Experience Rating in Medical Professional Liability Insurance: Comment

Abstract

Experience Rating in Medical Professional Liability Insurance: Comment Abstract Hofflander and Nye [3] (HN) attempt to make a case for experience rating of individual physicians for medical liability insurance. This is a timely issue that deserves careful analysis. The authors begin well by obtaining reliable data (something not easy to do in this area) on claim frequencies. Unfortunately, the data set is inadequate for answering the key question--is experience rating worthwhile? The purpose of this comment is to demonstrate this inadequacy and then indicate what needs to be done to resolve the issue. Experience Rating Any experience rating procedure depends on striking a balance between the variability from one physician to the next (the between variance) and the variability of the claims from a single physician (the within variance). If the between variance is small, the physicians are essentially all alike and there is no point in constructing an experience rating system. If the within variance is large then the experience for a specific physician will vary greatly over time and therefore the past will be inadequate for predicting the future. This would also indicate that experience rating is of little value. The second case could arise either because of a high natural variability, in which case the estimats from past data will be unreliable, or because the underlying propensity of the physician to produce claims is varying over time, in which case the future is unlikely to reflect the past. This notion can be represented by the following two state model. Let Xi, be the number of claims for the ith physician. The first stage gives probabilities for Xi given a parameter that reflects the ith physician's propensity for producing claims. It is customary to assume that given these parameters the observations are independent. So we have Pr(Xi = x) = p(x/ i), x = 0, 1,..., i = 1,..., k. The second stage describes how the parameters vary from physician to physician. The multivariate density is f(0/ ) where is a vector of parameters of this second level distribution. It is also customary to assume that 01,...,0k are independent. The two variances are Between: Var[E(X/0)] Within: E[Var(X/0)]. It is well known that the sum of these two quantities is Var(X/ ) the unconditional variance of the observations. The key, then, is to split this variance into its two components. Three Models In this section three models for the claims process will be presented. The first is the one given by HN. It postulates the Poisson distribution with parameter for the first stage (so the parameter 0 is univariate) and the gamma distribution with parameters k and m/k. The two variances are Between: Var[E(X/ )] = Var( ) = m2/k Within: E[Var(X/ )] = E( ) = m. This model would be appropriate if it could be established that individual physicians actually do generate claims according to a homogenous Poisson process and claims from a randomly selected physician follow the negative binomial distribution (for this is the unconditional distribution of X in this model). The second model produces one of the extreme cases from an experience rating viewpoint. Suppose that individual physicians generate claims according to the negative binomial distribution with parameters k and m/(m + k). The mean and variance for this distribution are m and m(m + k)/k. Further assume that all physicians are identical. That is, they all have the same values of m and k. In this case the two variances are Between: Var[E(X/m,k)] = Var(m) = 0 Within: E[Var(X/m,k)] = E[m(m + k)/k] = m(m + k)/k. In this case experience rating is of no value since all physicians are identical. While the hypothesis that all physicians are identical might be hard to defend, the negative binomial model is reasonable if we believe that the physician's propensity to produce claims varies over time. …