PubMed · 12041235
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Indiana. Supreme Court. 1988-08-24. Doe v. Smith.. https://pubmed.ncbi.nlm.nih.gov/12041235/
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When the number of potential controls is large relative to the number of available cases, or when little effort needs to be expended in collecting the relevant information on the controls, we often apply multiple matching to attain the validity or increase the efficiency of our inference in epidemiological studies. In this paper, we focus interval estimation on the difference in proportions for m-to-one matching. We consider four asymptotic interval estimators, including the estimator directly using the Mantel-Haenszel (MH) point estimator, the estimator using the tanh(-1)(x) transformation, the estimator derived from the Cochran-Mantel-Haenszel (CMH) test statistic, and the estimator derived from the quadratic inequality developed in this paper. To evaluate and compare the performance of these estimators, we employ Monte Carlo simulation. We find that the estimator directly using the MH estimator can have the coverage probability less than the desired confidence level when the number of matched sets is small. We note that the estimator derived from the quadratic inequality can perform well when the underlying difference is close to 0 even for a small number of matched sets. However, this estimator tends to have the coverage probability less than the desired confidence level as well when the underlying difference in proportions is large. By contrast, the estimator using the CMH statistic tends to have the coverage probability larger than the desired confidence level when the underlying difference is small. We also find that the estimator using the tanh(-1)(x) transformation consistently outperforms the interval estimator directly using the MH estimator. We use the data regarding the association between induced abortions and ectopic pregnancy to illustrate the use of these estimators.
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AIM: To estimate national rates of induced abortion in Australia from 1985 to 2003, using Medicare claim statistics for private patients and hospital morbidity statistics for public patients. DESIGN AND SETTING: Estimates were based on Australian and South Australian data collections relating to abortions. SA hospital morbidity statistics were compared with SA statutory notifications of abortions to estimate the accuracy of these collections. Medicare statistics on abortion procedures performed on private patients in South Australia were then compared with hospital morbidity statistics for private patients. National statistics on abortion derived from Medicare and hospital morbidity statistics were adjusted for inaccuracies found in these sources. MAIN OUTCOME MEASURES: Numbers of induced abortions in Australia for each year from 1985 to 2003; abortion rates per 1000 women aged 15-44 years. RESULTS: Abortion numbers based on Medicare claims by private patients overestimated by 18.7% the number of abortions derived from statutory notifications in South Australia during the period 1988-89 to 1999-00. Hospital morbidity data using principal diagnosis codes relating to medical abortion overestimated statutory notifications by 2.3% (mainly because of readmissions). National statistics were adjusted for these overestimations and for the estimated 14.1% of private patients who would not have submitted Medicare claims (based on surveys of private-clinic patients in New South Wales and Victoria). The estimated Australian abortion rate increased from 17.9 per 1000 women aged 15-44 in 1985 to a peak of 21.9/1000 in 1995, then declined to 19.7/1000 in 2003 (estimated number of abortions, 84,460). CONCLUSION: There are no data currently available for deriving accurate numbers of induced abortions in Australia. Suggestions are made for collection of national statistics.