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Status: OngoingResearch Proposal
Project Title: Comparative Evaluation of Carryover Adjustment Methods in Crossover Trials
Scientific Abstract:
Background:
Crossover trials are widely used in early-phase clinical research due to their efficiency in comparing treatments within the same participants. However, carryover effects--when a previous treatment's effect persists into the next period--can bias treatment comparisons and compromise trial validity. Although several methods exist to detect carryover, limited guidance is available on designing trials to detect clinically unacceptable levels of carryover.
Objective:
This study aims to develop a statistical method to determine the sample size needed to detect a carryover effect of a pre-specified minimum magnitude considered clinically unacceptable. This will help ensure sufficient power to identify meaningful carryover when present.
Study Design:
We derive a sample size formula for two-period, two-treatment crossover trials, incorporating a nonzero carryover effect. The formula links sample size with carryover effect size, significance level, and power. Analytical derivations are supported by simulations.
Participants:
Individual-level data from an existing crossover trial will be used to assess the method's performance.
Primary and Secondary Outcome Measure(s):
The primary outcome is the power to detect a carryover effect at or above the specified threshold. Secondary outcomes include empirical type I error rates and power under varying assumptions.
Statistical Analysis:
Analytical methods and Monte Carlo simulations will be used to evaluate type I error, power, and sample size accuracy.
Brief Project Background and Statement of Project Significance:
Crossover trials are widely used in early-phase clinical studies, especially in evaluating pharmacodynamic or short-acting therapeutic agents. Their design allows each subject to receive multiple treatments in different periods, thereby increasing statistical efficiency and reducing inter-subject variability. However, this efficiency comes with a critical vulnerability: the potential for carryover effects, wherein the effect of a treatment administered in an earlier period persists into a later period and biases the measurement of subsequent treatments.
Carryover can arise from pharmacological mechanisms, such as drug half-life or delayed biological action, as well as from physiological or psychological adaptation. If left undetected, carryover may lead to incorrect conclusions about treatment efficacy or safety, threatening both internal validity and the ethical integrity of the study. Traditionally, detection of carryover has relied on Grizzle's two-stage procedure or ANOVA-based interaction terms. While these methods are commonly used, they are not designed for trial planning--in particular, they do not answer the practical question: "How many subjects are needed to reliably detect a carryover effect of a magnitude we consider clinically unacceptable?"
The goal of this project is to fill that methodological gap. We propose to develop a new sample size calculation method that enables investigators to determine the number of participants required to detect a carryover effect of a specified minimum magnitude. This "tolerability threshold" can be set based on clinical or pharmacological reasoning. Our approach will be grounded in the variance structure of standard two-period, two-treatment crossover models and will allow the specification of Type I error, power, and minimum detectable carryover effect size. The method will be validated through simulation and applied to real-world crossover trial data to evaluate its practical performance.
This research is expected to enhance the methodological toolkit available to clinical trialists and statisticians. By allowing researchers to proactively design crossover trials that are adequately powered to detect problematic carryover effects, the proposed method will improve the scientific rigor and interpretability of trial findings. Moreover, it will support regulatory transparency and clinical decision-making by ensuring that crossover trials do not inadvertently obscure important treatment effects.
The findings from this work will contribute generalizable knowledge to both statistical methodology and clinical trial design. The sample size formula and its implementation guidelines will be made publicly available and can be applied to a wide range of therapeutic areas and study settings, particularly in early-phase research where crossover designs are prevalent.
Specific Aims of the Project:
The primary aim of this project is to develop and evaluate a new sample size calculation method for detecting clinically unacceptable carryover effects in crossover trials. Traditional carryover detection methods focus on post hoc testing and do not provide a framework for designing trials that are prospectively powered to detect carryover of a pre-specified magnitude. Our proposed method addresses this limitation by providing a way to plan crossover trials with sufficient statistical power to identify carryover effects that exceed a tolerability threshold.
The specific objectives of the project are:
To derive a sample size formula for detecting a minimum detectable carryover effect in a standard two-period, two-treatment crossover design, given user-specified power and Type I error rate.
To evaluate the empirical performance of the proposed formula through simulation studies under various parameter settings, including different effect sizes, variances, and sample sizes.
To apply the method to real-world clinical trial data to demonstrate its practical utility and assess how well the design properties hold in applied settings.
Hypothesis:
We hypothesize that the proposed method will yield sample size estimates that achieve the target power to detect carryover effects at or above the specified minimum threshold, while maintaining appropriate Type I error control. The method is expected to provide a practical, generalizable framework for improving the planning and validity of crossover trials.
Study Design: Methodological research
What is the purpose of the analysis being proposed? Please select all that apply.: Develop or refine statistical methods
Software Used: R
Data Source and Inclusion/Exclusion Criteria to be used to define the patient sample for your study:
We plan to use individual participant data from an existing crossover clinical trial available through the YODA Project. Our study will focus on methodological evaluation and does not require the application of additional clinical inclusion or exclusion criteria beyond those already defined in the original trial protocol.
Accordingly, all participants who were enrolled in the original study according to its predefined eligibility criteria and who were not excluded per the study's exclusion criteria will be included in our analysis. We will not impose any new inclusion or exclusion criteria of our own.
Our interest is solely in the subset of patients who completed at least two treatment periods as part of a randomized crossover design, and for whom the necessary outcome and covariate information is available to support evaluation of carryover effects.
Primary and Secondary Outcome Measure(s) and how they will be categorized/defined for your study:
The primary outcome measure for this study is the pharmacodynamic (PD) response variable collected at scheduled time points during the crossover trial. For NCT01876966, potential PD endpoints--if available in the individual participant data--include:
Antimalarial activity measures: parasite clearance rate, time to parasite clearance, or laboratory-based parasite density assessments.
Safety-related PD markers: QTc interval changes from ECG, relevant given the observed PK changes in lumefantrine exposure.
Biomarkers: plasma or serum levels of inflammatory mediators or other physiological indicators reflecting artemether/lumefantrine (A/L) pharmacological effects.
For etravirine (ETR) or darunavir/ritonavir (DRV/rtv): virological markers (e.g., HIV RNA) or immunological markers (e.g., CD4+ counts), if collected, though this healthy-volunteer study may not contain such measures.
If parasite-related endpoints are unavailable, a safety-related PD endpoint such as QTc change will be pre-specified. The final PD variable will be selected from available data before analysis and treated as a continuous endpoint.
The PD data will be analyzed to estimate treatment effects across periods and sequences, focusing on potential carryover effects. Analyses will be conducted at both the individual level and aggregated by treatment sequence. Sample size assumptions will be based on a continuous outcome with known or estimable variance, using a linear model structure appropriate for crossover designs.
No secondary outcome measures are planned. Exploratory analyses (e.g., time-specific PD dynamics or subgroup comparisons) will be clearly distinguished from the primary aim and reported separately. No changes to the primary outcome are expected in the final analysis.
Main Predictor/Independent Variable and how it will be categorized/defined for your study:
The main independent variable in this study is the presence and magnitude of a carryover effect in a two-period, two-treatment crossover trial. Specifically, we will evaluate whether the pharmacological effect of the treatment given in the first period persists into the second period, thereby influencing the pharmacodynamic (PD) measurements in that subsequent period.
For NCT01876966, potential PD endpoints--if available--include antimalarial activity measures (e.g., parasite clearance rate, time to clearance), safety-related markers (e.g., QTc interval changes from ECG), and relevant biomarkers (e.g., inflammatory mediator levels). The carryover effect will be modeled as an additive continuous parameter affecting the PD outcome in the second period, conditional on the first-period treatment. The magnitude of interest will be pre-specified as the minimum clinically relevant or unacceptable level, and the study's methodological focus is to determine the sample size required to detect such an effect with adequate power.
Treatment assignment in each period (active vs. control) will also serve as an independent variable, defined as a binary categorical indicator. These two independent variables--carryover effect (continuous) and treatment (binary)--will be included in the statistical model to estimate their influence on the PD outcome. All definitions will be fixed prior to analysis, remain consistent with the final analysis, and be reported unchanged in resulting publications.
Other Variables of Interest that will be used in your analysis and how they will be categorized/defined for your study:
In addition to the primary independent variables related to treatment and carryover, we plan to utilize the following patient-level variables to describe the study population and support interpretation of findings. These variables will not be included in the core sample size derivation but may be used in exploratory analyses and descriptive summaries.
Age: A continuous variable (in years), used to summarize the age distribution of the study sample.
Sex: A categorical variable (male/female), reported in demographic summaries.
Medical history/comorbidities: Categorical indicators of major relevant pre-existing conditions (e.g., cardiovascular disease, diabetes, hepatic impairment), used to characterize baseline risk profiles.
Baseline pharmacodynamic measurements: Continuous variables measured prior to the first treatment period, used to assess baseline comparability across treatment sequences or groups.
Treatment group/sequence: Categorical variable indicating the randomized order in which treatments were administered (e.g., AB or BA), which may be used to stratify descriptive statistics or sensitivity analyses.
These variables will be used to characterize the patient sample, check baseline balance, and support interpretation of carryover-related findings. Their definitions and roles will be clearly documented in any resulting publications and will not affect the primary analytic model for sample size determination.
Statistical Analysis Plan:
The primary goal of this study is to develop and evaluate a sample size calculation method for detecting clinically unacceptable carryover effects in crossover trials. The following steps outline the planned statistical analysis approach using both theoretical derivation and empirical evaluation based on real-world clinical trial data.
Analytical Derivation of Sample Size Formula
We will begin by deriving a sample size formula for detecting a non-zero carryover effect in a standard two-period, two-treatment crossover design. The derivation assumes a continuous pharmacodynamic (PD) outcome and an additive carryover model. The formula will link sample size (n) to the following design parameters:
Desired statistical power (e.g., 80% or 90%)
Type I error rate (e.g., alpha = 0.05)
Within-subject variance
Magnitude of carryover effect to be detected (delta)
This derivation provides a framework for determining how large a study needs to be in order to detect a specified minimum carryover effect with high probability, under typical crossover assumptions (e.g., no period-by-treatment interaction, equal variances).
Simulation-Based Validation of Sample Size Formula
To assess the accuracy and robustness of the sample size formula, we will conduct simulation studies. We will generate crossover trial datasets under varying parameter settings, including:
Multiple carryover effect sizes (including near-zero, moderate, and large)
Varying within-subject variance
Different true treatment effects
For each simulated scenario, we will estimate the empirical power of the carryover detection test using the sample size provided by the formula. These simulations will help validate that the formula achieves the target power and maintains type I error control across a range of plausible conditions.
Application to Real Clinical Trial Data
Using individual participant data from an existing crossover trial (obtained through the YODA Project), we will conduct the following analyses:
a. Descriptive Analyses
We will summarize demographic and clinical characteristics of the participants, stratified by randomized treatment sequence. Variables include age, sex, baseline PD values, and comorbidities. Summary statistics will include means and standard deviations for continuous variables and frequencies and percentages for categorical variables.
b. Carryover Detectability Assessment
Using the actual sample size and within-subject variability observed in the dataset, we will estimate the minimum detectable carryover effect--i.e., the smallest carryover magnitude that could be detected with 80% power using a two-sided hypothesis test at the 0.05 level. This provides a practical interpretation of what level of carryover could realistically be identified given the existing trial size and variability.
c. Formal Hypothesis Testing for Carryover
We will conduct formal testing for the presence of a carryover effect using a standard linear model that includes terms for treatment, period, and carryover (sequence). The model will be of the form:
PD_ij = mu + T_i + P_j + C_i + e_ij
where T_i is the treatment effect, P_j is the period effect, C_i is the carryover effect, and e_ij is the residual error. The primary test of interest will evaluate the null hypothesis H0: C_i = 0.
We will report the test statistic, p-value, and 95% confidence interval for the carryover term. If the carryover effect is found to be statistically significant and exceeds the tolerable threshold defined by the user, this will be interpreted as evidence of clinically meaningful carryover.
Sensitivity Analyses
We will conduct sensitivity analyses to examine how results vary across different model assumptions, including:
Alternate variance structures (e.g., unequal variances across periods)
Different methods for estimating within-subject variance
Exclusion of participants with missing periods or outcomes
Secondary Analyses (Optional)
If secondary PD outcomes or repeated measurements are available, we may explore extensions to the model such as mixed-effects models or generalized estimating equations (GEE), though these will be considered exploratory and reported separately from the primary analysis.
Narrative Summary: We are studying how carryover effects can bias results in crossover clinical trials. Carryover happens when the effects of a treatment in an earlier period influence the response in a later period. This can make it hard to correctly estimate how effective a treatment really is. Our research evaluates existing methods to detect and adjust for carryover, such as Grizzle's two-stage test. We also explore new statistical approaches that improve accuracy when carryover is present. By better identifying and correcting for these effects, our work will help ensure that results from crossover trials are more reliable. This can improve decision-making in medicine and public health.
Project Timeline:
We anticipate beginning the project in July 2025, immediately upon receipt of the approved clinical trial dataset from the YODA Project. Initial tasks, including data cleaning, variable checking, and descriptive summaries, will be conducted during July to early August.
From mid-August to early September, we will implement the proposed sample size calculation method under various simulated carryover effect scenarios, and apply the method to the actual trial data to estimate the minimum detectable carryover effect based on the observed sample size and variance.
Formal hypothesis testing for carryover will be conducted in September, followed by sensitivity analyses and result interpretation. The full analysis is expected to be completed by September 30, 2025.
The manuscript draft will be prepared in October 2025, with the goal of submitting the paper to a peer-reviewed journal by October 31, 2025.
A summary of findings will be prepared and reported back to the YODA Project by November 15, 2025.
If additional time is required for revision or secondary analyses, we may request an extension, but we expect the primary work to be completed well within the 12-month data use period.
Dissemination Plan:
We anticipate submitting the results of this study as a full-length research article to a peer-reviewed journal in the field of biostatistics or clinical trial methodology. A primary target journal is Statistics in Medicine, which is well suited for the dissemination of new statistical methods with direct applications to medical research. The manuscript will detail the proposed sample size calculation method for carryover detection in crossover trials, its theoretical foundation, simulation-based evaluation, and application to real clinical trial data.
The target audience includes biostatisticians, clinical trial methodologists, regulatory scientists, and clinical researchers involved in the design and evaluation of crossover trials, particularly in early-phase drug development. We also anticipate that the method will be of interest to statisticians working in regulatory agencies and the pharmaceutical industry, where rigorous design of crossover studies is essential.
In addition to journal publication, we may present the findings at relevant conferences such as the Joint Statistical Meetings (JSM) or the International Society for Clinical Biostatistics (ISCB), to promote wider adoption and feedback from the scientific community.
Bibliography:
Grizzle, J. E. (1965). The two-period change-over design and its use in clinical trials. Biometrics, 467-480.