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Khan JN, Kimani PK, Glimm E, Stallard N. Adjusting for treatment selection in phase II/III clinical trials with time to event data. Stat Med 2023; 42:146-163. [PMID: 36419206 PMCID: PMC10098876 DOI: 10.1002/sim.9606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 09/25/2022] [Accepted: 11/01/2022] [Indexed: 11/26/2022]
Abstract
Phase II/III clinical trials are efficient two-stage designs that test multiple experimental treatments. In stage 1, patients are allocated to the control and all experimental treatments, with the data collected from them used to select experimental treatments to continue to stage 2. Patients recruited in stage 2 are allocated to the selected treatments and the control. Combined data of stage 1 and stage 2 are used for a confirmatory phase III analysis. Appropriate analysis needs to adjust for selection bias of the stage 1 data. Point estimators exist for normally distributed outcome data. Extending these estimators to time to event data is not straightforward because treatment selection is based on correlated treatment effects and stage 1 patients who do not get events in stage 1 are followed-up in stage 2. We have derived an approximately uniformly minimum variance conditional unbiased estimator (UMVCUE) and compared its biases and mean squared errors to existing bias adjusted estimators. In simulations, one existing bias adjusted estimator has similar properties as the practically unbiased UMVCUE while the others can have noticeable biases but they are less variable than the UMVCUE. For confirmatory phase II/III clinical trials where unbiased estimators are desired, we recommend the UMVCUE or the existing estimator with which it has similar properties.
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Affiliation(s)
| | - Peter K Kimani
- Warwick Medical School, University of Warwick, Coventry, UK
| | | | - Nigel Stallard
- Warwick Medical School, University of Warwick, Coventry, UK
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2
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Lee KM, Robertson DS, Jaki T, Emsley R. The benefits of covariate adjustment for adaptive multi-arm designs. Stat Methods Med Res 2022; 31:2104-2121. [PMID: 35876412 PMCID: PMC7613816 DOI: 10.1177/09622802221114544] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
Covariate adjustment via a regression approach is known to increase the precision
of statistical inference when fixed trial designs are employed in randomized
controlled studies. When an adaptive multi-arm design is employed with the
ability to select treatments, it is unclear how covariate adjustment affects
various aspects of the study. Consider the design framework that relies on
pre-specified treatment selection rule(s) and a combination test approach for
hypothesis testing. It is our primary goal to evaluate the impact of covariate
adjustment on adaptive multi-arm designs with treatment selection. Our secondary
goal is to show how the Uniformly Minimum Variance Conditionally Unbiased
Estimator can be extended to account for covariate adjustment analytically. We
find that adjustment with different sets of covariates can lead to different
treatment selection outcomes and hence probabilities of rejecting hypotheses.
Nevertheless, we do not see any negative impact on the control of the familywise
error rate when covariates are included in the analysis model. When adjusting
for covariates that are moderately or highly correlated with the outcome, we see
various benefits to the analysis of the design. Conversely, there is negligible
impact when including covariates that are uncorrelated with the outcome.
Overall, pre-specification of covariate adjustment is recommended for the
analysis of adaptive multi-arm design with treatment selection. Having the
statistical analysis plan in place prior to the interim and final analyses is
crucial, especially when a non-collapsible measure of treatment effect is
considered in the trial.
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Affiliation(s)
- Kim May Lee
- Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | | | - Thomas Jaki
- 47959MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
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3
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Lane A. Conditional information and inference in response-adaptive allocation designs. Stat Med 2022; 41:390-406. [PMID: 34747523 DOI: 10.1002/sim.9243] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Revised: 10/12/2021] [Accepted: 10/13/2021] [Indexed: 11/10/2022]
Abstract
Response-adaptive allocation designs refer to a class of designs where the probability an observation is assigned to a treatment is changed throughout an experiment based on the accrued responses. Such procedures result in random treatment sample sizes. Most of the current literature considers unconditional inference procedures in the analysis of response-adaptive allocation designs. The focus of this article is inference conditional on the observed treatment sample sizes. The inverse of information is a description of the large sample variance of the parameter estimates. A simple form for the conditional information relative to unconditional information is derived. It is found that conditional information can be greater than unconditional information. A conditional bootstrap procedure is developed that, in the majority of cases examined, resulted in narrower confidence intervals than relevant unconditional procedures.
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Affiliation(s)
- Adam Lane
- Department of Pediatrics, University of Cincinnati, Cincinnati, Ohio, USA.,Cancer and Blood Diseases Institute, Cincinnati Childrens' Hospital Medical Center, Cincinnati, Ohio, USA
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Kimani PK, Todd S, Renfro LA, Glimm E, Khan JN, Kairalla JA, Stallard N. Point and interval estimation in two-stage adaptive designs with time to event data and biomarker-driven subpopulation selection. Stat Med 2020; 39:2568-2586. [PMID: 32363603 PMCID: PMC7785132 DOI: 10.1002/sim.8557] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Revised: 03/31/2020] [Accepted: 04/06/2020] [Indexed: 02/02/2023]
Abstract
In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two-stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous.
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Affiliation(s)
- Peter K Kimani
- Warwick Medical School, University of Warwick, Coventry, UK
| | - Susan Todd
- Department of Mathematics and Statistics, University of Reading, Reading, UK
| | - Lindsay A Renfro
- Division of Biostatistics, University of Southern California, Los Angeles, CA, USA
| | | | | | - John A Kairalla
- Department of Biostatistics, University of Florida, Gainesville, Florida, USA
| | - Nigel Stallard
- Warwick Medical School, University of Warwick, Coventry, UK
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5
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Kimani PK, Todd S, Renfro LA, Stallard N. Point estimation following two-stage adaptive threshold enrichment clinical trials. Stat Med 2018; 37:3179-3196. [PMID: 29855066 PMCID: PMC6175016 DOI: 10.1002/sim.7831] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Revised: 03/16/2018] [Accepted: 04/30/2018] [Indexed: 11/11/2022]
Abstract
Recently, several study designs incorporating treatment effect assessment in biomarker-based subpopulations have been proposed. Most statistical methodologies for such designs focus on the control of type I error rate and power. In this paper, we have developed point estimators for clinical trials that use the two-stage adaptive enrichment threshold design. The design consists of two stages, where in stage 1, patients are recruited in the full population. Stage 1 outcome data are then used to perform interim analysis to decide whether the trial continues to stage 2 with the full population or a subpopulation. The subpopulation is defined based on one of the candidate threshold values of a numerical predictive biomarker. To estimate treatment effect in the selected subpopulation, we have derived unbiased estimators, shrinkage estimators, and estimators that estimate bias and subtract it from the naive estimate. We have recommended one of the unbiased estimators. However, since none of the estimators dominated in all simulation scenarios based on both bias and mean squared error, an alternative strategy would be to use a hybrid estimator where the estimator used depends on the subpopulation selected. This would require a simulation study of plausible scenarios before the trial.
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Affiliation(s)
- Peter K. Kimani
- Warwick Medical SchoolUniversity of WarwickCoventry CV4 7ALUK
| | - Susan Todd
- Department of Mathematics and StatisticsUniversity of ReadingReading RG6 6AXUK
| | - Lindsay A. Renfro
- Division of Biomedical Statistics and InformaticsMayo ClinicRochesterMN 55905USA
| | - Nigel Stallard
- Warwick Medical SchoolUniversity of WarwickCoventry CV4 7ALUK
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Cologne J, Loo L, Shvetsov YB, Misumi M, Lin P, Haiman CA, Wilkens LR, Le Marchand L. Stepwise approach to SNP-set analysis illustrated with the Metabochip and colorectal cancer in Japanese Americans of the Multiethnic Cohort. BMC Genomics 2018; 19:524. [PMID: 29986644 PMCID: PMC6038257 DOI: 10.1186/s12864-018-4910-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Accepted: 06/29/2018] [Indexed: 12/19/2022] Open
Abstract
BACKGROUND Common variants have explained less than the amount of heritability expected for complex diseases, which has led to interest in less-common variants and more powerful approaches to the analysis of whole-genome scans. Because of low frequency (low statistical power), less-common variants are best analyzed using SNP-set methods such as gene-set or pathway-based analyses. However, there is as yet no clear consensus regarding how to focus in on potential risk variants following set-based analyses. We used a stepwise, telescoping approach to analyze common- and rare-variant data from the Illumina Metabochip array to assess genomic association with colorectal cancer (CRC) in the Japanese sub-population of the Multiethnic Cohort (676 cases, 7180 controls). We started with pathway analysis of SNPs that are in genes and pathways having known mechanistic roles in colorectal cancer, then focused on genes within the pathways that evidenced association with CRC, and finally assessed individual SNPs within the genes that evidenced association. Pathway SNPs downloaded from the dbSNP database were cross-matched with Metabochip SNPs and analyzed using the logistic kernel machine regression approach (logistic SNP-set kernel-machine association test, or sequence kernel association test; SKAT) and related methods. RESULTS The TGF-β and WNT pathways were associated with all CRC, and the WNT pathway was associated with colon cancer. Individual genes demonstrating the strongest associations were TGFBR2 in the TGF-β pathway and SMAD7 (which is involved in both the TGF-β and WNT pathways). As partial validation of our approach, a known CRC risk variant in SMAD7 (in both the TGF-β and WNT pathways: rs11874392) was associated with CRC risk in our data. We also detected two novel candidate CRC risk variants (rs13075948 and rs17025857) in TGFBR2, a gene known to be associated with CRC risk. CONCLUSIONS A stepwise, telescoping approach identified some potentially novel risk variants associated with colorectal cancer, so it may be a useful method for following up on results of set-based SNP analyses. Further work is required to assess the statistical characteristics of the approach, and additional applications should aid in better clarifying its utility.
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Affiliation(s)
- John Cologne
- Department of Statistics, Radiation Effects Research Foundation, Hiroshima, 732-0815, Japan.
| | - Lenora Loo
- Epidemiology Program, University of Hawaii Cancer Center, Honolulu, HI, 96813, USA
| | - Yurii B Shvetsov
- Epidemiology Program, University of Hawaii Cancer Center, Honolulu, HI, 96813, USA
| | - Munechika Misumi
- Department of Statistics, Radiation Effects Research Foundation, Hiroshima, 732-0815, Japan
| | - Philip Lin
- Epidemiology Program, University of Hawaii Cancer Center, Honolulu, HI, 96813, USA
| | - Christopher A Haiman
- Department of Preventive Medicine and Norris Comprehensive Cancer Center, Keck School of Medicine, University of Southern California, Los Angeles, CA, 90033, USA
| | - Lynne R Wilkens
- Biostatistics and Informatics Shared Resource, University of Hawaii Cancer Center, Honolulu, HI, 96813, USA
| | - Loïc Le Marchand
- Epidemiology Program, University of Hawaii Cancer Center, Honolulu, HI, 96813, USA
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Robertson DS, Glimm E. Conditionally unbiased estimation in the normal setting with unknown variances. COMMUN STAT-THEOR M 2018; 48:616-627. [PMID: 31217751 PMCID: PMC6540744 DOI: 10.1080/03610926.2017.1417429] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2017] [Accepted: 12/08/2017] [Indexed: 11/26/2022]
Abstract
To efficiently and completely correct for selection bias in adaptive two-stage trials, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been derived for trial designs with normally distributed data. However, a common assumption is that the variances are known exactly, which is unlikely to be the case in practice. We extend the work of Cohen and Sackrowitz (Statistics & Probability Letters, 8(3):273-278, 1989), who proposed an UMVCUE for the best performing candidate in the normal setting with a common unknown variance. Our extension allows for multiple selected candidates, as well as unequal stage one and two sample sizes.
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Affiliation(s)
| | - Ekkehard Glimm
- Novartis Pharma AG, Novartis Campus, Basel, Switzerland
- Medical Faculty, Institute for Biometrics and Medical Informatics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany
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8
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Broberg P, Miller F. Conditional estimation in two-stage adaptive designs. Biometrics 2017; 73:895-904. [PMID: 28099993 DOI: 10.1111/biom.12642] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2016] [Revised: 11/01/2016] [Accepted: 11/01/2016] [Indexed: 11/28/2022]
Abstract
We consider conditional estimation in two-stage sample size adjustable designs and the consequent bias. More specifically, we consider a design which permits raising the sample size when interim results look rather promising, and which retains the originally planned sample size when results look very promising. The estimation procedures reported comprise the unconditional maximum likelihood, the conditionally unbiased Rao-Blackwell estimator, the conditional median unbiased estimator, and the conditional maximum likelihood with and without bias correction. We compare these estimators based on analytical results and a simulation study. We show how they can be applied in a real clinical trial setting.
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Affiliation(s)
- Per Broberg
- Division of Cancer Epidemiology, Department of Clinical Sciences Lund, Lund University, Skane University Hospital, Lund, Sweden
| | - Frank Miller
- Department of Statistics, Stockholm University, 10691 Stockholm, Sweden
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Robertson DS, Prevost AT, Bowden J. Unbiased estimation in seamless phase II/III trials with unequal treatment effect variances and hypothesis-driven selection rules. Stat Med 2016; 35:3907-22. [PMID: 27103068 PMCID: PMC5026174 DOI: 10.1002/sim.6974] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2015] [Revised: 03/29/2016] [Accepted: 04/01/2016] [Indexed: 11/24/2022]
Abstract
Seamless phase II/III clinical trials offer an efficient way to select an experimental treatment and perform confirmatory analysis within a single trial. However, combining the data from both stages in the final analysis can induce bias into the estimates of treatment effects. Methods for bias adjustment developed thus far have made restrictive assumptions about the design and selection rules followed. In order to address these shortcomings, we apply recent methodological advances to derive the uniformly minimum variance conditionally unbiased estimator for two‐stage seamless phase II/III trials. Our framework allows for the precision of the treatment arm estimates to take arbitrary values, can be utilised for all treatments that are taken forward to phase III and is applicable when the decision to select or drop treatment arms is driven by a multiplicity‐adjusted hypothesis testing procedure. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
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Affiliation(s)
| | | | - Jack Bowden
- MRC Biostatistics Unit, Cambridge, U.K.,MRC Integrative Epidemiology Unit, University of Bristol, Bristol, U.K
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