The Performance of Risk Adjustment Models in Colombian Competitive Health Insurance Market

We introduce new risk groups to a standard capitation formula and evaluate risk selection incentives of insurers. The study uses a unique data set of almost 24 million affiliates to Government’s mandatory health insurance system. This data set is very rich in the sense of reporting all claims during year 2010, basic demographic variables, initial diagnostic, health services, pharmaceuticals used, etc. It compromises more than 300 million claims. We construct two diagnostic related groups: an adaptation of the 3M algorithm, and a ad hoc diagnostic related group constructed by the authors. Using standard linear capitations formulas we evaluate incentives for cream skimming using several measures. In general, results show a notable improvement in the explanatory power of health expenditures by introducing the ad hoc diagnostic related groups to the standard Colombian risk adjustment formula. With the new risk groups the R2 of the model is 13.53% as opposed to 1.45% of the current formula. Furthermore, for users in the highest expenditure quintile, expected expenditure is 71% of actual expenditure, as opposed to 27% under the current formula. This suggest there is much space for improving the current Colombian capitation formula using information that is currently available.

Multiple choice exams are frequently used as an efficient and objective instrument to evaluate knowledge. Nevertheless, they are more vulnerable to answer-copying than tests based on open questions. Several statistical tests (known as indices) have been proposed to detect cheating but to the best of our knowledge they all lack a mathematical support that guarantees optimality in any sense. This work aims at filling this void by deriving the uniform most powerful (UMP) test assuming the response distribution is known. In practice we must estimate a behavioral model that yields a response distribution for each question. We calculate the empirical type-I and type-II error rates for several indices, that assume different behavioral models, using simulations based on real data from twelve nation wide multiple choice exams taken by 5th and 9th graders in Colombia. We find that the index with the highest power among those studied, subject to the restriction of preserving the type-I error, is the one that uses a nominal response model for item answering, conditions on the answers of the individual suspected of being the source of copy and calculates critical values via a normal approximation. This index was first studied by Wollack (1997) and later by W. Van der Linden and Sotaridona (2006) and is superior to the indices studied and developed by Wesolowsky (2000) and Frary, Tideman, and Watts (1977). Furthermore, we compare the performance of the indices on examination rooms with different levels of proctoring and find that increasing the level of proctoring can reduce copying by as much as 50% and that simple strategies such as having different students answer different portions of the test at different times canal so reduce cheating by over 50%. Finally, a Bonferroni type false discovery rate procedure is used to detect massive cheating. The application is straightforward and we believe it could be use to make entire examination rooms retake an exam under stricter surveillance conditions.