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There are many problems in demography involving the smoothing or interpolation of data. Usually a solution is obtained by fitting a polynomial or a suitable model curve. Often, however, fitting a spline proves to be a simple recourse. Splines, were invented nearly 30 years ago and have been shown to have desirable properties. Although spline functions are by no means unknown to demographers, no simple and direct explanation of their application exists. We hope to remedy this deficiency with this expository piece.

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Advantage was taken of a natural experiment to investigate the relationship of clinic objectives and procedures with retention in methadone maintenance. Assessment, maximum dose, and time in treatment data on 238 patients were summarized using Cox regression. While allowing for patient descriptors and maximum dose of methadone, those subjects assigned to a strongly abstinence-oriented program were 26% (95% C.I., 18 to 33%), 98% (66 to 137%), 213% (132 to 322%), and 393% (224 to 651%) more likely to leave treatment in the first, second, third, fourth 6 months of treatment, respectively, than those subjects assigned to a more laissez-faire program.