Testing for Qualitative Interactions between Treatment Effects and Patient Subsets
Abstract
Evaluation of evidence that treatment efficacy varies substantially among different subsets of patients is an important feature of the analysis of large clinical trials. Qualitative or crossover interactions are said to occur when one treatment is superior for some subsets of patients and the alternative treatment is superior for other subsets. A non-crossover interaction arises when there is variation in the magnitude, but not in the direction, of treatment effects among subsets. Some authors use the term quantitative interaction to mean non-crossover interaction. Non-crossover interactions are usually of less clinical importance than qualitative interactions, which often have major therapeutic significance. A likelihood ratio test is developed to test for qualitative interactions. Exact critical values are determined and tabulated.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the 14-study set shifting meta-analysis, the test for qualitative interaction produces a statistically non-significant test statistic Q*=2.56, compared with a critical value of 14.15 for a significance level of 5%.
“Correspondingly, the test for qualitative interaction (9) produces a statistically non-significant test statistic Q*=2.56, compared with a critical value of 14.15 for a significance level of 5% (Gail and Simon, 1985).”
From A Re-Evaluation of Random-Effects Meta-Analysis (2009) · cites this paper as Gail and Simon, 1985
Cites
Regression Models and Life-Tables
Cox, D. R. (1992) · Springer Series in Statistics · doi:10.1007/978-1-4612-4380-9_37 · Cited by 26,297 · see citing works
Peto, R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J., & Smith, P. G. (1977) · British Journal of Cancer · doi:10.1038/bjc.1977.1 · Cited by 8,285 · see citing works
Inequalities: Theory of Majorization and its Applications.
Arnold, B. C., Marshall, A. W., & Olkin, I. (1981) · Journal of the American Statistical Association · doi:10.2307/2287859 · Cited by 4,989 · see citing works
A multivariate analogue of the one-sided test
Kudô, A. (1963) · Biometrika · doi:10.1093/biomet/50.3-4.403 · Cited by 359 · see citing works
Childhood Non-Hodgkin's Lymphoma
Anderson, J. R., Wilson, J. F., Jenkin, R. D. T., et al. (1983) · New England Journal of Medicine · doi:10.1056/nejm198303103081003 · Cited by 327 · see citing works
Fisher, B., Redmond, C. K., Brown, A., Wickerham, D. L., Wolmark, N., Allegra, J. C., Escher, G. C., Lippman, M. E., Savlov, E. D., & Wittliff, J. L. (1983) · Journal of Clinical Oncology · doi:10.1200/jco.1983.1.4.227 · Cited by 260 · see citing works
Lee, K. L., McNeer, J. F., Starmer, C. F., et al. (1980) · Circulation · doi:10.1161/01.cir.61.3.508 · Cited by 153 · see citing works
Patient subsets and variation in therapeutic efficacy.
Simon, R. M. (1982) · British Journal of Clinical Pharmacology · doi:10.1111/j.1365-2125.1982.tb02015.x · Cited by 130 · see citing works
Self-citationMajorization in Multivariate Distributions
Marshall, A. W., & Olkin, I. (1974) · The Annals of Statistics · doi:10.1214/aos/1176342873 · Cited by 124 · see citing works
Selecting optimal treatment in clinical trials using covariate information
Byar, D. P., & Corle, D. K. (1977) · Journal of Chronic Diseases · doi:10.1016/0021-9681(77)90037-6 · Cited by 89 · see citing works
Two New Tests Associated with Analysis of Variance
Azzalini, A., & Cox, D. R. (1984) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1984.tb01306.x · Cited by 79 · see citing works
Interaction between prognostic factors and treatment
Shuster, J. J., & van Eys, J. (1983) · Controlled Clinical Trials · doi:10.1016/s0197-2456(83)80026-9 · Cited by 51 · see citing works
Quadratic programming for nonlinear regression
Shrager, R. I. (1972) · Communications of the ACM · doi:10.1145/361237.361248 · Cited by 29 · see citing works
Clinical judgment and statistics.
Detre, K. M., Peduzzi, P. N., & Chan, Y.-K. (1981) · Circulation · doi:10.1161/01.cir.63.1.239 · Cited by 22 · see citing works
Patient heterogeneity in clinical trials.
Simon, R. M. (1980) · PubMed · Cited by 21 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Alirocumab and Cardiovascular Outcomes after Acute Coronary Syndrome
Schwartz, G. G., Steg, P. G., Szarek, M., Bhatt, D. L., Bittner, V. A., Diaz, R., Edelberg, J. M., Goodman, S. G., Hanotin, C., Harrington, R. A., et al. (2018) · New England Journal of Medicine · doi:10.1056/nejmoa1801174 · Cited by 3,634 · see citing works
Amado, R. G., Wolf, M., Peeters, M., Van Cutsem, E., Siena, S., Freeman, D. J., Juan, T., Sikorski, R., Suggs, S., Radinsky, R., et al. (2008) · Journal of Clinical Oncology · doi:10.1200/jco.2007.14.7116 · Cited by 3,207 · see citing works
FOLFIRINOX or Gemcitabine as Adjuvant Therapy for Pancreatic Cancer
Conroy, T., Hammel, P., Hebbar, M., Ben Abdelghani, M., Wei, A. C., Raoul, J.-L., Choné, L., Francois, E., Artru, P., Biagi, J. J., et al. (2018) · New England Journal of Medicine · doi:10.1056/nejmoa1809775 · Cited by 2,874 · see citing works
Overall Survival with Osimertinib in Untreated, <i>EGFR</i> -Mutated Advanced NSCLC
Ramalingam, S. S., Vansteenkiste, J., Planchard, D., Cho, B. C., Gray, J. E., Ohe, Y., Zhou, C., Reungwetwattana, T., Cheng, Y., Chewaskulyong, B., et al. (2020) · New England Journal of Medicine · doi:10.1056/nejmoa1913662 · Cited by 2,914 · see citing works
A Re-Evaluation of Random-Effects Meta-Analysis
Higgins, J. P. T., Thompson, S. G., & Spiegelhalter, D. J. (2009) · Journal of the Royal Statistical Society Series A: Statistics in Society · doi:10.1111/j.1467-985x.2008.00552.x · Cited by 2,569 · see citing works
“…been developed (Gail and Simon, 1985; Piantadosi and Gail, 1993; Pan and Wolfe, 1997), addressing a null hypothesis: H0 :{θi < 0 ∀i} or {θi > 0 ∀i}: Gail and Simon (1985) described the use of a test statistic QÅ =min{∑ θ̂2i σ̂−2i I+i , ∑ θ̂2i σ̂−2i I−i }, .9/ where I+i =1 if θ̂i >0 and I+i =0…”
MethodInfluentialRastogi, P., Anderson, S. J., Bear, H. D., Geyer, C. E., Kahlenberg, M. S., Robidoux, A., Margolese, R. G., Hoehn, J. L., Vogel, V. G., Dakhil, S. R., et al. (2008) · Journal of Clinical Oncology · doi:10.1200/jco.2007.15.0235 · Cited by 1,789 · see citing works
Statistics in Medicine — Reporting of Subgroup Analyses in Clinical Trials
Wang, R., Lagakos, S. W., Ware, J. H., Hunter, D. J., & Drazen, J. M. (2007) · New England Journal of Medicine · doi:10.1056/nejmsr077003 · Cited by 1,445 · see citing works
Chastre, J., Wolff, M., Fagon, J.-Y., Chevret, S., Thomas, F., Wermert, D., Clementi, E., Gonzalez, J., Jusserand, D., Asfar, P., et al. (2003) · JAMA · doi:10.1001/jama.290.19.2588 · Cited by 1,376 · see citing works
Pocock, S. J., Assmann, S. E., Enos, L. E., & Kasten, L. E. (2002) · Statistics in Medicine · doi:10.1002/sim.1296 · Cited by 1,077 · see citing works
VanderWeele, T. J., & Knol, M. J. (2014) · Epidemiologic Methods · doi:10.1515/em-2013-0005 · Cited by 1,127 · see citing works
Cholesterol Lowering in Intermediate-Risk Persons without Cardiovascular Disease
Yusuf, S., Bosch, J., Dagenais, G., Zhu, J., Xavier, D., Liu, L., Pais, P., López-Jaramillo, P., Leiter, L. A., Dans, A., et al. (2016) · New England Journal of Medicine · doi:10.1056/nejmoa1600176 · Cited by 848 · see citing works
Treatment selection in depression.
Cohen, Z. D., & DeRubeis, R. J. (2018) · Annual Review of Clinical Psychology · doi:10.1146/annurev-clinpsy-050817-084746 · Cited by 435 · see citing works
Rituximab plus Lenalidomide in Advanced Untreated Follicular Lymphoma
Morschhauser, F., Fowler, N. H., Feugier, P., Bouabdallah, R., Tilly, H., Palomba, M. L., Fruchart, C., Libby, E. N., Casasnovas, R.-O., Flinn, I. W., et al. (2018) · New England Journal of Medicine · doi:10.1056/nejmoa1805104 · Cited by 373 · see citing works
Benjamini, Y., & Liu, W. (1999) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(99)00040-3 · Cited by 242 · see citing works
Peeters, M., Douillard, J.-Y., Van Cutsem, E., Siena, S., Zhang, K., Williams, R., & Wiezorek, J. (2013) · Journal of Clinical Oncology · doi:10.1200/jco.2012.45.1492 · Cited by 232 · see citing works
Mao, C., Yang, Z. Y., Hu, X. F., Chen, Q., & Tang, J. L. (2012) · Annals of Oncology · doi:10.1093/annonc/mdr464 · Cited by 188 · see citing works
Detecting moderator effects using subgroup analyses
Wang, R., & Ware, J. H. (2013) · Prevention Science · doi:10.1007/s11121-011-0221-x · Cited by 165 · see citing works
Controversies concerning randomization and additivity in clinical trials.
Senn, S. (2004) · Statistics in Medicine · doi:10.1002/sim.2074 · Cited by 132 · see citing works
The Intellectual Crisis of Psychiatric Research
Fava, G. A. (2006) · Psychotherapy and Psychosomatics · doi:10.1159/000092890 · Cited by 79 · see citing works
Zelniker, T. A., Raz, I., Mosenzon, O., Dwyer, J. P., Heerspink, H. H. J. L., Cahn, A., Goodrich, E. L., Im, K., Bhatt, D. L., Leiter, L. A., et al. (2021) · JAMA Cardiology · doi:10.1001/jamacardio.2021.0660 · Cited by 52 · see citing works
Davis, S. N., Horton, E. S., Battelino, T., Rubin, R. R., Schulman, K. A., & Tamborlane, W. V. (2010) · Diabetes Technology & Therapeutics · doi:10.1089/dia.2009.0145 · Cited by 40 · see citing works
- Authors
- Gail, M., & Simon, R.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1985-06
- Volume
- 41
- Issue
- 2
- Pages
- 361
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W1988985184
- Cited by
- 651
- References
- 15
- Citations by year
- 2026: 14 · 2025: 13 · 2024: 13 · 2023: 12 · 2022: 21 · 2021: 23 · 2020: 24 · 2019: 29 · 2018: 24 · 2017: 23 · 2016: 28 · 2015: 24 · 2014: 27 · 2013: 22 · 2012: 27
- FWCI
- 10.38
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrics (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- crossover interaction, treatment effect heterogeneity, likelihood ratio test, exact critical values, clinical trials, subgroup analysis, treatment efficacy
- MeSH terms
- Biometry, Clinical Trials as Topic, Humans
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
