The optimal method to make inferences about a linear combination of proportions
Asymptotic inferences about a linear combination of K independent binomial proportions are very frequent in applied research. Nevertheless, until quite recently research had been focused almost exclusively on cases of K≤2 (particularly on cases of one proportion and
the difference of two proportions). This article focuses on cases of K>2, which have recently begun to receive more attention due to their great practical interest. In order to make this inference, there are several procedures which have not been compared: the score method (S0) and
the method proposed by Martín Andrés et al. (W3) for adjusted Wald (which is a generalization of the method proposed by Price and Bonett) on the one hand and, on the other hand, the method of Zou et al. (N0) based on the Wilson confidence interval (which is a generalization
of the Newcombe method). The article describes a new procedure (P0) based on the classic Peskun method, modifies the previous methods giving them continuity correction (methods S0c, W3c, N0c and P0c, respectively) and, finally, a simulation is made to compare the
eight aforementioned procedures (which are selected from a total of 32 possible methods). The conclusion reached is that the S0c method is the best, although for very small samples (n
i
≤10, ∀ i) the W3 method is better. The P0 method would
be the optimal method if one needs a method which is almost never too liberal, but this entails using a method which is too conservative and which provides excessively wide CIs. The W3 and P0 methods have the additional advantage of being very easy to apply. A free programme which allows the
application of the S0 and S0c methods (which are the most complex) can be obtained at http://www.ugr.es/local/bioest/Z_LINEAR_K.EXE.
Keywords: Peskun method; Wald method; Wilson method; confidence interval; linear combination of proportions; score method
Document Type: Research Article
Affiliations: 1: Department of Biostatistics, Faculty of Medicine,Granada University, 18071,Granada, Spain 2: Department of Biostatistics, Faculty of Medicine,Complutense University, 28040,Madrid, Spain
Publication date: 01 January 2012
- Access Key
- Free content
- Partial Free content
- New content
- Open access content
- Partial Open access content
- Subscribed content
- Partial Subscribed content
- Free trial content