Controversies concerning randomization and additivity in clinical trials.
Abstract
'As ye randomise so shall ye analyse', is one way of describing Fisher's defence of randomization. Yet, when it comes to clinical trials we nearly always randomize but we rarely analyse the way we randomize and Fisher himself was no exception. Two controversies involving Fisher in the 1930s are discussed: one with Neyman concerning additivity and the other with Student concerning randomization. Their relevance today is considered, as is whether randomization inference in clinical trials is dead and whether modelling rules the day, whether minimization is an acceptable procedure and to what extent trialists confuse experiments with surveys. It will be maintained that a number of different possible purposes of clinical trials have been confused because in the case of the general linear model, under strong additivity, they can all be satisfied by a single analysis. More generally, however, this is not the case.
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Heteroscedasticity may suggest a need to specify further the eligibility criteria or search for an additive scale.
“Otherwise, heteroscedasticity may suggest a need to specify further the eligibility criteria or search for an additive scale 25, 29.”
From Does evidence support the high expectations placed in precision medicine? A bibliographic review (2019) · cites this paper as [25]
Subgroup analyses suggest that significant interventions had an effect on reducing variability.
“Subgroup analyses suggest that significant interventions had an effect on reducing variability ( Supplementary File 1 : Figures S5–S7), a fact which has already been observed in other studies 25, 26.”
From Does evidence support the high expectations placed in precision medicine? A bibliographic review (2019) · cites this paper as [25]
Many clinical trials are not completely randomized.
“A fifth limitation is that many clinical trials are not completely randomized. For example, multicenter trials often use a permuted blocks method. This means that if variances are calculated as if the trial were completely randomized (which is standard practice), the standard simple theory covering the random variation of variances from arm to arm is at best approximately true 25”
From Does evidence support the high expectations placed in precision medicine? A bibliographic review (2019) · cites this paper as [25]
If variances are calculated as if the trial were completely randomized, the standard simple theory covering random variation of variances from arm to arm is at best approximately true.
“A fifth limitation is that many clinical trials are not completely randomized. For example, multicenter trials often use a permuted blocks method. This means that if variances are calculated as if the trial were completely randomized (which is standard practice), the standard simple theory covering the random variation of variances from arm to arm is at best approximately true 25”
From Does evidence support the high expectations placed in precision medicine? A bibliographic review (2019) · cites this paper as [25]
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References 84 · Cited by 132
- Authors
- Senn, S.
- Affiliations
- University College London (GB)
- Corresponding author
- Senn, Stephen
- ORCID
- Senn, Stephen
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2004-12-06
- Volume
- 23
- Issue
- 24
- Pages
- 3729-3753
- ISSN
- 0277-6715 (ISSN-L)
- 1097-0258
- OpenAlex
- W2154727986
- Cited by
- 132
- References
- 84
- Citations by year
- 2026: 2 · 2025: 7 · 2024: 12 · 2023: 7 · 2022: 4 · 2021: 12 · 2020: 2 · 2019: 5 · 2018: 10 · 2017: 4 · 2016: 7 · 2015: 3 · 2014: 7 · 2013: 4 · 2012: 10
- FWCI
- 5.76
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Statistics in Medicine (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- randomization, additivity, clinical trials, fishermen, students, randomization inference, general linear model, minimization, history of statistics
- MeSH terms
- Data Interpretation, Statistical, Female, Humans, Male, Statistics as Topic, Survival Analysis, Randomized Controlled Trials as Topic, History, 20th Century
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