Abstract
Cost-effectiveness—increasing the benefit obtained for a given expenditure of time or money—is an important idea in many applied research fields. It is one important quality that a researcher interested in the multiphase optimization strategy (MOST) may wish to optimize. However, further research is needed about how to best incorporate cost information into the analysis of factorial experiments typically used during the optimization phase of MOST. This chapter will review the issues involved in making cost-effectiveness judgments using the results of factorial experiments and explore some possibilities for further methodological research on how best to estimate and compare cost-effectiveness using the results of factorial experiments.
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- 1.
Weight loss is actually a change score (value after minus value before). Change scores are not the only way to measure change from baseline. It has been argued that it is more statistically efficient to model posttreatment outcome adjusted for pretreatment status as a covariate, rather than using change scores directly (see, e.g., Vickers, 2001; Vickers & Altman, 2001). However, weight loss in kilograms is the simplest choice here and therefore the best choice for illustrative purposes.
- 2.
This chapter will use the term “dominate” in a somewhat informal way. The economics literature sometimes distinguishes between strong and weak dominance. Option A is said to strongly dominate Option B if A is both less costly and more effective. Option A is sometimes said to weakly dominate Option B if A is either equally costly but more effective or less costly but equally effective. This is not a large distinction for our purposes, first because it is unlikely that two treatments would have exactly the same cost or exactly the same benefit (Drummond et al., 2005) and second because it does not necessarily change the implied decision. The term weak dominance is also sometimes used when Option A delivers more effectiveness per unit cost than Option B (Gift et al., 2003). However, this kind of “dominance” does not necessarily imply that Option A is better in every sense, as Option B might still have less total cost or more total effectiveness. Therefore, the sense of the term “dominance” in this chapter is essentially that of strong dominance.
- 3.
In practice the farm or factory owner might use a weight other than one; for example, they might discount (proportionally reduce) E, in order to reflect time delay in production and uncertainties in sales (see Harrington, 1981; Petrou & Gray, 2011). However, the basic intuition still applies: convert a gross gain to a net gain by subtracting off some measure of cost. This kind of discounting of future predictions can also be done in cost-benefit analysis in promoting human health. The discounted benefits minus discounted cost (essentially, E-λC) is therefore called the “net present value” of an intervention (see Messonier & Meltzer, 2003). In the weight loss example, if a particular λ is used to convert kilogram units into money units, and the decision-maker is trying to find out how much money to spend on weight loss versus other priorities, then cost-benefit analysis is being done, rather than cost-effectiveness analysis. The focus of this chapter is on cost-effectiveness rather than cost-benefit analysis, so the question of how to choose λ is beyond the scope of this chapter.
- 4.
One alternative could be to consider two conditions at a time and compute a confidence interval for the ICER, or for the cost-effectiveness acceptability curve at a given λ, for each of these pairwise comparisons. Another alternative would be to designate a control condition and compare every other condition with that one only. Furthermore, if one is using a Bayesian approach with posterior probabilities, one could calculate, for each candidate intervention, either its posterior probability of being having the best utility measure λE-C among the conditions available, or its posterior probability of having a utility measure above some threshold.
- 5.
As a caveat, if it were known in advance that only three of the four conditions were of interest, then an incomplete factorial comparing only those three conditions might be more appropriate than a complete 2 × 2 factorial (see Collins et al., 2009 for advantages and disadvantages of incomplete designs). However, if, say, only four out of six components could affordably be implemented at a time in practice, there are still many affordable conditions, so a complete or fractional factorial experiment might still be appropriate. As another caveat, the challenge of creating special programs for resource-poor settings has raised important debates about equity and disparities which are beyond the scope of this chapter; for example, consider the criticism by Kozol (2005) and defense in Slavin (2006) of the use of a particular program for disadvantaged schools.
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Acknowledgment
The author thanks Dr. Linda Collins, Dr. Inbal Nahum-Shani, Dr. Daniel Max Crowley, and Dr. Kari Kugler for helpful discussions and comments on previous versions of this chapter and Amanda Applegate for proofreading assistance. Graphics were created using the R software package (https://www.r-project.org/).
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Dziak, J.J. (2018). Optimizing the Cost-Effectiveness of a Multicomponent Intervention Using Data from a Factorial Experiment: Considerations, Open Questions, and Tradeoffs Among Multiple Outcomes. In: Collins, L., Kugler, K. (eds) Optimization of Behavioral, Biobehavioral, and Biomedical Interventions. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-91776-4_7
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