Medicaid case management: Kentucky's patient access and care program - Medicare and Medicaid Managed Care: Issues and Evidence

Health Care Financing Review,  Fall, 1993  by Mark E. Miller,  Daniel J. Gengler

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TECHNICAL NOTE

There are two estimation problems that models of this kind can encounter: multicollinearity and autocorrelation. Both are problems of efficiency, rather than bias, in the parameter estimates.

Multicollinearity was diagnosed using a condition index (Belsey, Kuh, and Welsch, 1980). Condition index values of 10 indicate moderate multicollinearity, values of 30 indicate strong multicollinearity, and values above 30 indicate severe multicollinearity. When condition index values did not exceed 9.44 in our models, we determined the degree of multicollinearity to be minor. Even if multicollinearity were present, it is likely that the standard errors are inflated. Highly inflated standard errors reduce t-values, which has the effect of rendering statistically insignificant results (i.e., Type 11 errors). All statistically significant results in this article are at the 99-percent confidence level.

Time-series models can encounter autocorrelation problems. The effect of its presence on the estimated standard errors depends on the direction of autocorrelation. Durbin-Watson tests were run on all models. Only two models (that for outpatient services in Table 2 [DW = 2.63], and that for physician services in Table 3 [DW = 2.64]) clearly exhibited autocorrelation. In both instances, the direction of autocorrelation was negative, which tends to inflate standard errors. These models were re-estimated by deriving the value of rho from the Durbin-Watson statistic and using it in a generalized difference equation (Gujarti, 1988).

This correction reduced the standard errors making the post-KenPAC parameter estimates significant at the 99-percent confidence level rather than the 95-percent confidence level.

ACKNOWLEDGMENTS

We would like to acknowledge the excellent research assistance of Maria Perozek and to thank Janie Miller and Mark Birdwhistell of the Kentucky Department for Medicaid Services for their patient and thorough explanations of the KenPAC program.

(1) Two other points are worth noting. Hurley, Freund, and Taylor, and Freund et al. both depend on non-enrollee comparison groups from different sites. Non-equivalent comparison groups raise the possibility of comparing two systematically different populations, although we hasten to point out that both studies employ controls for population differences expected to affect use. Nonetheless, there can be differences in supply or market characteristics (e.g., beds per capita; physicians per capita) that influence utilization. (2) A counterargument is that requiring Medicaid enrollees to choose a primary provider results in establishing new patient-provider relationships, which, in turn, results in a shortrun increase in diagnostic services. Holahan, Bell, and Adler (1987) find only weak support for increased use of diagnostic services during program enrollment and startup. However, our analysis found statistically significant reductions in outpatient and laboratory utilization during the enrollment period. No significant changes in utilization of inpatient, physician, and drug services were found during the enrollment period. (3) Exponential smoothing techniques are sensitive to two fundamental assumptions: the time trend (constant, linear, or quadratic), which models the long-term underlying trend of the time series, and the smoothing weight, which determines how short-term fluctuations are estimated. Obviously, the assumption made regarding the underlying trend is important. However, even relatively minor changes in the smoothing parameter can produce marked differences in expected utilization (and estimated cost effectiveness). The time trend and smoothing assumptions are not explicit in the report, and evaluative statistics (e.g., relative mean standard percentage error assessing the accuracy of the models are not provided.