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Title: Continuity correction for RSS-structured cluster randomized designs with binary outcomes Authors:  Soohyun Ahn - Ajou University (Korea, South) [presenting]
Xinlei Wang - Southern Methodist University (United States)
Johan Lim - Seoul National University (Korea, South)
Abstract: Correction for continuity is commonly used to improve the inference procedures with binary data in which the interesting event rate is rare or sample size is small. A standard approach of bias reduction in logit estimation is to add a correction factor 0.5 to both event count and non-event count. The correction factor 0.5 is known as a factor rendering the estimation be unbiased up to the order of $O(K^{-1})$, where $K$ samples are observed from simple random sampling (SRS). However, for more general designs beyond SRS, it no longer makes the bias in order of $O(K^{-1})$ be 0 in estimating the logit. We find the formula of the correction factor to make the bias be order of $O(K^{-2})$ for general designs. We then apply it to estimating the logit with the samples from cluster randomized design (CRD) with ranked set sampling (RSS), named as RSS-structured CRD (RSS-CRD). The RSS-structured CRD is a two-stage design which incorporates a cost-efficient ranked set sampling (RSS) into cluster randomized design (CRD) to have more efficient estimation on treatment effect. We propose two versions of the correction factors for the RSS-CRD. We numerically compare the proposed correction methods with the correction factor 0.5 in terms of the bias and mean squared error in estimating the treatment effect. Based on our results, recommendations and suggestions will be made to practitioners about when to use which correction factor.