic surgery than for the other two specialties examined. Based on an annual premium of $44,200 (upstate New York, 1988) corresponding to the nonexperience rated mean of .0519, one claim increases the premium from an amount proportional to .0246 to an amount proportional to .1299, or from $21,000 to $110,600, an increase of almost $90,000 per year. Over five years, this one paid claim would increase premiums to an orthopedic surgeon by nearly $450,000.

Discussion

Medical malpractice liability continues to be a troubled area of insurance. Public commissions have recently viewed malpractice liability with alarm, and suggested various reforms, including limiting awards by modification of this area of tort law, institution no-fault coverage for certain medical events, or requiring arbitration (General Accounting Office, 1986; New York State Insurance Department, 1988; Department of Health and Human Services, 1987). Writing from the perspective of insurance, some authors have suggested changes in the premium setting for medical malpractice liability in order to incorporate a physicians' past claims experience into his or her rate determination (Nye and Hofflander, 1988; Rolph, 1981).

Analyzing four years of data from a large state in some ways corresponds to a setting favorable for the application of experience rating. On the other hand, the form of experience rating examined is a mechanical application of statistical information. One conclusion is that substantial modification of the use of Bayesian conditional means will be necessary in the design of an acceptable system.

Experience rating moves premiums towards fair rates for practitioners on average, but even with five years of data (and the assumption that underlying risks are constant), these improvements are modest. Further, the gains in fairness need to be weighed against the introduction of financial risk for physicians at all malpractice risk categories. It is unclear whether the majority of physicians in most specialties would accept a lower expected payment in return for the risk of the unfair premium rate increases implied by experience rating.

This analysis does, however, show the potential of experience rating for improving fairness in a way that a majority of physicians in some specialties should be willing to accept. In any specialty where the median risk is less than the mean risk, the median physician (and therefore the majority of physicians) should favor some experience rating, i.e., adjusting some portion of the total premium in response to experience in accordance with Bayesian conditional means. Specialties where the distribution of risk is highly skewed, and the median risk is very much below the mean, will be characterized by a large majority of physicians with expected gains from experience rating.

As mentioned earlier in this article, a source of error in this analysis is associated with using the number of prior paid claims for purposes of experience rating without recognizing that paid claims are for different amounts. The data used for research so far on experience rating does not contain information on size of claims on a disaggregated basis, so it has been impossible for researchers to assess the potential importance of this for experience rating. Nonetheless, this remains an important area for future research.

The current study underlines the potential importance of information other than past claims experience for purposes of setting rates. Other characteristics of a physician's practice, such as years of experience, case mix, volume of practice, and the specific procedures performed, may be more reliable predictors of future claims than are past claims, and because randomness plays a smaller role, introduce fewer inequities across physicians with similar risks. For example, suppose all of the difference in inherent risk of malpractice among obstetricians were due to differences in practice volume. Obstetricians could all be equally skillful and careful, but differ in their risk per year because of the number of babies they deliver. Premium setting on the basis of volume would be a much fairer system (and provide more appropriate incentives) than one that sets rates according to the number of past paid claims. Although it is impossible with the present data set, whether inherent rates differ when one controls for other characteristics of a physician's practice, such as volume, case mix, years of experience, etc., is clearly a question that deserves investigation.

(1) The sample used by Rolph (1981) did not contain accurate counts of the number of physicians in each specialty, while the Pennsylvania data used by Nye and Hofflander (1988) provides information only on claims of at least $100,000 qualifying for payment from a special catastrophic loss fund set up by the state.

(2) Although not reported in the original data from New York State, because the total claims represented by the physicians in the category of six or more claims are known, and because these numbers are consistent with a unique distribution of physicians in the final category, the exact number of claims experienced by each physician in the column labeled "6+" could be inferred. One general practitioner who experienced 244 claims during the sample period was dropped, although this did not affect gamma parameter estimates (see the following footnote).

(3) By inspecting the row for general practitioners in Table 1, it can be seen that the number of physicians with two or more claims (56) is unexpectedly low given the number of physicians with only one claim (475). Since 26.2 percent of all physicians have at least one claim, one would expect at least the same percentage of those with one or more to have at least two claims. Instead, only 11.8 percent of those with at least one claim have two or more. The gamma distribution is consistent with a disproportionately high number of multiple claims, not a disproportionately low number.

(4) The tenth percentiles shown in Table 2 were derived by solving F([lambda][alpha], [beta]) = .10 for [lambda], where F() is the cumulative gamma distribution function with parameters [alpha] and [beta], defined over [lambda], the Poisson probability of experiencing a paid claim. The 50th and 90th percentiles were found in an analogous manner.

(5) Complete simulation results for all specialties listed above are available from the authors.

(6) This assumes the system is in steady state and five years of data are available before the paid claim occurs. In a system beginning in year one, the actual financial impact would be greater because the claim in year one would be given greater weight in an experience rating formula.

(7) Data on premiums for the specialties examined in this section are from the Medical Liability Mutual Insurance Company (1987), the largest insurer in New York State. Premiums are for an occurrence policy. Rates for New York City or Long Island are roughly twice the upstate amounts.

References

[1.] Department of Health and Human Services, 1987, Report of the Task

Force on Medical Liability and Malpractice (Washington, D.C.: U.S.

Government Printing Office). [2.] General Accounting Office, 1986, Medical Malpractice: Six State Case

Studies Show Claims and Insurance Costs Still Rise Despite Tort Reforms

(Washington, D.C.: U.S. Government Printing Office). [3.] Medical Liability Mutual Insurance Company, 1987, Premium Rate

Schedules for Physicians and Surgeons: Occurrence and Claims Made

Policy Forms (New York: Medical Liability Mutual Insurance Company). [4.] New York State Department of Health, 1988, Monitoring Health Care

Quality: Malpractice, Misconduct, Quality Assurance (New York: New

York State Department of Health). [5.] New York State Insurance Department, 1988, A Balanced Prescription for

Change: Report of the New York State Insurance Department on Medical

Malpractice (New York: New York State Insurance Department). [6.] Nye, Blaine F. and Hofflander, Alfred E., 1988, Experience Rating in

Medical Professional Liability Insurance, The Journal of Risk and

Insurance, 60: 150-157. [7.] Rolph, J.E., 1981, Some Statistical Evidence on Merit Rating in Medical

Malpractice Insurance, The Journal of Risk and Insurance, 48: 247-260.

Randall P. Ellis is Associate Professor of Economics at Boston University. Cynthia L. Gallup is a Ph.D. candidate in Economics at the University of California, Berkeley. Thomas G. McGuire is Professor of Economics at Boston University.

The authors are grateful to Professors Chris Ruhm and Pankaj Tandon, and to Karen Clark, President of Applied Insurance Research, for helpful comments on an earlier draft.

Introduction

In a recent article in this Journal, Nye and Hofflander (1988) corroborate earlier work by Rolph (1981) and demonstrate that the probability of incurring a medical malpractice claim is not constant for all physicians within a given specialty, but is instead highly skewed, with some physicians accounting for disproportionate numbers of such claims. Based on these findings, both articles argue in favor of experience rating based on prior claims experience for medical malpractice insurance.

This study reexamines the evidence concerning experience rating of medical malpractice insurance using a similar statistical approach as in Nye and Hofflander, and Rolph, but on a larger, more complete, and more recent data set.(1) As in these previous studies, clear evidence is presented that physicians do indeed differ significantly in their probabilities of experiencing malpractice claims, and that conditional means for physicians with different numbers of claims incurred during the previous five years vary substantially.

This study extends earlier research by consideration of the financial implications of experience rating from an individual physician's point of view. Doing so highlights two points important for assessing the desirability of experience rating. The first is that although rating based on prior claims experience does improve the correlation between premiums and expected claims costs, it remains a highly imperfect tool for doing so. Expected premiums for physicians with different underlying risks move only slightly towards the actuarially fair rates within five years.

The second point is that using prior claims for experience rating introduces serious financial risk for many providers. The research literature to date (Nye and Hofflander, 1988; Rolph, 1981) implies that premiums should reflect Bayesian conditional means. As shown in this article, for many provider specialties, even low-risk physicians face significant risk of large premium increases if premiums are set using conditional means using Bayes' law. A single paid claim implies that premiums increase by a factor of four or more in more than half of all physician specialties examined. This introduces serious inequities in the pricing of insurance to physicians with identical underlying risks.

At present, past claims experience plays a very limited role in rate setting. Medical malpractice liability insurers now set premiums on the basis of the physician specialty and in some cases, tasks performed within that specialty (such as making a distinction between major and minor surgery), and geographic location. Physicians working less than full time generally pay lower rates. None of these factors depends on the physicians' prior claims experience. In a few cases, however, malpractice liability policies include surcharges related to past instances of malpractice. Limited experience rating has emerged in New York and Massachusetts - two states where rates are heavily regulated.

Data

Since 1975, insurers and self-insured hospitals in New York have been required to submit data on malpractice claims to the New York State Insurance Department. As part of a larger study (New York Department of Health, 1988), the New York State Department of Health assembled a data set consisting of the 9,268 malpractice claims closed against New York physicians between 1980 and 1983. Slightly less than half of these claims resulted in payment to the patient. Table 1 contains a summary of the 4,305 paid claims in the data. Over the four years patients received a total of $343,143,671 in compensation for their injuries.

Dollar awards for malpractice liability are highly skewed. Of the claims closed with payment, 11 percent resulted in awards in excess of $200,000. This 11 percent of paid claims consumed 53.8 percent of the total indemnification. In this analysis (as in the research by Nye and Hofflander, 1988 and Rolph, 1981) large and small paid claims are treated identically for purposes of experience rating. In principle, information on the size of the award should be used in an experience-rating formula. This form of experience rating could not be pursued with access only to aggregate information about claims. An important area for further research is the feasibility and desirability of taking into account the size as well as the frequency of paid claims.

From the third column of Table 1, which shows the percentage of physicians with at least one paid claim, it is clear that paid claims are not evenly distributed across physician specialties. For general practitioners, 29.2 percent experienced at least one claim over the four-year period, versus only 1.2 percent of psychiatrists, or 4.9 percent of pediatricians. Clearly, physician specialties should be treated separately for purposes of experience rating.

Table 1 also indicates that the occurrence of multiple claims differs markedly across provider specialties. Orthopedic surgeons accounted for 5 percent of physicians but 26 percent of all physicians with more than four paid claims between 1980 and 1983. Obstetricians, general surgeons, and otolaryngologists are also over represented in the multiple paid claims pool. Hence, Table 1 also provides evidence that the dispersion of claim rates among physicians differs across physician specialties. The next section develops a model which reflects differences in average claim rates both across provider specialties and across physicians in the same specialty. [Tabular Data Omitted]

A Statistical Model of Paid Claim Incidence

A model of the incidence of medical malpractice claims identical to that found in Nye and Hofflander, and Rolph is used in this study. The model assumes that the number of claims experienced by an individual physician is Poisson distributed with a constant probability of a claim throughout the sample period. Moreover, it also assumes that individual physician Poisson probabilities are not constant across all physicians, but are themselves distributed according to a gamma distribution, with parameters [alpha] (a shaping parameter) and [beta] (a scaling parameter). Small values of [alpha] correspond to a wide dispersion in Poisson probabilities, while the ratio [alpha]/[beta] corresponds to the expected claims rate across all physicians.

Using the frequency distribution of claims for each specialty shown in Table 1, the maximum likelihood values of parameters [alpha] and [beta] for each specialty was first estimated.(2) For one specialty, general practitioners, estimates of gamma distribution parameters were unobtainable, since the distribution of claims appears to be inconsistent with the gamma distribution.(3) Results for general practitioners are not presented in the remainder of this article.

Next the null hypothesis of no differences in the underlying claims rate within a physician specialty was tested using a likelihood ratio (LR) test of the negative binomial distribution versus the Poisson distribution at their respective maximum likelihood values. The results of this test are shown in Table 2. For all specialties except anesthesiology the null hypothesis of no differences in the underlying claims rate could be rejected at the 5 percent significance level. Since failure to reject the null hypothesis for anesthesiology may be due to imprecision in the estimates of [alpha] rather than the absence of any differences, results are reported for that specialty as well as the others.

To illustrate what is implied by the estimated gamma distribution parameters for individual physicians that are at low, moderate, and high risk of experiencing a paid claim, the expected claims rate for the 10th, 50th, and 90th percentile physicians were calculated for each specialty.(4) The results are contrasted with the mean claims rate for each specialty in Table 2.

The magnitude of the differences in underlying claims rates for different physicians in the same specialty is striking. For ten of the 17 specialties, the low-risk physicians (10th percentile) have a one-year expected claims rate of less than one in 10,000. In contrast, in all but five of the physician specialties, high-risk physicians (90th percentile) have one-year expected claims rates of at least one in 20. The specialties showing the smallest dispersion, as measured by the ratio of the 90th to 10th percentile physician are anesthesiology, general surgery, neurosurgery, and obstetrics/gynecology.

The results in Table 2 indicate that a low-risk, 10th percentile physician and a high-risk, 90th percentile physician do indeed experience vastly different claims rates. How well will experience rating based on the number of paid claims over a period of five prior years reflect these differences? The first step in examining the impact of experience rating on individual physicians is to generate the experience-rated premium structure. Following Nye and Hofflander, and Rolph, estimated gamma distribution parameters can be used to calculate the experience-rated premiums appropriate for physicians with different numbers of observed claims over a five-year base period. The conditional means needed for the calculation can conveniently be calculated using the Bayesian updating formula for a gamma distribution. If the one period prior distribution of claims before experience is taken into account is gamma distributed with parameters ([alpha],[beta]), then after N periods in which X claims are experienced, the posterior distribution is gamma distributed with parameters ([alpha] + X, [beta] + N) (Rolph, 1981). The mean of this posterior distribution is ([alpha] + X)/([beta] + N); this formula was used to calculate the conditional means in Table 3. [Tabular Data Omitted]

Table 3 confirms the result in Nye and Hofflander, that for most specialties conditional means differ substantially according to the number of prior claims experienced. For all specialties but anesthesiology (for the hypothesis that all risks are identical cannot be rejected) and general surgery, the conditional mean claims rate more than doubles as soon as the first paid claim is experienced. The largest proportional change in the conditional mean occurs for psychiatrists, where the conditional mean changes by a factor of 19.8. In eight other specialties, the conditional mean increases by a factor of four or more once the physician experiences at least one paid claim. The fact that experience rating according to conditional means implies such large changes in premiums is of central importance and will be considered further below. [Tabular Data Omitted]

Experience Rating for Low, Median, and High-Risk Physicians

From Table 3, it is clear that experience rating will make a difference in the premium paid by physicians with different number of paid claims. A related issue is the difference experience rating will make to physicians of different inherent risks (due to type of patient seen, volume of practice, medical skills, or other factors). This issue is addressed by examining the likely impact of experience rating for physicians at the 10th, 50th, and 90th percentile of the gamma distribution of rate of claims for three large specialties with different patterns of paid claims: internal medicine, obstetrics/gynecology, and orthopedic surgery.(5) We assume that five years of data are available for setting premiums. This seems about as long a period as it is reasonable to assume that the underlying probabilities for physicians remain constant.

In order to forecast the impact of experience rating on a physician with a certain risk of a paid claim, the probability that a physician will have zero, one, two, three, etc. claims over the five year period is estimated. The difference in these probabilities is responsible for the differential impact of experience rating on physicians of different risks. Any physician in a specialty, given one paid claim, would pay the same rate with experience rating. Low-risk physicians will in general benefit from experience rating because they are less likely to incur a paid claim.

The results for internal medicine are first discussed in detail and then the findings for the other two specialties are contrasted. Applying the Poisson distribution to the rates shown in Table 2, we calculated the probability distribution that a 10th percentile specialist in internal medicine has zero, 1,2,3, etc. paid claims over five years. From Table 2 the rate of claims for one year is zero to four decimal places. Applying this small positive rate for five periods implies that the probability the 10th percentile internist has no claims over five years is .9999 (see Table 4). [Tabular Data Omitted]

The internist at the 90th percentile is much more likely to run into trouble with malpractice. The high-risk internist has one claim with a 19 percent probability, and more than one claim with a two percent probability. It is still notable, however, that almost eighty percent of the time, the internist at the 90th percentile looks, for purposes of experience rating, as skilled as can be - that is, has no paid claims. The median-risk internist has less than a two percent chance of having one paid claim, and a very small chance of having more than one.

Table 5 summarizes the average financial impact of experience rating on the low, median, and high-risk physicians. In terms of financial impact, a .9999 chance of having no claims after five years for an internist at the 10th percentile means a .9999 chance of paying the rate corresponding to .0126 from Table 3. In other words, the low-risk internist is extremely likely to pay the best rate.

The internist at the 50th percentile also generally benefits from experience rating. This median-risk internist can expect to save 19 percent on liability premiums because of experience rating. However, the median internist bears more risk than the internist at the 10th percentile. There is a two percent chance that the median-risk internist will have a paid claim and pay premiums three and a half times greater than the nonexperience rated amount.

Experience rating can be seen to have two effects on the premium fairness. Experience rating improves the fairness of the insurance system for groups of physicians with different degrees of risk; however, it worsens fairness for individual physicians facing the same risk. In terms of groups of physicians, experience rating lowers expected liability premiums for internists below the average rate and increases them for those above the average rate. However, although the gains for some physicians can be substantial, even after five years, experience rating does not move the pricing very close to the actuarially fair premiums. As Table 5 shows, for example, the median internist can expect to pay a premium still four times too high in relation to his or her true rate. [Tabular Data Omitted]

On the other hand, for physicians facing the same true risk of a paid claim, experience rating introduces inequities: some physicians pay too little and some too much. For example, the 2 percent of the median-risk internists who have a claim will be paying too much in premiums. Even the 20 percent of the 90th percentile internists who pay the rate corresponding to one claim in five years are paying a rate (.0605) above their actuarially fair rate (.0496).

It is important to keep in mind that full experience rating using conditional means would imply that a paid claim has an impact on premiums for several years. If records were used for experience rating for five years, a physician in internal medicine with one paid claim would pay a rate proportional to .0605 (from Table 3) for five years(6) instead of proportional to .0126 (with no claims and experience rating) or, with no experience rating, a rate proportional to .0166. If the nonexperience rated premium of .0166 corresponds to $8,800 (the 1988 premium for an internist in New York State outside of New York City and Long Island), and premiums under an experience - rated system are proportional to the conditional means, the premiums after one paid claim would rise from $6,700 to $32,100, and involve an annual penalty of the difference, about $25,000.(7) Over five years, then, the penalty to a physician for the one paid claim would amount to $125,000.

Experience rating will never appeal to the 90th percentile physicians, and probably will always appeal to the 10 percentile physicians. It may be most interesting to ask about experience rating from the median-risk physicians' point of view. For the 50th percentile physician, are the potential gains from experience rating worth the potential costs?

The median-risk internist can be viewed as facing a choice between two lotteries. If the experience-rated lottery is chosen, the internist pays $8,800 with probability .9841, $32,000 with probability .0156, and $57,400 with probability .0001. Although, the expected cost of the experience-rated lottery is $1,700 less than a lottery without experience rating, it is not obvious that a risk averse physician would prefer experience rating.

Two observations can be made on this situation. The first is that if the physician has the option of introducing some experience rating, adjusting a fraction of the premium on the basis of experience, the median physician would desire some of the premium to be experience rated. Initially, the risk costs introduced by uncertainty would be small in relation to reductions in expected premiums introduced by experience rating. Second, the median physician will tend to favor experience rating the greater the expected gains. Expected gains to the median physician will be larger in specialties where malpractice risk is concentrated in the upper tail of the distribution. The median physician in a specialty with a few "bad apples" will favor experience rating. In seven of the specialties listed in Table 2, the mean claims per year exceeds the median claim rate by a factor of five or more. These are specialties where experience rating is more likely to appeal to the majority of physicians.

Obstetricians provide an interesting contrast to internists, since the occurrence of a paid claim is much more common for obstetricians. The unconditional mean is .0798 per year compared to .0166 for internists. Obstetricians at all risk levels, as shown in the middle portion of Table 4, are more likely to have a paid claim in five years. The probability of having no paid claims for five years is 96 percent for low-risk, 76 percent for median-risk, and only 40 percent for high-risk obstetricians. This increased probability of incurring a paid claim more than offsets the more gradual increase in conditional means shown in Table 3. Hence, experience rating imposes greater financial risk on obstetricians than on internists in the current sample.

Malpractice premiums for obstetricians in upstate New York for 1988, as set by the largest insurer in the state, Medical Liability Mutual Insurance Company are $42,600. Assuming that this corresponds to the unconditional mean of .0798 for obstetricians and that premiums in an experience-rated system are proportional to the conditional means, one paid claim in an experience rated system increases the obstetricians' premium from about $30,000 (with no claims in five years) to $61,500 (with one claim in five years). Over a five-year period, this one claim would increase the obstetrician's liability premiums by more than $150,000, a major financial risk for an individual physician.

Orthopedic surgery is an interesting specialty because of the great differences in risk between the low and high-risk practitioners. As can be seen from Table 2, the low-risk orthopedic surgeon (in the 10th percentile of the gamma distribution) is virtually risk free, while the high-risk orthopedic surgeon has an annual rate of .1565, one of the highest for any specialty. In such a circumstance, a claim for malpractice, because it serves as a strong indicator that this physician is at a high-risk, will be associated with a large increase in the conditional mean, as shown in Table 3.

The expected experience of the physicians of different inherent risk differs markedly, as is evident from the last section of Table 4. Orthopedic surgeons in the 90th percentile are highly likely to have one or multiple claims paid in five years, while the low-risk orthopedic surgeons are unlikely to have any. The expected impact of experience rating is very large. Both low and median-risk orthopedic surgeons can expect to gain significantly, but the high-risk physicians in this specialty can expect a very large increase in premiums. For any of the 4 percent of the high-risk specialists who have three or more claims, the malpractice premium will be six times higher than it would be under no experience rating.

One paid claim appears to be more costly in orthopedic surgery than for the other two specialties examined. Based on an annual premium of $44,200 (upstate New York, 1988) corresponding to the nonexperience rated mean of .0519, one claim increases the premium from an amount proportional to .0246 to an amount proportional to .1299, or from $21,000 to $110,600, an increase of almost $90,000 per year. Over five years, this one paid claim would increase premiums to an orthopedic surgeon by nearly $450,000.

Discussion

Medical malpractice liability continues to be a troubled area of insurance. Public commissions have recently viewed malpractice liability with alarm, and suggested various reforms, including limiting awards by modification of this area of tort law, institution no-fault coverage for certain medical events, or requiring arbitration (General Accounting Office, 1986; New York State Insurance Department, 1988; Department of Health and Human Services, 1987). Writing from the perspective of insurance, some authors have suggested changes in the premium setting for medical malpractice liability in order to incorporate a physicians' past claims experience into his or her rate determination (Nye and Hofflander, 1988; Rolph, 1981).

Analyzing four years of data from a large state in some ways corresponds to a setting favorable for the application of experience rating. On the other hand, the form of experience rating examined is a mechanical application of statistical information. One conclusion is that substantial modification of the use of Bayesian conditional means will be necessary in the design of an acceptable system.

Experience rating moves premiums towards fair rates for practitioners on average, but even with five years of data (and the assumption that underlying risks are constant), these improvements are modest. Further, the gains in fairness need to be weighed against the introduction of financial risk for physicians at all malpractice risk categories. It is unclear whether the majority of physicians in most specialties would accept a lower expected payment in return for the risk of the unfair premium rate increases implied by experience rating.

This analysis does, however, show the potential of experience rating for improving fairness in a way that a majority of physicians in some specialties should be willing to accept. In any specialty where the median risk is less than the mean risk, the median physician (and therefore the majority of physicians) should favor some experience rating, i.e., adjusting some portion of the total premium in response to experience in accordance with Bayesian conditional means. Specialties where the distribution of risk is highly skewed, and the median risk is very much below the mean, will be characterized by a large majority of physicians with expected gains from experience rating.

As mentioned earlier in this article, a source of error in this analysis is associated with using the number of prior paid claims for purposes of experience rating without recognizing that paid claims are for different amounts. The data used for research so far on experience rating does not contain information on size of claims on a disaggregated basis, so it has been impossible for researchers to assess the potential importance of this for experience rating. Nonetheless, this remains an important area for future research.

The current study underlines the potential importance of information other than past claims experience for purposes of setting rates. Other characteristics of a physician's practice, such as years of experience, case mix, volume of practice, and the specific procedures performed, may be more reliable predictors of future claims than are past claims, and because randomness plays a smaller role, introduce fewer inequities across physicians with similar risks. For example, suppose all of the difference in inherent risk of malpractice among obstetricians were due to differences in practice volume. Obstetricians could all be equally skillful and careful, but differ in their risk per year because of the number of babies they deliver. Premium setting on the basis of volume would be a much fairer system (and provide more appropriate incentives) than one that sets rates according to the number of past paid claims. Although it is impossible with the present data set, whether inherent rates differ when one controls for other characteristics of a physician's practice, such as volume, case mix, years of experience, etc., is clearly a question that deserves investigation.

(1) The sample used by Rolph (1981) did not contain accurate counts of the number of physicians in each specialty, while the Pennsylvania data used by Nye and Hofflander (1988) provides information only on claims of at least $100,000 qualifying for payment from a special catastrophic loss fund set up by the state.

(2) Although not reported in the original data from New York State, because the total claims represented by the physicians in the category of six or more claims are known, and because these numbers are consistent with a unique distribution of physicians in the final category, the exact number of claims experienced by each physician in the column labeled "6+" could be inferred. One general practitioner who experienced 244 claims during the sample period was dropped, although this did not affect gamma parameter estimates (see the following footnote).

(3) By inspecting the row for general practitioners in Table 1, it can be seen that the number of physicians with two or more claims (56) is unexpectedly low given the number of physicians with only one claim (475). Since 26.2 percent of all physicians have at least one claim, one would expect at least the same percentage of those with one or more to have at least two claims. Instead, only 11.8 percent of those with at least one claim have two or more. The gamma distribution is consistent with a disproportionately high number of multiple claims, not a disproportionately low number.

(4) The tenth percentiles shown in Table 2 were derived by solving F([lambda][alpha], [beta]) = .10 for [lambda], where F() is the cumulative gamma distribution function with parameters [alpha] and [beta], defined over [lambda], the Poisson probability of experiencing a paid claim. The 50th and 90th percentiles were found in an analogous manner.

(5) Complete simulation results for all specialties listed above are available from the authors.

(6) This assumes the system is in steady state and five years of data are available before the paid claim occurs. In a system beginning in year one, the actual financial impact would be greater because the claim in year one would be given greater weight in an experience rating formula.

(7) Data on premiums for the specialties examined in this section are from the Medical Liability Mutual Insurance Company (1987), the largest insurer in New York State. Premiums are for an occurrence policy. Rates for New York City or Long Island are roughly twice the upstate amounts.

References

[1.] Department of Health and Human Services, 1987, Report of the Task

Force on Medical Liability and Malpractice (Washington, D.C.: U.S.

Government Printing Office). [2.] General Accounting Office, 1986, Medical Malpractice: Six State Case

Studies Show Claims and Insurance Costs Still Rise Despite Tort Reforms

(Washington, D.C.: U.S. Government Printing Office). [3.] Medical Liability Mutual Insurance Company, 1987, Premium Rate

Schedules for Physicians and Surgeons: Occurrence and Claims Made

Policy Forms (New York: Medical Liability Mutual Insurance Company). [4.] New York State Department of Health, 1988, Monitoring Health Care

Quality: Malpractice, Misconduct, Quality Assurance (New York: New

York State Department of Health). [5.] New York State Insurance Department, 1988, A Balanced Prescription for

Change: Report of the New York State Insurance Department on Medical

Malpractice (New York: New York State Insurance Department). [6.] Nye, Blaine F. and Hofflander, Alfred E., 1988, Experience Rating in

Medical Professional Liability Insurance, The Journal of Risk and

Insurance, 60: 150-157. [7.] Rolph, J.E., 1981, Some Statistical Evidence on Merit Rating in Medical

Malpractice Insurance, The Journal of Risk and Insurance, 48: 247-260.

Randall P. Ellis is Associate Professor of Economics at Boston University. Cynthia L. Gallup is a Ph.D. candidate in Economics at the University of California, Berkeley. Thomas G. McGuire is Professor of Economics at Boston University.

The authors are grateful to Professors Chris Ruhm and Pankaj Tandon, and to Karen Clark, President of Applied Insurance Research, for helpful comments on an earlier draft.

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Author: | Ellis, Randall P.; Gallup, Cynthia L.; McGuire, Thomas G. |
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Publication: | Journal of Risk and Insurance |

Date: | Mar 1, 1990 |

Words: | 4687 |

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