Optimal allocations for two treatment comparisons within the proportional odds cumulative logits model
This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance i...
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| Published in | PloS one Vol. 16; no. 4; p. e0250119 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
United States
Public Library of Science
21.04.2021
Public Library of Science (PLoS) |
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| Online Access | Get full text |
| ISSN | 1932-6203 1932-6203 |
| DOI | 10.1371/journal.pone.0250119 |
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| Abstract | This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance is minimal for a given total sample size or a given budget, meaning that the power for the test on treatment effect is maximal, or it is sought so that a required power level is achieved at a minimal total sample size or budget. Results are presented for three, five and seven ordered response categories, three treatment effect sizes and a skewed, bell-shaped or polarized distribution of the response probabilities. The optimal proportion subjects in the intervention condition decreases with the number of response categories and the costs for the intervention relative to those for the control. The relation between the optimal proportion and effect size depends on the distribution of the response probabilities. The widely used balanced design is not always the most efficient; its efficiency as compared to the optimal design decreases with increasing cost ratio. The optimal design is highly robust to misspecification of the response probabilities and treatment effect size. The optimal design methodology is illustrated using two pharmaceutical examples. A Shiny app is available to find the optimal treatment allocation, to evaluate the efficiency of the balanced design and to study the relation between budget or sample size and power. |
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| AbstractList | This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance is minimal for a given total sample size or a given budget, meaning that the power for the test on treatment effect is maximal, or it is sought so that a required power level is achieved at a minimal total sample size or budget. Results are presented for three, five and seven ordered response categories, three treatment effect sizes and a skewed, bell-shaped or polarized distribution of the response probabilities. The optimal proportion subjects in the intervention condition decreases with the number of response categories and the costs for the intervention relative to those for the control. The relation between the optimal proportion and effect size depends on the distribution of the response probabilities. The widely used balanced design is not always the most efficient; its efficiency as compared to the optimal design decreases with increasing cost ratio. The optimal design is highly robust to misspecification of the response probabilities and treatment effect size. The optimal design methodology is illustrated using two pharmaceutical examples. A Shiny app is available to find the optimal treatment allocation, to evaluate the efficiency of the balanced design and to study the relation between budget or sample size and power. About the Authors: Mirjam Moerbeek Roles Conceptualization, Formal analysis, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing * E-mail: m.moerbeek@uu.nl Affiliation: Department of Methodology and Statistics, Utrecht University, Utrecht, The Netherlands ORCID logo https://orcid.org/0000-0001-5537-1237 Introduction The randomized controlled trial is considered the gold standard for the comparison of multiple treatment conditions [1,2]. The effects of the number of categories, response probabilities across categories, treatment effect size and costs on the optimal allocation are explored. [...]the proportional odds model is a more parsimonious model than the non-proportional odds model, especially so when the number of categories is large. The costs of enrolling, treating and measuring subjects may not exceed some pre-defined budget B. This constraint is formulated as cCnC+cInI≤B, where nC and nI are the number of subjects in the control and intervention condition and cC and cI are the costs per subject in these two treatments. This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance is minimal for a given total sample size or a given budget, meaning that the power for the test on treatment effect is maximal, or it is sought so that a required power level is achieved at a minimal total sample size or budget. Results are presented for three, five and seven ordered response categories, three treatment effect sizes and a skewed, bell-shaped or polarized distribution of the response probabilities. The optimal proportion subjects in the intervention condition decreases with the number of response categories and the costs for the intervention relative to those for the control. The relation between the optimal proportion and effect size depends on the distribution of the response probabilities. The widely used balanced design is not always the most efficient; its efficiency as compared to the optimal design decreases with increasing cost ratio. The optimal design is highly robust to misspecification of the response probabilities and treatment effect size. The optimal design methodology is illustrated using two pharmaceutical examples. A Shiny app is available to find the optimal treatment allocation, to evaluate the efficiency of the balanced design and to study the relation between budget or sample size and power.This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance is minimal for a given total sample size or a given budget, meaning that the power for the test on treatment effect is maximal, or it is sought so that a required power level is achieved at a minimal total sample size or budget. Results are presented for three, five and seven ordered response categories, three treatment effect sizes and a skewed, bell-shaped or polarized distribution of the response probabilities. The optimal proportion subjects in the intervention condition decreases with the number of response categories and the costs for the intervention relative to those for the control. The relation between the optimal proportion and effect size depends on the distribution of the response probabilities. The widely used balanced design is not always the most efficient; its efficiency as compared to the optimal design decreases with increasing cost ratio. The optimal design is highly robust to misspecification of the response probabilities and treatment effect size. The optimal design methodology is illustrated using two pharmaceutical examples. A Shiny app is available to find the optimal treatment allocation, to evaluate the efficiency of the balanced design and to study the relation between budget or sample size and power. About the Authors: Mirjam Moerbeek Roles Conceptualization, Formal analysis, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing * E-mail: m.moerbeek@uu.nl Affiliation: Department of Methodology and Statistics, Utrecht University, Utrecht, The Netherlands ORCID logo https://orcid.org/0000-0001-5537-1237 Introduction The randomized controlled trial is considered the gold standard for the comparison of multiple treatment conditions [1,2]. The effects of the number of categories, response probabilities across categories, treatment effect size and costs on the optimal allocation are explored. [...]the proportional odds model is a more parsimonious model than the non-proportional odds model, especially so when the number of categories is large. The costs of enrolling, treating and measuring subjects may not exceed some pre-defined budget B. This constraint is formulated as cCnC+cInI≤B, where nC and nI are the number of subjects in the control and intervention condition and cC and cI are the costs per subject in these two treatments. |
| Audience | Academic |
| Author | Moerbeek, Mirjam |
| AuthorAffiliation | Roswell Park Cancer Institute, UNITED STATES Department of Methodology and Statistics, Utrecht University, Utrecht, The Netherlands |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33882086$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1016_j_ajcnut_2023_02_013 crossref_primary_10_1371_journal_pone_0283382 |
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| Copyright | COPYRIGHT 2021 Public Library of Science 2021 Mirjam Moerbeek. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2021 Mirjam Moerbeek 2021 Mirjam Moerbeek |
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| Snippet | This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative... About the Authors: Mirjam Moerbeek Roles Conceptualization, Formal analysis, Methodology, Software, Visualization, Writing – original draft, Writing – review &... |
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| SubjectTerms | Allocations Categories Comparative analysis Cost allocation Costs Design optimization Drafting software Logits Medicine and Health Sciences Physical Sciences Research and Analysis Methods Statistical analysis Survival analysis |
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| Title | Optimal allocations for two treatment comparisons within the proportional odds cumulative logits model |
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