A Case Study of Using Finite Difference Approximation Methods for SUDAAN Statistical Software

Finite difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. SUDAAN, an internationally recognized statistical software created and marketed by RTI International [1], uses finite difference methods to estimate design-based variances that cannot be directly computed. SUDAAN is a single program comprising a family of nine analytic and two pre-analytic procedures. The analytic procedures include model-based procedures and descriptive procedures. The descriptive procedures compute the statistics using exact methods. Over the years, however, there have been requests from SUDAAN customers asking for the ability to compute design-based variances for user-defined functions. The user-defined function is not limited to include just a single statistic; rather, the user-defined function can include any statistics expressed as a function of means, totals, proportions, ratios, population variances, population standard deviations, and correlations. The design-based variance cannot be obtained using exact methods. This paper presents a case study that focuses on the way the finite difference approximation methods work for computing the design-based variances. A newly developed SUDAAN descriptive procedure, VARGEN, will provide examples.