ESTIMATES OF CARRY-OVER EFFECTS IN TWO-PRODUCT HOME USAGE CONSUMER TESTS

In-house use consumer test data from four studies dealing with three pairs of household products and a pair of antiperspirant products were examined for significant carry-over (product usage order) effects, which would confound the analysis of treatment (product) effects. In each study, two products were compared using a two-period crossover design. One hundred twenty panelists participated in each study. A forced choice preference scale or a 9-point hedonic scale was used to obtain responses from various sensory attributes. In all studies, the estimates of carry-over effects were not significant at the 5% level. Transformation of hedonic scale data into preference dichotomy also gave estimates of carry-over effects which were not significant at the 5% level, but led to a loss of test sensitivity for detecting treatment differences. The authors recommend that all comparative crossover design studies in sensory evaluation be monitored for carry-over effects and that statistically determined sample size should be used to reduce the possibility of obtaining significant carry-over effects.     

Empirical power and sample size calculations for cluster-randomized and cluster-randomized crossover studies

In recent years, the number of studies using a cluster-randomized design has grown dramatically. In addition, the cluster-randomized crossover design has been touted as a methodological advance that can increase efficiency of cluster-randomized studies in certain situations. While the cluster-randomized crossover trial has become a popular tool, standards of design, analysis, reporting and implementation have not been established for this emergent design. We address one particular aspect of cluster-randomized and cluster-randomized crossover trial design: estimating statistical power. We present a general framework for estimating power via simulation in cluster-randomized studies with or without one or more crossover periods. We have implemented this framework in the clusterPower software package for R, freely available online from the Comprehensive R Archive Network. Our simulation framework is easy to implement and users may customize the methods used for data analysis. We give four examples of using the software in practice. The clusterPower package could play an important role in the design of future cluster-randomized and cluster-randomized crossover studies. This work is the first to establish a universal method for calculating power for both cluster-randomized and cluster-randomized clinical trials. More research is needed to develop standardized and recommended methodology for cluster-randomized crossover studies.     

Bioequivalence trials with the incomplete 3 x 3 crossover design

In bioequivalence trials, one often considers two or more generic products with the original one. The 3 x 3 crossover design can be adopted to evaluate the two generic candidates with a brand name drug, rather than conducting two separate 2 x 2 crossover trials. Dropouts, however, are more likely to occur due to various administrative reasons when we consider a higher order crossover design. A modified method, which was originally given by Chow and Shao (1997), is extended to compare two generic products with a reference in the incomplete 3 x 3 crossover design. A simulation study and discussion are also presented.     

Sample size determination for testing nonequality under a three‐treatment two‐period incomplete block crossover trial

To reduce the lengthy duration of a crossover trial for comparing three treatments, the incomplete block design has been often considered. A sample size calculation procedure for testing nonequality between either of the two experimental treatments and a placebo under such a design is developed. To evaluate the performance of the proposed sample size calculation procedure, Monte Carlo simulation is employed. The accuracy of the sample size calculation procedure developed here is demonstrated in a variety of situations. As compared with the parallel groups design, a substantial proportional reduction in the total minimum required sample size in use of the incomplete block crossover design is found. A crossover trial comparing two different doses of formoterol with a placebo on the forced expiratory volume is applied to illustrate the use of the sample size calculation procedure.     

Design and Analysis of Crossover Trials for Absorbing Binary Endpoints

Summary The crossover is a popular and efficient trial design used in the context of patient heterogeneity to assess the effect of treatments that act relatively quickly and whose benefit disappears with discontinuation. Each patient can serve as her own control as within‐individual treatment and placebo responses are compared. Conventional wisdom is that these designs are not appropriate for absorbing binary endpoints, such as death or HIV infection. We explore the use of crossover designs in the context of these absorbing binary endpoints and show that they can be more efficient than the standard parallel group design when there is heterogeneity in individuals' risks. We also introduce a new two‐period design where first period “survivors” are rerandomized for the second period. This design combines the crossover design with the parallel design and achieves some of the efficiency advantages of the crossover design while ensuring that the second period groups are comparable by randomization. We discuss the validity of the new designs and evaluate both a mixture model and a modified Mantel–Haenszel test for inference. The mixture model assumes no carryover or period effects while the Mantel–Haenszel approach conditions out period effects. Simulations are used to compare the different designs and an example is provided to explore practical issues in implementation.     

Design,Analysis, and Reporting of Crossover Trials for Inclusion in a Meta-Analysis

Randomized crossover trials are clinical experiments in which participants are assigned randomly to a sequence of treatments and each participant serves as his/her own control in estimating treatment effect. We need a better understanding of the validity of their results to enable recommendations as to which crossover trials can be included in meta-analysis and for development of reporting guidelines.

Objective

To evaluate the characteristics of the design, analysis, and reporting of crossover trials for inclusion in a meta-analysis of treatment for primary open-angle glaucoma and to provide empirical evidence to inform the development of tools to assess the validity of the results from crossover trials and reporting guidelines.

Methods

We searched MEDLINE, EMBASE, and Cochrane’s CENTRAL register for randomized crossover trials for a systematic review and network meta-analysis we are conducting. Two individuals independently screened the search results for eligibility and abstracted data from each included report.

Results

We identified 83 crossover trials eligible for inclusion. Issues affecting the risk of bias in crossover trials, such as carryover, period effects and missing data, were often ignored. Some trials failed to accommodate the within-individual differences in the analysis. For a large proportion of the trials, the authors tabulated the results as if they arose from a parallel design. Precision estimates properly accounting for the paired nature of the design were often unavailable from the study reports; consequently, to include trial findings in a meta-analysis would require further manipulation and assumptions.

Conclusions

The high proportion of poorly reported analyses and results has the potential to affect whether crossover data should or can be included in a meta-analysis. There is pressing need for reporting guidelines for crossover trials.     

Analysis of two-period crossover design in a multicenter clinical trial

A technique is discussed for analyzing a two-period crossover design for a multicenter trial using identical study protocols. The technique is a modification of the analysis originally proposed by Grizzle (1965, Biometrics 21, 467-480; 1974, Biometrics 30, 727) for analyzing a two-period crossover design when study is not a factor. A mixed model using the first baseline as a covariate is analyzed to increase the power of the test of significance of the treatment-by-period interaction. The baseline values are also used in a preliminary test.     

A computer program for the analysis of crossover designs.

We describe a program, CROSS, which we have written to obtain potency estimates and other parameters for bioassay data from assays of crossover design. The program permits testing of all assays for statistical validity and calculates the complete analysis of variance for assays of balanced design. The form of data input and the complete documentation of assay results make this program particularly useful for anyone carrying out crossover assays on a routine basis. The analysis of variance presented is also useful for more general biological or medical situations.     

Nonparametric Methods in Crossover Trials

The crossover design is often used in biomedical trials since it eliminates between subject variability. This paper is concerned with the statistical analysis of data arising from such trials when assumptions like normality do not necessarily apply. Nonparametric analysis of the two-period, two-treatment design was first described by Koch in a paper 1972. The purpose of this paper is to study nonparametric methods in crossover designs with three or more treatments and an equal number of periods. The proposed test for direct treatment effects is based on within subject comparisons after removing a possible period effect. With only two treatments this test reduces to the twosided Wilcoxon signed rank test. By simulation experiments the validity of the significance level of the test when using the asymptotic distribution of the test statistic are manifested and the power against different alternatives illustrated. A test for first order carryover effects can be constructed by a straightforward generalization of the test proposed by Koch in 1972. However, since this test is based on between subject comparisons its power will be low. Our recommendation is to consider the crossover design rather than the parallel group design if the carryover effects are assumed to be neglible or positive and smaller then the direct treatment effects.     

Randomization and Additivity in the Two-Period Crossover Clinicial Trial

In certain areas of medical research, the two-period crossover design is a frequent choice for comparing treatments A and B in a randomized clinical trial. Earlier work by Grizzle and by Brown was based upon a parametric theory linear model. Recently, the present authors employed D. R. Cox's additive randomization models and, for the case of zero residual effect, found a discrepancy between it and the parametric model with respect to the precision of period effects. In the present note, this divergence is accounted for by allowing for the possibility of non-additivity through the use of a completely general randomization model. It is concluded that the structure of the crossover design is such that use of the parametric theory linear model is required if a single, consistent model is desired.     

Using the maximum test statistic in the two-period crossover clinical trial

In a two-period crossover trial where residual carryover is suspected, it is often advised that first-period data only be used in an analysis appropriate for a parallel design. However, it has been shown (Willan and Pater, 1986, Biometrics 42, 593-599) that the crossover analysis is more powerful than the parallel analysis if the residual carryover, expressed as a proportion of treatment effect, is less than 2- square root of 2(1 - rho), where rho is the intrasubject correlation coefficient. Choosing between the analyses based on the empirical evaluation of this condition is equivalent to choosing the analysis with the larger corresponding test statistic. Approximate nominal significance levels are presented that maintain the desired level when basing the analysis on the maximum test statistic. Furthermore, the power and precision of the analysis based on the maximum test statistic are compared to the crossover and parallel analyses.     

EFFECT OF EXERCISE ON APPETITE-REGULATING HORMONES IN OVERWEIGHT WOMEN

Over the past decade, our knowledge of how homeostatic systems regulate food intake and body weight has increased with the discovery of circulating peptides such as leptin, acyl ghrelin, des-acyl ghrelin and obestatin. These hormones regulate the appetite and food intake by sending signals to the brain regarding the body''s nutritional status. The purpose of this study was to investigate the response of appetite-regulating hormones to exercise. Nine overweight women undertook two 2 h trials in a randomized crossover design. In the exercise trial, subjects ran for 60 min at 50% of maximal oxygen uptake followed by a 60 min rest period. In the control trial, subjects rested for 2 h. Obestatin, acyl ghrelin, des-acyl ghrelin and leptin concentrations were measured at baseline and at 20, 40, 60, 90 and 120 min after baseline. A two-way ANOVA revealed a significant (P < 0.05) interaction effect for leptin and acyl ghrelin. However, changes in obestatin and des-acyl ghrelin concentration were statistically insignificant (P > 0.05). The data indicated that although acute treadmill exercise resulted in a significant change in acyl ghrelin and leptin levels, it had no effect on plasma obestatin and des-acyl ghrelin levels.     

Estimating individualized treatment regimes from crossover designs

The field of precision medicine aims to tailor treatment based on patient-specific factors in a reproducible way. To this end, estimating an optimal individualized treatment regime (ITR) that recommends treatment decisions based on patient characteristics to maximize the mean of a prespecified outcome is of particular interest. Several methods have been proposed for estimating an optimal ITR from clinical trial data in the parallel group setting where each subject is randomized to a single intervention. However, little work has been done in the area of estimating the optimal ITR from crossover study designs. Such designs naturally lend themselves to precision medicine since they allow for observing the response to multiple treatments for each patient. In this paper, we introduce a method for estimating the optimal ITR using data from a 2 × 2 crossover study with or without carryover effects. The proposed method is similar to policy search methods such as outcome weighted learning; however, we take advantage of the crossover design by using the difference in responses under each treatment as the observed reward. We establish Fisher and global consistency, present numerical experiments, and analyze data from a feeding trial to demonstrate the improved performance of the proposed method compared to standard methods for a parallel study design.     

Improving quantitative trait loci mapping resolution in experimental crosses by the use of genotypically selected samples

One of the key factors contributing to the success of a quantitative trait locus (QTL) mapping experiment is the precision with which QTL positions can be estimated. We show, using simulations, that QTL mapping precision for an experimental cross can be increased by the use of a genotypically selected sample of individuals rather than an unselected sample of the same size. Selection is performed using a previously described method that optimizes the complementarity of the crossover sites within the sample. Although the increase in precision is accompanied by a decrease in QTL detection power at markers distant from QTL, only a modest increase in marker density is needed to obtain equivalent power over the whole map. Selected samples also show a slight reduction in the number of false-positive QTL. We find that two features of selected samples independently contribute to these effects: an increase in the number of crossover sites and increased evenness in crossover spacing. We provide an empirical formula for crossover enrichment in selected samples that is useful in experimental design and data analysis. For QTL studies in which the phenotyping is more of a limiting factor than the generation of individuals and the scoring of genotypes, selective sampling is an attractive strategy for increasing genome-wide QTL map resolution.     

DO MALES MATTER? TESTING THE EFFECTS OF MALE GENETIC BACKGROUND ON FEMALE MEIOTIC CROSSOVER RATES IN DROSOPHILA MELANOGASTER

Meiotic recombination is a critical genetic process as well as a pivotal evolutionary force. Rates of crossing over are highly variable within and between species, due to both genetic and environmental factors. Early studies in Drosophila implicated female genetic background as a major determinant of crossover rate and recent work has highlighted male genetic background as a possible mediator as well. Our study employed classical genetics to address how female and male genetic backgrounds individually and jointly affect crossover rates. We measured rates of crossing over in a 33 cM region of the Drosophila melanogaster X chromosome using a two‐step crossing scheme exploiting visible markers. In total, we measured crossover rates of 10 inbred lines in a full diallel cross. Our experimental design facilitates measuring the contributions of female genetic background, male genetic background, and female by male genetic background interaction effects on rates of crossing over in females. Our results indicate that although female genetic background significantly affects female meiotic crossover rates in Drosophila, male genetic background and the interaction of female and male genetic backgrounds have no significant effect. These findings thus suggest that male‐mediated effects are unlikely to contribute greatly to variation in recombination rates in natural populations of Drosophila.     

Blinded and unblinded sample size reestimation in crossover trials balanced for period

The determination of the sample size required by a crossover trial typically depends on the specification of one or more variance components. Uncertainty about the value of these parameters at the design stage means that there is often a risk a trial may be under‐ or overpowered. For many study designs, this problem has been addressed by considering adaptive design methodology that allows for the re‐estimation of the required sample size during a trial. Here, we propose and compare several approaches for this in multitreatment crossover trials. Specifically, regulators favor reestimation procedures to maintain the blinding of the treatment allocations. We therefore develop blinded estimators for the within and between person variances, following simple or block randomization. We demonstrate that, provided an equal number of patients are allocated to sequences that are balanced for period, the proposed estimators following block randomization are unbiased. We further provide a formula for the bias of the estimators following simple randomization. The performance of these procedures, along with that of an unblinded approach, is then examined utilizing three motivating examples, including one based on a recently completed four‐treatment four‐period crossover trial. Simulation results show that the performance of the proposed blinded procedures is in many cases similar to that of the unblinded approach, and thus they are an attractive alternative.     

Behavioral testing of antidepressant compounds: an analysis of crossover design for correlated binary data

The differential reinforcement of low-rate 72 seconds schedule (DRL-72) is a standard behavioral test procedure for screening potential antidepressant compounds. The protocol for the DRL-72 experiment, proposed by Evenden et al. (1993), consists of using a crossover design for the experiment and one-way ANOVA for the statistical analysis. In this paper we discuss the choice of several crossover designs for the DRL-72 experiment and propose to estimate the treatment effects using either generalized linear mixed models (GLMM) or generalized estimating equation (GEE) models for clustered binary data.     

On the Role of Baseline Measurements for Crossover Designs under the Self and Mixed Carryover Effects Model

Summary .  It is well known that optimal designs are strongly model dependent. In this article, we apply the Lagrange multiplier approach to the optimal design problem, using a recently proposed model for carryover effects. Generally, crossover designs are not recommended when carryover effects are present and when the primary goal is to obtain an unbiased estimate of the treatment effect. In some cases, baseline measurements are believed to improve design efficiency. This article examines the impact of baselines on optimal designs using two different assumptions about carryover effects during baseline periods and employing a nontraditional crossover design model. As anticipated, baseline observations improve design efficiency considerably for two-period designs, which use the data in the first period only to obtain unbiased estimates of treatment effects, while the improvement is rather modest for three- or four-period designs. Further, we find little additional benefits for measuring baselines at each treatment period as compared to measuring baselines only in the first period. Although our study of baselines did not change the results on optimal designs that are reported in the literature, the problem of strong model dependency problem is generally recognized. The advantage of using multiperiod designs is rather evident, as we found that extending two-period designs to three- or four-period designs significantly reduced variability in estimating the direct treatment effect contrast.     

Comparative bioavailability of two oral preparations of digoxin in healthy volunteers

The serum levels of digoxin resulting from the oral administration of 0.25 mg. of Lanoxin and Rougoxin preparations were studied in 12 healthy volunteers by means of a double-blind crossover design. No differences between the two brands could be demonstrated with respect to disintegration time, content uniformity, peak serum levels and cumulative areas under the curve for an eight-hour period.     

Effects of a 30 kV/m, 60 Hz electric field on the social behavior of baboons: a crossover experiment.

Using a crossover experimental design, we evaluated our earlier findings that exposure to a 30 kV/m, 60 Hz electric field for 12 hours per day, 7 days per week for 6 weeks produced significant changes in the performance rates of social behaviors among young adult male baboons. In the crossover experiment, the former control group was exposed to a 30 kV/m, 60 Hz electric field for 3 weeks. Only an extremely small, incidental magnetic field was generated by the exposure apparatus. We found that electric-field exposure again produced increases in the performance rates that index Passive Affinity, Tension, and Stereotypy. These findings, combined with results from our other electric-field experiments, indicate that exposure to strong electric fields, in the absence of associated magnetic fields, consistently produces effects that are expressed as increases in rates of performance of social behaviors in young adult male baboons.