While experimental designs are regarded as the gold standard for establishing causal relationships, such designs are usually impractical owing to common methodological limitations. The objective of this article is to illustrate how propensity score matching (PSM) and using propensity scores (PS) as a covariate are viable alternatives to reduce estimation error when experimental designs cannot be implemented. To mimic common pediatric research practices, data from 140 simulated participants were used to resemble an experimental and nonexperimental design that assessed the effect of treatment status on participant weight loss for diabetes. Pretreatment participant characteristics (age, gender, physical activity, etc.) were then used to generate PS for use in the various statistical approaches. Results demonstrate how PSM and using the PS as a covariate can be used to reduce estimation error and improve statistical inferences. References for issues related to the implementation of these procedures are provided to assist researchers.

Tiao and Lund [The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. J Amer Statist Assoc. 1970;65(329):370-386] tabulated the coefficients of the best linear unbiased estimators (BLUEs) of location and scale for a particular family of symmetric distributions. This family was a reparameterization of the extended exponential power distribution (EEPD) with the shape parameter restricted to be greater than or equal to one. In this work, we consider the BLU estimation of the location and scale parameters of the EEPD when the shape parameter is one-third and one-half. We obtain closed-form expressions for the single and product moments of the order statistics when the shape parameter is in general in the form of a reciprocal of an integer. These expressions are then used to determine the BLUEs and the corresponding variances for complete samples of size 20 and less. We consider some other linear estimators of the location and scale parameters and then compare them with the BLUEs. Finally, we present a numerical example to illustrate the developed results.

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