title: Recommendations on multiple testing adjustment in multi-arm trials with a shared control group.
abstract: Multi-arm clinical trials assessing multiple experimental treatments against a shared control group can offer efficiency advantages over independent trials through assessing an increased number of hypotheses. Published opinion is divided on the requirement for multiple testing adjustment to control the family-wise type-I error rate (FWER). The probability of a false positive error in multi-arm trials compared to equivalent independent trials is affected by the correlation between comparisons due to sharing control data. We demonstrate that this correlation in fact leads to a reduction in the FWER, therefore FWER adjustment is not recommended solely due to sharing control data. In contrast, the correlation increases the probability of multiple false positive outcomes across the hypotheses, although standard FWER adjustment methods do not control for this. A stringent critical value adjustment is proposed to maintain equivalent evidence of superiority in two correlated comparisons to that obtained within independent trials. FWER adjustment is only required if there is an increased chance of making a single claim of effectiveness by testing multiple hypotheses, not due to sharing control data. For competing experimental therapies, the correlation between comparisons can be advantageous as it eliminates bias due to the experimental therapies being compared to different control populations.
authors.affiliation: 1 Leeds Institute of Clinical Trials Research, University of Leeds, Leeds, UK.
authors.forename: Dena R
authors.initials: DR
authors.lastname: Howard
authors.affiliation: 1 Leeds Institute of Clinical Trials Research, University of Leeds, Leeds, UK.
authors.forename: Julia M
authors.initials: JM
authors.lastname: Brown
authors.affiliation: 2 Department of Mathematics and Statistics, University of Reading, Reading, UK.
authors.forename: Susan
authors.initials: S
authors.lastname: Todd
authors.affiliation: 1 Leeds Institute of Clinical Trials Research, University of Leeds, Leeds, UK.
authors.forename: Walter M
authors.initials: WM
authors.lastname: Gregory
mesh_terms: D000911:Antibodies, Monoclonal / Q000627:therapeutic use; D061067:Antibodies, Monoclonal, Humanized; D000970:Antineoplastic Agents / Q000627:therapeutic use; D015179:Colorectal Neoplasms / Q000188:drug therapy; D035061:Control Groups; D003627:Data Interpretation, Statistical; D003879:Dermatologic Agents / Q000627:therapeutic use; D006801:Humans; D009101:Multiple Myeloma / Q000188:drug therapy; D011336:Probability; D011565:Psoriasis / Q000188:drug therapy; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D016019:Survival Analysis; D016896:Treatment Outcome
chemical_list: D000911:Antibodies, Monoclonal; D061067:Antibodies, Monoclonal, Humanized; D000970:Antineoplastic Agents; D003879:Dermatologic Agents; C571216:brodalumab
keywords: Multiple testing; alpha adjustment; correlated comparisons; family-wise error rate; multi-arm clinical trial; multiplicity; shared control group; type-I error