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Unbalanced 2 x 2 factorial designs and the interaction effect: a troublesome combination.

ABSTRACT: In this power study, ANOVAs of unbalanced and balanced 2 x 2 datasets are compared (N = 120). Datasets are created under the assumption that H1 of the effects is true. The effects are constructed in two ways, assuming: 1. contributions to the effects solely in the treatment groups; 2. contrasting contributions in treatment and control groups. The main question is whether the two ANOVA correction methods for imbalance (applying Sums of Squares Type II or III; SS II or SS III) offer satisfactory power in the presence of an interaction. Overall, SS II showed higher power, but results varied strongly. When compared to a balanced dataset, for some unbalanced datasets the rejection rate of H0 of main effects was undesirably higher. SS III showed consistently somewhat lower power. When the effects were constructed with equal contributions from control and treatment groups, the interaction could be re-estimated satisfactorily. When an interaction was present, SS III led consistently to somewhat lower rejection rates of H0 of main effects, compared to the rejection rates found in equivalent balanced datasets, while SS II produced strongly varying results. In data constructed with only effects in the treatment groups and no effects in the control groups, the H0 of moderate and strong interaction effects was often not rejected and SS II seemed applicable. Even then, SS III provided slightly better results when a true interaction was present. ANOVA allowed not always for a satisfactory re-estimation of the unique interaction effect. Yet, SS II worked better only when an interaction effect could be excluded, whereas SS III results were just marginally worse in that case. Overall, SS III provided consistently 1 to 5% lower rejection rates of H0 in comparison with analyses of balanced datasets, while results of SS II varied too widely for general application.

SUBMITTER: Landsheer JA

PROVIDER: S-EPMC4373880 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Unbalanced 2 x 2 factorial designs and the interaction effect: a troublesome combination.

Landsheer Johannes A JA van den Wittenboer Godfried G

PloS one 20150325 3

In this power study, ANOVAs of unbalanced and balanced 2 x 2 datasets are compared (N = 120). Datasets are created under the assumption that H1 of the effects is true. The effects are constructed in two ways, assuming: 1. contributions to the effects solely in the treatment groups; 2. contrasting contributions in treatment and control groups. The main question is whether the two ANOVA correction methods for imbalance (applying Sums of Squares Type II or III; SS II or SS III) offer satisfactory p ...[more]

PMID: 25807514

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Project description:BackgroundA 2×2 factorial design evaluates two interventions (A versus control and B versus control) by randomising to control, A-only, B-only or both A and B together. Extended factorial designs are also possible (e.g. 3×3 or 2×2×2). Factorial designs often require fewer resources and participants than alternative randomised controlled trials, but they are not widely used. We identified several issues that investigators considering this design need to address, before they use it in a late-phase setting.MethodsWe surveyed journal articles published in 2000-2022 relating to designing factorial randomised controlled trials. We identified issues to consider based on these and our personal experiences.ResultsWe identified clinical, practical, statistical and external issues that make factorial randomised controlled trials more desirable. Clinical issues are (1) interventions can be easily co-administered; (2) risk of safety issues from co-administration above individual risks of the separate interventions is low; (3) safety or efficacy data are wanted on the combination intervention; (4) potential for interaction (e.g. effect of A differing when B administered) is low; (5) it is important to compare interventions with other interventions balanced, rather than allowing randomised interventions to affect the choice of other interventions; (6) eligibility criteria for different interventions are similar. Practical issues are (7) recruitment is not harmed by testing many interventions; (8) each intervention and associated toxicities is unlikely to reduce either adherence to the other intervention or overall follow-up; (9) blinding is easy to implement or not required. Statistical issues are (10) a suitable scale of analysis can be identified; (11) adjustment for multiplicity is not required; (12) early stopping for efficacy or lack of benefit can be done effectively. External issues are (13) adequate funding is available and (14) the trial is not intended for licensing purposes. An overarching issue (15) is that factorial design should give a lower sample size requirement than alternative designs. Across designs with varying non-adherence, retention, intervention effects and interaction effects, 2×2 factorial designs require lower sample size than a three-arm alternative when one intervention effect is reduced by no more than 24%-48% in the presence of the other intervention compared with in the absence of the other intervention.ConclusionsFactorial designs are not widely used and should be considered more often using our issues to consider. Low potential for at most small to modest interaction is key, for example, where the interventions have different mechanisms of action or target different aspects of the disease being studied.

Project description:BackgroundIn certain diseases clinical experts may judge that the intervention with the best prospects is the addition of two treatments to the standard of care. This can either be tested with a simple randomized trial of combination versus standard treatment or with a 2 x 2 factorial design.MethodsWe compared the two approaches using the design of a new trial in tuberculous meningitis as an example. In that trial the combination of 2 drugs added to standard treatment is assumed to reduce the hazard of death by 30% and the sample size of the combination trial to achieve 80% power is 750 patients. We calculated the power of corresponding factorial designs with one- to sixteen-fold the sample size of the combination trial depending on the contribution of each individual drug to the combination treatment effect and the strength of an interaction between the two.ResultsIn the absence of an interaction, an eight-fold increase in sample size for the factorial design as compared to the combination trial is required to get 80% power to jointly detect effects of both drugs if the contribution of the less potent treatment to the total effect is at least 35%. An eight-fold sample size increase also provides a power of 76% to detect a qualitative interaction at the one-sided 10% significance level if the individual effects of both drugs are equal. Factorial designs with a lower sample size have a high chance to be underpowered, to show significance of only one drug even if both are equally effective, and to miss important interactions.ConclusionsPragmatic combination trials of multiple interventions versus standard therapy are valuable in diseases with a limited patient pool if all interventions test the same treatment concept, it is considered likely that either both or none of the individual interventions are effective, and only moderate drug interactions are suspected. An adequately powered 2 x 2 factorial design to detect effects of individual drugs would require at least 8-fold the sample size of the combination trial.Trial registrationCurrent Controlled Trials ISRCTN61649292.

Project description:Key messageWe validated the efficiency of genomic predictions calibrated on sparse factorial training sets to predict the next generation of hybrids and tested different strategies for updating predictions along generations. Genomic selection offers new prospects for revisiting hybrid breeding schemes by replacing extensive phenotyping of individuals with genomic predictions. Finding the ideal design for training genomic prediction models is still an open question. Previous studies have shown promising predictive abilities using sparse factorial instead of tester-based training sets to predict single-cross hybrids from the same generation. This study aims to further investigate the use of factorials and their optimization to predict line general combining abilities (GCAs) and hybrid values across breeding cycles. It relies on two breeding cycles of a maize reciprocal genomic selection scheme involving multiparental connected reciprocal populations from flint and dent complementary heterotic groups selected for silage performances. Selection based on genomic predictions trained on a factorial design resulted in a significant genetic gain for dry matter yield in the new generation. Results confirmed the efficiency of sparse factorial training sets to predict candidate line GCAs and hybrid values across breeding cycles. Compared to a previous study based on the first generation, the advantage of factorial over tester training sets appeared lower across generations. Updating factorial training sets by adding single-cross hybrids between selected lines from the previous generation or a random subset of hybrids from the new generation both improved predictive abilities. The CDmean criterion helped determine the set of single-crosses to phenotype to update the training set efficiently. Our results validated the efficiency of sparse factorial designs for calibrating hybrid genomic prediction experimentally and showed the benefit of updating it along generations.

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Unbalanced 2 x 2 factorial designs and the interaction effect: a troublesome combination.

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Unbalanced 2 x 2 factorial designs and the interaction effect: a troublesome combination.

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