Optimal Allocation Ratio Research Articles

Optimal treatment allocation and study duration for trials with discrete-time survival endpoints

Studies on event occurrence may be conducted in experiments, where one or more treatment groups are compared to a control group. Most of the randomized trials are designed with equally sized groups, but this design is not always the best one. The statistical power of the study may be larger with unequal sample sizes, and researchers may want to place more participants in one group relative to the other due to resource constraints or costs. The optimal designs for discrete-time survival endpoints in trials with two groups, where different proportions of subjects in the experimental group are taken into account, can be studied using the generalized linear model. Applying a cost function, the optimal combination of the number of subjects and periods in the study and the optimal allocation ratio can be found. It is observed that the ratio of the recruitment costs in both groups, the ratio of the recruitment cost in the control group to the cost of obtaining a measurement, the size of the treatment effect, and the shape of the survival distribution have the greatest influence on the optimal design.

A two-way enriched clinical trial design: combining advantages of placebo lead-in and randomized withdrawal

A new clinical trial design, designated the two-way enriched design (TED), is introduced, which augments the standard randomized placebo-controlled trial with second-stage enrichment designs in placebo non-responders and drug responders. The trial is run in two stages. In the first stage, patients are randomized between drug and placebo. In the second stage, placebo non-responders are re-randomized between drug and placebo and drug responders are re-randomized between drug and placebo. All first-stage data, and second-stage data from first-stage placebo non-responders and first-stage drug responders, are utilized in the efficacy analysis. The authors developed one, two and three degrees of freedom score tests for treatment effect in the TED and give formulae for asymptotic power and for sample size computations. The authors compute the optimal allocation ratio between drug and placebo in the first stage for the TED and compare the operating characteristics of the design to the standard parallel clinical trial, placebo lead-in and randomized withdrawal designs. Two motivating examples from different disease areas are presented to illustrate the possible design considerations.

Route-based data envelopment analysis models

This paper proposes two novel route-based data envelopment analysis (DEA) models that jointly measure the route-level and company-level efficiencies amongst transport carriers. The core logics comprise a three-stage procedure that determines company efficiency, route efficiency and optimal allocation ratios for the common inputs. We prove that the ranking order of company performance determined by the route-based DEA model is identical to that determined by the company-based DEA model. An empirical case demonstrates the superiority of the proposed models in identifying the less efficient routs/companies as well as in reducing the input slacks without subjective conjectures.

Optimality, sample size, and power calculations for the sequential parallel comparison design

The sequential parallel comparison design (SPCD) has been proposed to increase the likelihood of success of clinical trials in therapeutic areas where high-placebo response is a concern. The trial is run in two stages, and subjects are randomized into three groups: (i) placebo in both stages; (ii) placebo in the first stage and drug in the second stage; and (iii) drug in both stages. We consider the case of binary response data (response/no response). In the SPCD, all first-stage and second-stage data from placebo subjects who failed to respond in the first stage of the trial are utilized in the efficacy analysis. We develop 1 and 2 degree of freedom score tests for treatment effect in the SPCD. We give formulae for asymptotic power and for sample size computations and evaluate their accuracy via simulation studies. We compute the optimal allocation ratio between drug and placebo in stage 1 for the SPCD to determine from a theoretical viewpoint whether a single-stage design, a two-stage design with placebo only in the first stage, or a two-stage design is the best design for a given set of response rates. As response rates are not known before the trial, a two-stage approach with allocation to active drug in both stages is a robust design choice.

Statistical Efficiency in Multiple-to-One Comparison Trials with Optimal Allocation Ratio

This paper discusses multiple-to-one comparison trials testing a multivalent vaccine product against multiple comparators with respect to immunologic responses. An optimal subject allocation ratio between the multivalent vaccine group and any of the comparators is introduced. This optimal ratio leads to higher statistical efficiency in terms of savings in sample size compared to equal allocation or any other allocation ratios. Several trial design scenarios are considered including assumptions of equal standardized effect size, unequal variance, and unequal standardized effect sizes of the multivalent vaccines versus the multiple comparators.

A group sequential type design for three-arm non-inferiority trials with binary endpoints

The three-arm design with a test treatment, an active control and a placebo group is the gold standard design for non-inferiority trials if it is ethically justifiable to expose patients to placebo. In this paper, we first use the closed testing principle to establish the hierarchical testing procedure for the multiple comparisons involved in the three-arm design. For the effect preservation test we derive the explicit formula for the optimal allocation ratios. We propose a group sequential type design, which naturally accommodates the hierarchical testing procedure. Under this proposed design, Monte Carlo simulations are conducted to evaluate the performance of the sequential effect preservation test when the variance of the test statistic is estimated based on the restricted maximum likelihood estimators of the response rates under the null hypothesis. When there are uncertainties for the placebo response rate, the proposed design demonstrates better operating characteristics than the fixed sample design.

A simulation study for comparing testing statistics in response-adaptive randomization

BackgroundResponse-adaptive randomizations are able to assign more patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent. At large sample sizes, many asymptotic properties of test statistics derived for independent sample comparison are still applicable in adaptive randomization provided that the patient allocation ratio converges to an appropriate target asymptotically. However, the small sample properties of commonly used test statistics in response-adaptive randomization are not fully studied.MethodsSimulations are systematically conducted to characterize the statistical properties of eight test statistics in six response-adaptive randomization methods at six allocation targets with sample sizes ranging from 20 to 200. Since adaptive randomization is usually not recommended for sample size less than 30, the present paper focuses on the case with a sample of 30 to give general recommendations with regard to test statistics for contingency tables in response-adaptive randomization at small sample sizes.ResultsAmong all asymptotic test statistics, the Cook's correction to chi-square test (TMC) is the best in attaining the nominal size of hypothesis test. The William's correction to log-likelihood ratio test (TML) gives slightly inflated type I error and higher power as compared with TMC, but it is more robust against the unbalance in patient allocation. TMC and TML are usually the two test statistics with the highest power in different simulation scenarios. When focusing on TMC and TML, the generalized drop-the-loser urn (GDL) and sequential estimation-adjusted urn (SEU) have the best ability to attain the correct size of hypothesis test respectively. Among all sequential methods that can target different allocation ratios, GDL has the lowest variation and the highest overall power at all allocation ratios. The performance of different adaptive randomization methods and test statistics also depends on allocation targets. At the limiting allocation ratio of drop-the-loser (DL) and randomized play-the-winner (RPW) urn, DL outperforms all other methods including GDL. When comparing the power of test statistics in the same randomization method but at different allocation targets, the powers of log-likelihood-ratio, log-relative-risk, log-odds-ratio, Wald-type Z, and chi-square test statistics are maximized at their corresponding optimal allocation ratios for power. Except for the optimal allocation target for log-relative-risk, the other four optimal targets could assign more patients to the worse arm in some simulation scenarios. Another optimal allocation target, RRSIHR, proposed by Rosenberger and Sriram (Journal of Statistical Planning and Inference, 1997) is aimed at minimizing the number of failures at fixed power using Wald-type Z test statistics. Among allocation ratios that always assign more patients to the better treatment, RRSIHR usually has less variation in patient allocation, and the values of variation are consistent across all simulation scenarios. Additionally, the patient allocation at RRSIHR is not too extreme. Therefore, RRSIHR provides a good balance between assigning more patients to the better treatment and maintaining the overall power.ConclusionThe Cook's correction to chi-square test and Williams' correction to log-likelihood-ratio test are generally recommended for hypothesis test in response-adaptive randomization, especially when sample sizes are small. The generalized drop-the-loser urn design is the recommended method for its good overall properties. Also recommended is the use of the RRSIHR allocation target.

Noninferiority trial designs for odds ratios and risk differences

This study presents constrained maximum likelihood derivations of the design parameters of noninferiority trials for binary outcomes with the margin defined on the odds ratio (ψ) or risk-difference (δ) scale. The derivations show that, for trials in which the group-specific response rates are equal under the point-alternative hypothesis, the common response rate, π(N), is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point-null, {π(C), π(E)}. We show that setting π(N) equal to the value of π(C) that holds under H(0) underestimates the overall sample size requirement. Given {π(C), ψ} or {π(C), δ} and the type I and II error rates, or algorithm finds clinically meaningful design values of π(N), and the corresponding minimum asymptotic sample size, N=n(E)+n(C), and optimal allocation ratio, γ=n(E)/n(C). We find that optimal allocations are increasingly imbalanced as ψ increases, with γ(ψ)<1 and γ(δ)≈1/γ(ψ), and that ranges of allocation ratios map to the minimum sample size. The latter characteristic allows trialists to consider trade-offs between optimal allocation at a smaller N and a preferred allocation at a larger N. For designs with relatively large margins (e.g. ψ>2.5), trial results that are presented on both scales will differ in power, with more power lost if the study is designed on the risk-difference scale and reported on the odds ratio scale than vice versa.

Productivity Analysis of Eggs Production in Khorasan Razavi Province, Iran

Egg production is one of most important agricultural economic activities in Iran. According to latest information in Iran, there were about 1432 poultry eggs farms producing about 576478 tons of edible eggs in 2005. The poultry farmers, however, complained that cost of production was very high and that failed to gain considerable profit from their farming operations. The consumers, on other hand, protested that poultry price was very high. The purpose of this study is to determine productivity of industry so that a more sustainable and high productivity production system can be developed . Production function was used to measure productivity. A transcendental production function was estimated using cross-sectional data collected from 47 farmers in Khorasan Razavi province. Secondary data from Iranian Statistical Year Book (published by Statistical Center of Iran) were also used. The results of study found that cost-benefit ratio was 0.96. The Average Product (AP), Marginal Product (MP), Value Marginal Product (VMP), Optimal Allocation Ratio and Elasticity of Production (EP) of feed input were 0.41, 0.16, 577 Rials, 0.48 and 41% respectively. The findings for similar measures above for pullet input were 18.38, 4.24, 14826 Rials, 1.23 and 0.23 respectively. From study, average productivity of poultry farm was 1.04. This shows that income approximately equals variable cost. When fixed costs were taken into consideration, profit of average farm was negative. The results indicated that farmers were using feed more than the optimal level and that they were using pullet less than the optimal level. Therefore, to improve profitability, they should use less feed and keep more pullets. In this manner, cost of production can be reduced.

Overpriced Puts Puzzle in KOSPI 200 Options Market

The purpose of this paper is to examine the argument that the put options traded in the exchanges are too high, compared to the asset prices based on the classical CAPM model, and thus the short position of the put option would make a significant profit from trading. In order to explore the earlier report, this paper, using the KOSPI 200 index options market price, estimates the historical rate of return on several option trading strategies such as naked option, protective put, covered call, straddle, and strangle. Secondly this paper compares the historical rates of return on the option trading strategies and Sharpe ratios with those generated by Monte-Carlo simulation and examines whether the historical option returns are inconsistent with Black-Scholes model, Jump-diffusion model, Stochastic Volatility model, or Stochastic Volatility with Jump model. Thirdly, this paper computes the optimal asset allocation ratio among the risk-free asset, risky assets, and option trading strategies in the viewpoint of rational investors who maximize the CRRA utility function. The results show that the historical returns on short position of ATM and OTM puts are too high to explain based on the classical CAPM, and the optimal allocation ratios among put, risky asset, and the risk-free asset are different from those derived using Monte-Carlo simulation.

Least-energy optimization of forced convection plate-fin heat sinks

A coefficient of performance (COP/sub T/) analysis for plate fin heat sinks in forced convection is presented and shown to provide a viable technique for combining least-material optimization with the entropy minimization methodology. The COP/sub T/ metric relates the heat sink cooling capability to the invested fan pumping work and the thermodynamic work required to manufacture and assemble the heat sink. The proposed optimization methodology maximizes the forced convection cooling that can be achieved by a heat sink occupying a specified volume, with a fixed energy investment and entropy generation rate. In addition, the study identifies the presence of an optimal resource allocation ratio, providing the most favorable distribution of existing energy resources, between heat sink manufacturing and operation, over a fixed product life cycle.

Video scalability rate control method by dynamic controlling of hierarchical bit allocation ratio

AbstractThis paper considers the hierarchical video coding system, and proposes a bit allocation rate control method by dynamic control of the hierarchical bit allocation ratio. As the first step, the MPEG‐2 SNR scalability method is considered as the hierarchical video coding, and the relation between the hierarchical bit allocation and the basic/enhancement layer quality is analyzed. It is shown that the intermediate bit allocation ratio may degrade greatly the quality in the enhancement layer. The dependency of the image quality on the hierarchical bit allocation is noted, and video coding bit allocation control is proposed, where the hierarchical loss can be suppressed by dynamically controlling the bit allocation ratio for each picture. A control method is proposed particularly, where the optimal bit allocation ratio is calculated so that the characteristic function is maximized under the constraint that the bit allocation ratio for each GOP is kept constant. Lastly, a simulation experiment is presented. It is shown that the hierarchical loss, which is generated in the conventional bit allocation control, can be suppressed by the proposed control method, and the effectiveness of the proposed method is demonstrated. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 86(1): 83–96, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.1149

Modeling for point–non-point source effluent trading: perspective of non-point sources regulation in China

In the past decades, little abatement efforts have been implemented on China's non-point source water pollution, and studies aiming at non-point sources regulation were also rare. Watershed abatement trading between point and non-point sources may serve as a cost-effective way to deal with the problem. The inherent uncertainty of non-point emissions, however, could affect the feasibility and outcome of point–non-point effluent trading. The purpose of this paper is to model the watershed point–non-point abatement trading incorporating the uncertainty of non-point source emissions, and to examine its impacts on trading equilibrium and trading ratio. The uncertainties of non-point emissions were taken into consideration by setting an acceptable probability by which the watershed emission constraints were achieved. Using the watershed optimization model, the optimal abatement allocation and trading ratio were explicitly illustrated. It was found that they were affected significantly by the variances of non-point emissions, the reliability requirement assigned to the non-point abatement, and the marginal abatement costs of point and non-point sources. Since the variances of non-point emissions may increase or decrease at the abatement level, the impacts of these factors were discussed in different circumstances. Based on the illumination of the trading model, future directions and implications of point–non-point trading in China were discussed.

配電系統における電圧安定性の向上を目的としたNAS電池の最適配置および最適PQ出力比

In recent years, many studies have been made on allocating Na-S batteries in distribution substations to make good use of power facilities and improve the load factor. Besides, it has also been a hope to utilize Na-S batteries for controls such as AFC (automatic frequency control) or VQC (voltage reactive-power control), because Na-S batteries can respond faster than existing generator units and can control active and reactive power outputs independently by the function of AC-DC converter systems. In this paper, the authors propose a method for determining the optimal allocation and PQ output ratio of Na-S batteries in order to improve voltage stability. The proposed method combines a sensitivity method with an optimal power flow calculation method to determine the allocation and PQ output ratio efficiently and optimally. Simulations are carried out for a 73-bus distribution system to illustrate and verify the proposed method.

98/02247 First year of operation of Provence SOPROLIF 250 MW CFB boiler

In this paper we determine the fundamental relation between global performance and flow configuration (constructal design) in the case of steam power generation with superheater and reheater placed in parallel in the same stream of hot gases of combustion. The superheater heats the steam for the high pressure turbine, and the reheater supplies steam to the low pressure turbine. Both turbines operate irreversibly. We consider superheaters and reheaters with balanced counter flows and unbalanced counter flows. The total heat transfer area (or the overall number of heat transfer units) is finite. We show that the heat transfer area can be allocated to the superheater and reheater such that the overall power output is maximum. The optimal area allocation ratio is reported for two scenarios: designs with and without a maximum allowable steam temperature.

98/00669 Influence of internal heat leak on the performance of refrigerators

In the present study, an optimization model is developed for plate-fin heat exchangers (PFHEs) based on the entropy generation minimization method. In the modeling, the entropy generation rate per unit partition plate area, i.e., specific entropy generation rate is proposed as an optimization objective function and the total heat transfer area of a PFHE is considered as a constraint. The model takes into account the irreversibility due to both irreversible heat transfer and pressure drop. The analysis of optimal allocation of total heat transfer area between the hot- and cold-side for a PFHE is conducted with a case study. The results show that optimal geometric parameters of a PFHE such as the fin spacing and fin height on both the hot- and cold-sides can be achieved when the finite total heat transfer area is optimally allocated with minimizing the specific entropy generation rate. In addition, the effects of total heat transfer area, heat transfer rate, as well as the ratio of mass flow rate between the cold- and hot-side fluid on the specific entropy generation rate and optimal allocation ratio of total heat transfer area are also analyzed.