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The formulae for calculating the sample size required to study the interaction between a continuous exposure and a genetic factor on a continuous outcome variable in the face of measurement error will be of considerable utility in designing studies with appropriate power. These calculations suggest that smaller studies with repeated and more precise measurement of the exposure and outcome will be as powerful as studies even 20 times bigger, which necessarily employ less precise measures because of their size. Even though the cost of genotyping is falling, the magnitude of the effect of measurement error on the power to detect interaction on continuous traits suggests that investment in studies with better measurement may be a more appropriate strategy than attempting to deal with error by increasing sample sizes.
The aim of sensitivity analysis (SA) is to ascertain how much the uncertainty in the output of a model is influenced by the uncertainty in its input factors. An SA can be performed using different methods, which are classified according to various criteria. One possible classification is that in which global and local approaches are identified. This paper strengthens the role of global SA methods and suggests their use in the context of MCDA. Useful applications of global SA already exist in a variety of fields where numerical models are considered, e.g. in economics, engineering and chemistry. Global SA is quite different in its formulation and application from local SA, which is seen more frequently in the literature. The global sensitivity indices adopted are derived from a variance decomposition scheme: they can be estimated by alternative computational strategies, such as the extended FAST or the method proposed by Sobol'. A truly global SA is capable of apportioning the output uncertainty according to any subgroup of input factors. Hence, the output uncertainty of an MCDA can, for instance, be decomposed into a part due to uncertain model inputs and a part due to poorly defined (or variable) weights attached to the criteria. This information could be useful to the decision maker (DM) since it explains synthetically how much the assessment of an MCDA study is biased by the assessor judgements. Alternative regrouping of the uncertain input elements might shed light on other features of the problem addressed by the DM.
The motivation of the present work is to provide an auxiliary tool for the decision-maker (DM) faced with predictive model uncertainty. The tool is especially suited for the allocation of R&D resources. When taking decisions under uncertainties, making use of the output from mathematical or computational models, the DM might be helped if the uncertainty in model predictions be decomposed in a quantitative-rather than qualitativefashion, apportioning uncertainty according to source. This would allow optimal use of resources to reduce the imprecision in the prediction. For complex models, such a decomposition of the uncertainty into constituent elements could be impractical as such, due to the large number of parameters involved. If instead parameters could be grouped into logical subsets, then the analysis could be more useful, also because the decision maker might likely have different perceptions (and degrees of acceptance) for different kinds of uncertainty. For instance, the decomposition in groups could involve one subset of factors for each constituent module of the model; or one set for the weights, and one for the factors in a multicriteria analysis; or phenomenological parameters of the model vs. factors driving the model configuratiodstructure aggregation level, etc.); finally, one might imagine that a partition of the uncertainty could be sought between stochastic (or aleatory) and subjective (or epistemic) uncertainty. The present note shows how to compute rigorous decomposition of the output's variance with grouped parameters, and how this approach may be beneficial for the efficiency and transparency of the analysis.KEY WORDS: Sensitivity analysis; decision making; uncertainty in model predictions.
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