A cautionary note on the analysis of randomized block designs with a few missing values |
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Authors: | Devan V Mehrotra |
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Institution: | (1) Merck Research Labs., UM-A102, 785 Jolly Rd., Bldg. C, 19422 Blue Bell, PA, USA |
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Abstract: | The randomized block design is routinely employed in the social and biopharmaceutical sciences. With no missing values, analysis
of variance (AOV) can be used to analyze such experiments. However, if some data are missing, the AOV formulae are no longer
applicable, and iterative methods such as restricted maximum likelihood (REML) are recommended, assuming block effects are
treated as random. Despite the well-known advantages of REML, methods like AOV based on complete cases (blocks) only (CC-AOV)
continue to be used by researchers, particularly in situations where routinely only a few missing values are encountered.
Reasons for this appear to include a natural proclivity for non-iterative, summary-statistic-based methods, and a presumption
that CC-AOV is only trivially less efficient than REML with only a few missing values (say≤10%). The purpose of this note
is two-fold. First, to caution that CC-AOV can be considerably less powerful than REML even with only a few missing values.
Second, to offer a summary-statistic-based, pairwise-available-case-estimation (PACE) alternative to CC-AOV. PACE, which is
identical to AOV (and REML) with no missing values, outperforms CC-AOV in terms of statistical power. However, it is recommended
in lieu of REMLonly if software to implement the latter is unavailable, or the use of a “transparent” formula-based approach is deemed necessary.
An example using real data is provided for illustration. |
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Keywords: | analysis of variance linear mixed model restricted maximum likelihood Satterthwaite approximation |
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