Optimal sample size allocation for two-arm superiority and non-inferiority trials with binary endpoints.

The sample size of a clinical trial has to be large enough to ensure sufficient power for achieving the aim the study. On the other side, for ethical and economical reasons it should not be larger than necessary. The sample size allocation is one of the parameters that influences the required total sample size. For two-arm superiority and non-inferiority trials with binary endpoints, we performed extensive computations over a wide range of scenarios to determine the optimal allocation ratio that minimizes the total sample size if all other parameters are fixed. The results demonstrate, that for both superiority and non-inferiority trials the optimal allocation may deviate considerably from the case of equal sample size in both groups. However, the saving in sample size when allocating the total sample size optimally as compared to balanced allocation is typically small.

Numerical investigation on the influence of dual-frequency coupling parameters on acoustic cavitation and its analysis of the enhancement and attenuation effect.

To understand the effect of coupling parameters between two ultrasonic waves on acoustic cavitation, in this work, Keller-Miksis equation was introduced to built a bubble dynamics model that was used to describe the dynamic evolution of bubble and to discuss the effect of dual-frequency coupling parameters, such as frequency difference f (5 âˆ¼ 280 kHz), phase difference φ (0 âˆ¼ 7π/4 rad), and power allocation ratio ß (0 âˆ¼ 9), on acoustic cavitation in the presence of two ultrasonic waves irradiation. The enhancement and attenuation effect of cavitation have also been analyzed in detail by comparing the different dual-frequency combinations with single-frequency mode. It was found that all coupling parameters have a significant impact on acoustic cavitation, where the smaller values of f and φ were employed when ß = 1, the stronger cavitation intensity was observed. Nevertheless, as the power allocation ratio is increased from 1 to 9 at φ = 0 for different frequency differences, the acoustic cavitation exhibits an attenuation trend. When the total acoustic power is evenly distributed, namely ß = 1, the largest maximum expansion ratio (i.e. 12.96) was obtained at φ = 0 and f = 5 kHz, which represents a strongest cavitation effect. In addition, for different frequency combinations, the enhancement effect is found under the mixture of low and low frequency, whereas attenuation effect is generated easily by the combination of high and low frequency. Moreover, the effect become more pronounced as the proportion of high frequency component increases.

Climate change increases carbon allocation to leaves in early leaf green-up.

Global greening, characterized by an increase in leaf area index (LAI), implies an increase in foliar carbon (C). Whether this increase in foliar C under climate change is due to higher photosynthesis or to higher allocation of C to leaves remains unknown. Here, we explored the trends in foliar C accumulation and allocation during leaf green-up from 2000 to 2017 using satellite-derived LAI and solar-induced chlorophyll fluorescence (SIF) across the Northern Hemisphere. The accumulation of foliar C accelerated in the early green-up period due to both increased photosynthesis and higher foliar C allocation driven by climate change. In the late stage of green-up, however, we detected decreasing trends in foliar C accumulation and foliar C allocation. Such stage-dependent trends in the accumulation and allocation of foliar C are not represented in current terrestrial biosphere models. Our results highlight that a better representation of C allocation should be incorporated into models.

Statistical considerations of phase 3 umbrella trials allowing adding one treatment arm mid-trial.

Master protocols, in particular umbrella trials and platform trials, when evaluating multiple experimental treatments with a common control, could save patient resource, increase trial efficiency, and reduce drug development cost. Compared to the phase 3 platform trials that allow unlimited number of experimental arms to be added, it is more practical for individual companies to evaluate two experimental arms with a common control in an umbrella trial and allow the second experimental arm to be added at a later time. There have been limited research done in this type of trials in terms of statistical properties and guidance. In this article, we present statistical considerations of a phase 3 three-arm umbrella design including Type I error control and power, as well as the optimal allocation ratio. We intend to not only complement the existing literature, but more importantly to provide practical guidance to pave the way for its implementation by individual companies.

Subgroup-adaptive randomization for subgroup confirmation in clinical trials.

A well-known issue when testing for treatment-by-subgroup interaction is its low power, as clinical trials are generally powered for establishing efficacy claims for the overall population, and they are usually not adequately powered for detecting interaction (Alosh, Huque, & Koch [2015] Journal of Biopharmaceutical Statistics, 25, 1161-1178). Hence, it is necessary to develop an adaptive design to improve the efficiency of detecting heterogeneous treatment effects within subgroups. Considering Neyman allocation can maximize the power of usual Z-test (see p. 194 of the book edited by Rosenberger and Lachin), we propose a subgroup-adaptive randomization procedure aiming to achieve Neyman allocation in both predefined subgroups and overall study population in this paper. To verify whether the proposed randomization procedure works as intended, relevant theoretical results are derived and displayed . Numerical studies show that the proposed randomization procedure has obvious advantages in power of tests compared with complete randomization and Pocock and Simon's minimization method.

How quota allocation affects the unified ETS of China: a simulation with dynamic CGE model.

The national unified carbon trading market has been officially launched at the end of 2017. The carbon emission quotas should be primary concern, which can be allocated in the form of free and paid ways. However, few literatures studied the economic and environmental impacts of quotas allocation. Thus, this paper constructs 7 scenarios and employs a dynamic, recursive computable general equilibrium (CGE) model to simulate carbon trading market, to probe the relationship between quota allocation and carbon price, and the economic and environmental impact of carbon trading scheme (ETS). Empirical results indicate (1) carbon price has an upward trend with time, which reflects a corresponding increase in emission reduction pressure. Specifically, carbon price increases from 12.44-90.57 CNY/t in 2017 to 65.20-523.44 CNY/t in 2030. In addition, whether under carbon intensity criterion (CIC) or carbon emission criterion (CEC), there is a positive relationship between carbon price and free allocation ratio due to the change of the relationship between supply and demand of quota. With a given free allocation ratio, the price formed with CIC grows faster than that with CEC. (2) Compared with the benchmark scenario, the GDP of China decreases in all scenarios. However, a high level of free allocation ratio combined with CIC may prevent GDP dropping too fast. (3) As for industrial output, covered industries in ETS undertake the largest output losses with an average decline by 4.03-13.60%. Similar to GDP variation, a high free allocation ratio combined with CIC is helpful for sustainable development of industry. (4) Carbon trading has a remarkable effect on emission reductions both in covered and uncovered industries of ETS. Free allocation will reduce market efficiency, which implies it should be cut down gradually at the later stages.

Implementing unequal randomization in clinical trials with heterogeneous treatment costs.

Equal randomization has been a popular choice in clinical trial practice. However, in trials with heterogeneous variances and/or variable treatment costs, as well as in settings where maximization of every trial participant's benefit is an important design consideration, optimal allocation proportions may be unequal across study treatment arms. In this paper, we investigate optimal allocation designs minimizing study cost under statistical efficiency constraints for parallel group clinical trials comparing several investigational treatments against the control. We show theoretically that equal allocation designs may be suboptimal, and unequal allocation designs can provide higher statistical power for the same budget or result in a smaller cost for the same level of power. We also show how optimal allocation can be implemented in practice by means of restricted randomization procedures and how to perform statistical inference following these procedures, using invoked population-based or randomization-based approaches. Our results provide further support to some previous findings in the literature that unequal randomization designs can be cost efficient and can be successfully implemented in practice. We conclude that the choice of the target allocation, the randomization procedure, and the statistical methodology for data analysis is an essential component in ensuring valid, powerful, and robust clinical trial results.

A comparative study of restricted randomization procedures for multiarm trials with equal or unequal treatment allocation ratios.

Randomization designs for multiarm clinical trials are increasingly used in practice, especially in phase II dose-ranging studies. Many new methods have been proposed in the literature; however, there is lack of systematic, head-to-head comparison of the competing designs. In this paper, we systematically investigate statistical properties of various restricted randomization procedures for multiarm trials with fixed and possibly unequal allocation ratios. The design operating characteristics include measures of allocation balance, randomness of treatment assignments, variations in the allocation ratio, and statistical characteristics such as type I error rate and power. The results from the current paper should help clinical investigators select an appropriate randomization procedure for their clinical trial. We also provide a web-based R shiny application that can be used to reproduce all results in this paper and run simulations under additional user-defined experimental scenarios.

Proposal Allocation Ratio as a Moderator of Interpersonal Responsibility Effects on Hostile Decision-Making in the Ultimatum Game.

Interpersonal responsibility is an indigenous Chinese personality construct, which is regarded to have positive social functions. Two studies were designed to explore the relationship among interpersonal responsibility, proposal allocation ratio, and responders' hostile decisions in an ultimatum game. Study 1 was a scenario study using a hypothetical ultimatum game with a valid sample of 551 high school students. Study 2 was an experimental study which recruited 54 undergraduate students to play the incentivized ultimatum game online. The results of the two studies showed a significantly negative correlation between interpersonal responsibility and responders' rejection responses only when the proposal allocation ratio was 3:7. In addition, in Study 2, interpersonal responsibility had negative effects on responders' rejection responses under the offer of 3:7, even after controlling for the Big Five personality traits. Taken together, proposal allocation ratio might moderate the effects of interpersonal responsibility on hostile decision-making in the ultimatum game. The social function of interpersonal responsibility might be beyond the Big Five.

Approaches to expanding the two-arm biased coin randomization to unequal allocation while preserving the unconditional allocation ratio.

The paper discusses three methods for expanding the biased coin randomization (BCR) to unequal allocation while preserving the unconditional allocation ratio at every step. The first method originally proposed in the contexts of BCR and minimization is based on mapping from an equal allocation multi-arm BCR. Despite the improvement proposed in this paper to ensure tighter adherence to the targeted unequal allocation, this method still distributes the probability mass at least as wide as the permuted block randomization (PBR). This works for smaller block sizes, but for larger block sizes, a tighter control of the imbalance in the treatment assignments is desired. The second method, which has two versions, allows to tighten the distribution of the imbalance compared with that achieved with the PBR. However, the distribution of the imbalance remains considerably wider than that of the brick tunnel randomization - the unequal allocation procedure with the tightest possible imbalance distribution among all allocation ratio preserving procedures with the same allocation ratio. Finally, the third method, the BCR with a preset proportion of maximal forcing, mimics the properties of the equal allocation BCR. With maximum forcing, it approaches the brick tunnel randomization, similar to how 1:1 BCR approaches 1:1 PBR with the permuted block size of 2 (the equal allocation procedure with the lowest possible imbalance) when the bias approaches 1. With minimum forcing, the BCR with a preset proportion of maximal forcing approaches complete randomization (similar to 1:1 BCR). Copyright © 2017 John Wiley & Sons, Ltd.

Brick tunnel randomization and the momentum of the probability mass.

The allocation space of an unequal-allocation permuted block randomization can be quite wide. The development of unequal-allocation procedures with a narrower allocation space, however, is complicated by the need to preserve the unconditional allocation ratio at every step (the allocation ratio preserving (ARP) property). When the allocation paths are depicted on the K-dimensional unitary grid, where allocation to the l-th treatment is represented by a step along the l-th axis, l = 1 to K, the ARP property can be expressed in terms of the center of the probability mass after i allocations. Specifically, for an ARP allocation procedure that randomizes subjects to K treatment groups in w1 :⋯:wK ratio, w1 +⋯+wK =1, the coordinates of the center of the mass are (w1 i,…,wK i). In this paper, the momentum with respect to the center of the probability mass (expected imbalance in treatment assignments) is used to compare ARP procedures in how closely they approximate the target allocation ratio. It is shown that the two-arm and three-arm brick tunnel randomizations (BTR) are the ARP allocation procedures with the tightest allocation space among all allocation procedures with the same allocation ratio; the two-arm BTR is the minimum-momentum two-arm ARP allocation procedure. Resident probabilities of two-arm and three-arm BTR are analytically derived from the coordinates of the center of the probability mass; the existence of the respective transition probabilities is proven. Probability of deterministic assignments with BTR is found generally acceptable. Copyright © 2015 John Wiley & Sons, Ltd.

The cavity-nest ant Temnothorax crassispinus prefers larger nests.

Colonies of the ant Temnothorax crassispinus inhabit mostly cavities in wood and hollow acorns. Typically in the field, nest sites that can be used by the ant are a limited resource. In a field experiment, it was investigated whether the ants prefer a specific size of nest, when different ones are available. In July 2011, a total of 160 artificial nests were placed in a beech-pine forest. Four artificial nests (pieces of wood with volume cavities, ca 415, 605, 730, and 980 mm3, respectively) were located on each square meter of the experimental plot. One year later, shortly before the emergence of new sexuals, the nests were collected. In July 2012, colonies inhabited more frequently bigger nests. Among queenright colonies, the ones which inhabited bigger nests had more workers. However, there was no relationship between volume of nest and number of workers for queenless colonies. Queenright colonies from bigger nests produced more sexual individuals, but there was no correlation between number of workers and sex allocation ratio, or between volume of nest and sex allocation ratio. In a laboratory experiment where ant colonies were kept in 470 and 860 mm3 nests, larger colonies allocated more energy to produce sexual individuals. The results of this study show the selectivity of T. crassispinus ants regarding the size of nest cavity, and that the nest volume has an impact on life history parameters.

Efficient treatment allocation in two-way nested designs.

Cluster randomized and multicenter trials sometimes combine two treatments A and B in a factorial design, with conditions such as A, B, A and B, or none. This results in a two-way nested design. The usual issue of sample size and power now arises for various clinically relevant contrast hypotheses. Assuming a fixed total sample size at each level (number of clusters or centers, number of patients), we derive the optimal proportion of the total sample to be allocated to each treatment arm. We consider treatment assignment first at the highest level (cluster randomized trial) and then at the lowest level (multicenter trial). We derive the optimal allocation ratio for various sets of clinically relevant hypotheses. We then evaluate the efficiency of each allocation and show that the popular balanced design is optimal or highly efficient for a range of research questions except for contrasting one treatment arm with all other treatment arms. We finally present simple equations for the total sample size needed to test each effect of interest in a balanced design, as a function of effect size, power and type I error α. All results are illustrated on a cluster-randomized trial on smoking prevention in primary schools and on a multicenter trial on lifestyle improvement in general practices.

Bayesian methods for the design and interpretation of clinical trials in very rare diseases.

This paper considers the design and interpretation of clinical trials comparing treatments for conditions so rare that worldwide recruitment efforts are likely to yield total sample sizes of 50 or fewer, even when patients are recruited over several years. For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible. Rather, the expectation of any such trial has to be limited to the generation of an improved understanding of treatment options. We propose a Bayesian approach for the conduct of rare-disease trials comparing an experimental treatment with a control where patient responses are classified as a success or failure. A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters. The process of determining the prior is described, including the possibility of formally considering results from related trials. As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates. A number of allocation ratios between the two treatment groups can be considered with a view to maximising the prior probability that the trial concludes recommending the new treatment when in fact it is non-inferior to control. Consideration of the extent to which opinion can be changed, even by data from the best feasible design, can help to determine whether such a trial is worthwhile.

Managing competing demands in the implementation of response-adaptive randomization in a large multicenter phase III acute stroke trial.

It is well known that competing demands exist between the control of important covariate imbalance and protection of treatment allocation randomness in confirmative clinical trials. When implementing a response-adaptive randomization algorithm in confirmative clinical trials designed under a frequentist framework, additional competing demands emerge between the shift of the treatment allocation ratio and the preservation of the power. Based on a large multicenter phase III stroke trial, we present a patient randomization scheme that manages these competing demands by applying a newly developed minimal sufficient balancing design for baseline covariates and a cap on the treatment allocation ratio shift in order to protect the allocation randomness and the power. Statistical properties of this randomization plan are studied by computer simulation. Trial operation characteristics, such as patient enrollment rate and primary outcome response delay, are also incorporated into the randomization plan.

POPULATION STRUCTURE, LOCAL MATE COMPETITION, AND SEX-ALLOCATION PATTERN IN THE ANT MESSOR ACICULATUS.

Population-genetic structure and sex-allocation ratios were investigated for the ant Messor aciculatus, a species that conducts mass nuptial flights. An electrophoretic survey on two polymorphic loci revealed excessive homozygosities in two populations. Because inbreeding inside nests does not occur, the heterozygote deficiency may result from population subdivision rather than assortative inbreeding during nuptial flights. Assuming no inbreeding, a simulation based on the observed genotype distribution in the study site suggested that, on average, a breeding swarm consists of alates from only 1.7 colonies. This population genetic structure seems to cause local mate competition (LMC), a factor that can shift population sex ratio toward females. The sex-allocation ratio to males in the population (0.166 ± 0.030; mean ± SE) was significantly female biased and lower than the expected optima for queens (0.5) and for workers (0.25) without LMC. Sex-ratio variability among colonies was explained by a pattern of constant male investment, which is predictable assuming LMC. Thus, the study provides the first evidence of LMC in ants with mass nuptial flights and contradicts previous assumptions about breeding structure in swarming ants. The results suggest that LMC can affect sex-allocation patterns for ant colonies and populations.