Sample Allocation Research Articles

Stochastic Control Framework for Determining Feasible Alternatives in Sampling Allocation

We formulate the optimal dynamic sampling allocation decision problem for feasibility determination as a stochastic control problem in a Bayesian setting. This new formulation addresses the limitations of previous static optimization formulations. In an approximate dynamic programming paradigm, we propose an approximately optimal allocation policy that maximizes a single feature of the value function one step ahead. Numerical results demonstrate the efficiency of the proposed method.

Economic Analysis of Silkworm Rearing and Cocoon Production in Bilaspur District of Himachal Pradesh

Sericulture is an agro-based multitudinous activity which involves cultivation of mulberry, production of laying, rearing of silkworms for cocoons, marketing and reeling of cocoons for value added products such as processing and weaving of the yarn. It is a short gestation period labour intensive enterprise which can go a long way in promoting inclusive growth and alleviating poverty in rural areas. The present study was therefore carried out in order to analyse investment and returns pattern of cocoon production in Bilaspur district of Himachal Pradesh. Two-stage random sampling and proportional allocation method was used to prepare a list of sample farmers. Out of 60 silkworm rearers, 19 were large and 41 were small. The dry cocoon production per farm on small and large category was estimated at 8.25 kg (6.20 kg in spring and 2.05 kg in autumn) and 19.51 kg (16.67 kg in spring and 2.84 kg in autumn). The dry cocoon production per ounce of seed was found to be 20.28 kg and 26.14 kg on small and large category households for both the seasons together. The fixed cost of production / ounce for spring crop varied from 9.92 per cent on small farms to 14.75 per cent on large farms. The variable cost varied from 90.08 per cent on small farms to 85.25 per cent on large farms implying the economical use of fixed and variable resources by large growers. The gross returns per ounce seed basis ranged between ` 1,626 and ` 5,535 on small and large farms for the spring crop. The autumn crop was found to give negative returns; therefore farmers should be provided with technology which could reduce the moisture in the rearing room, develop humidity resistant races of silkworms as well as develop varieties of mulberry plantation which may yield good leaves just after rainy season.

Effect of cluster configuration and auxiliary variables on the efficiency of local pivotal method for national forest inventory

ABSTRACTPlanning a forest inventory comprises making decisions related to the sampling strategy: cluster configuration, sample size and sample allocation within the survey area. Cluster configuration includes deciding on the number of sample plots within the cluster and distances between them. Available resources set the limit for field work in terms of man-days. If the time consumption for measurements is known, the sample size can be determined under the constraint. In this study, we simulated the second phase of inventory sampling with fixed time resources by replicating sample selection with a spatially balanced sampling utilizing local pivotal method (LPM) for different cluster configurations to find the most efficient. As a result, the temporary cluster configuration was changed from 9 to 5-sample plot configuration in a pilot inventory. Further, the sample selection was performed with LPM having total growing stock volume and broadleaf volume proportion as auxiliary information. The pilot results were aligned with the time series in respect to forest area and total growing stock volume, but in tree species groups deviations were observed in growing stock volume. A more comprehensive optimization should include the travelling routes, the plot-to-plot distances and the plot design. In any case, the result is region specific.

Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions

One-shot devices, such as rockets, airbags of automobiles, and electro-explosive devices, can be used only once and will be extensively destroyed. The actual lifetimes of the devices cannot be observed, no matter whether the outcomes are successful or not. Step-stress accelerated life tests, which are useful for shortening the lifetimes of devices and quickly collecting lifetime data in a limited time, are widely adopted in engineering reliability studies. However, optimal designs of step-stress accelerated life tests for one-shot devices have not been well studied. This paper provides a procedure of determining optimal designs of simple step-stress accelerated life tests for one-shot devices by minimizing the asymptotic variance of the maximum likelihood estimate of reliability at normal operating conditions under Weibull distributions, with respect to inspection times and sample allocations. Comprehensive simulation studies are carried out to study the optimal designs under Weibull distributions with various hazard rates, showing that the optimal designs can maintain the simulated standard deviations at the nominal level of standard error. Besides, sensitivity analysis is conducted to evaluate the robustness of determined designs when mis-specification on planning values of model parameters exists. Finally, an application in grease-based magnetorheological fluids is presented to illustrate the optimal designs.

Multi-objective ranking and selection: Optimal sampling laws and tractable approximations via SCORE

ABSTRACTConsider the multi-objective ranking and selection (MORS) problem in which we select the Pareto-optimal set from a finite set of systems evaluated on three or more stochastic objectives. Toward determining how to allocate a simulation budget among the systems, we characterise the asymptotically optimal sample allocation that maximises the misclassification-probability decay rate, and we provide an implementable allocation called MO-SCORE. The MO-SCORE allocation simultaneously controls the probabilities of misclassification by exclusion and inclusion, identifies phantom Pareto systems crucial for computational efficiency, and models dependence between the objectives. The MO-SCORE allocation is fast and accurate for problems with three objectives or a small number of systems. For problems with four or more objectives and a large number of systems, we propose independent MO-SCORE (iMO-SCORE). Our numerical experience is extensive and promising: MO-SCORE and iMO-SCORE can be used to solve MORS problems involving several thousand systems in three and four objectives.

Robustness of Statistical Power in Group-Randomized Studies of Mediation Under an Optimal Sampling Framework

Abstract. When planning group-randomized studies probing mediation, effective and efficient sample allocation is governed by several parameters including treatment-mediator and mediator-outcome path coefficients and the mediator and outcome intraclass correlation coefficients. In the design stage, these parameters are typically approximated using information from prior research and these approximations are likely to deviate from the true values eventually realized in the study. This study investigates the robustness of statistical power under an optimal sampling framework to misspecified parameter values in group-randomized designs with group- or individual-level mediators. The results suggest that estimates of statistical power are robust to misspecified parameter values across a variety of conditions and tests. Relative power remained above 90% in most conditions when the incorrect parameter value ranged between 50% and 150% of the true parameter.

Bound Constrained Optimization of Sample Sizes Subject to Monetary Restrictions in Planning Multilevel Randomized Trials and Regression Discontinuity Studies

Sample size determination in multilevel randomized trials (MRTs) and multilevel regression discontinuity designs (MRDDs) can be complicated due to multilevel structure, monetary restrictions, differing marginal costs per treatment and control units, and range restrictions in sample size at one or more levels. These issues have sparked a set of studies under optimal design literature where scholars consider sample size determination as an allocation problem. The literature on optimal design of MRTs and MRDDs and their implementation in software packages has been scarce, scattered, and incomplete. This study unifies optimal design literature and extends currently available software under bound constrained optimal sample allocation (BCOSA) framework via bound constrained optimization technique. The BCOSA framework, introduction to the cosa R library, and an illustration that replicates and extends minimum required sample size determination for an evaluation report is provided.

Impact of Green Marketing Mix (4Ps) on Firm Performance: Insights from Industrial Sector Peshawar, Pakistan

Abstract Background & Purpose- After the year 2000, the market for environmentally friendly products become mature and substantially expanded. In the present condition, environmental poverty has appeared as a very scorching issue of concern. The alarming level effects of commercial sector on climate and atmosphere have shaped several life threatening worries. To manage with this, it becomes a great challenge for organizations. The current research work is aim to achieve a better understanding of the corporate sector and their adaptation of green strategies in their production and decisions; associated to firm performance. This is an effort to check the belongings of green marketing strategy (GMS) on firm performance. Methodology- The current work was grounded on quantitative technique to test the framed hypotheses. Survey procedure is used to collect the data. 264 respondent were taken into account by applying method of sample determination and allocation. Purposive sampling technique with “five-point Likert scale” was utilized for data assortment. PCA were utilized to measure the unifactoriality. Structure Equation Modeling were used to check the hypothesized relationship b/w the variables. Findings- Findings of the study suggests that green product (GPD), green price (GPC), green promotion (GPM) and green place are absolutely correlated to firm performance with significant P-value <.05. Originality/Value- The current research study can help industrial sector in identifying best solutions for replacing conventional activities used. Limitation & Future Directions- Research study is restricted only to Peshawar, Khyber Pakhtunkhwa, other areas were not in the domain of interest. It is suggested for the forthcoming research to splay the study background across the country. Larger sample size is also recommended. It can provide more faultless data, though the current population and sample size was enough for the justification of the results.

Robustness of asymptotic accelerated life test plans to small‐sample settings

AbstractMuch of the statistical literature on optimal test planning for accelerated life testing utilize asymptotic methods to derive optimal test plans. While sufficient effort is made to assess the robustness of these test plans to the choice of design parameters and distribution assumptions, there is very little literature on the performance of asymptotic test plans relative to small samples (on the order of 10‐15 samples). An alternative concern is that the asymptotic test plans may not necessarily be the true “optimal” test plan for a given sample size. The purpose of this research is to present exact or “near‐exact” methods for developing test plans and compare the performance of these test plans with corresponding asymptotic test plans in small‐sample settings. The optimal location of design points and sample allocation is determined using each method for lognormal and Weibull lifetime distributions with both complete and Type 1 right‐censored data under two selected acceleration factor models. The investigations reveal that asymptotic test plans tend to corroborate quite well with exact test plans and thus are suitably robust to small‐sample settings in terms of optimal variance.

Handheld flow meter improves COPD detectability regardless of using a conventional questionnaire: A split-sample validation study.

Improved detectability of chronic obstructive pulmonary disease (COPD) using a handheld flow meter (HFM) with symptom-based questionnaires has not been sufficiently evaluated. This study aimed to identify the benefit of using an HFM in COPD screening. A total of 2008 participants, who were ≥ 40 years of age, from Isumi City, Japan, were recruited. We developed two novel point systems for detecting COPD, one incorporated score of HFM alone (sHFM) and the other incorporated the score of International Primary Care Airway Group questionnaire (IPAG) and HFM (sIPAG + HFM). Validation using random sample allocation (split-sample validation) was carried out to assess the predictive performance of these models. Participants were assigned to a data set for model creation (n = 1007) or a data set for model assessment (n = 1001) to perform split-sample validation. Decision curve analysis showed that the net benefits of sHFM and sIPAG + HFM were higher than that of the IPAG score (sIPAG) and specificity of the former two were also significantly higher than that of sIPAG. However, the curves of sHFM and sIPAG + HFM were crossing and practically the same with no significant difference in sensitivity and specificity. This study confirms that HFM is significantly advantageous in detecting COPD despite the use of a conventional questionnaire.

Methodological elements for optimising the spatial monitoring design to support regional benthic ecosystem assessments.

Benthic habitat condition assessments are a requirement under various environmental directives. The Marine Strategy Framework Directive (MSFD), for example, challenges member states in a European sea region to perform comparable assessments of good environmental status and improve coherence of their monitoring programmes by 2020. Currently, North Sea countries operate independent monitoring programmes using nationally defined assessment areas. Lack of an agreed OSPAR or EU scale monitoring method and programme has been identified as a priority science need. This paper proposes a method for the development of a coherent and efficient spatial sampling design for benthic habitats on regional level and gives advice on optimal monitoring effort to get more accurate assessments. We use ecologically relevant assessment areas (strata) across national borders and test spatial sample allocation methods. Furthermore, we investigate the number of samples needed in each stratum to reduce the variance for estimating mean number of taxa and abundance. The stratification needs to take into account the spatial heterogeneity of the entire ecosystem. The total sample effort is optimal when sample allocation takes into account the size and benthic variability within those strata. Change point analysis helps to find a balance between sampling effort and precision of the benthic parameter estimate. A joint sampling design for the North Sea could be generated by combining current efforts, and where needed adapting existing national programmes. This serves a coordinated, region-wide, benthic condition status assessment and strengthens regional cooperation to fulfil multiple monitoring tasks, with a scientifically underpinned common approach.

CLASSIFICATION ACCURACY ASSESSMENT FOR REGIONAL VECTOR DATA PRODUCT BASED ON SPATIAL SAMPLING: A CASE STUDY OF JAPAN

Abstract. Spatial vector data is a kind of data that represents real spatial information through points, lines and polygons. Spatial data quality is one of the basic theoretical research in geographic information science. Accurate and reliable data quality assessment is very important for its theoretical significance and practical value. This paper proposes an improved method for the traditional classification accuracy evaluation of spatial vector data: (1) Quantitative estimation of sample size. According to the statistical principle of probability theory, the overall quantity is estimated by controlling the sampling error and the acceptance quality level. The sample quality is the unbiased estimate of the overall quality. (2) Stratification strategy: the overall objects are divided into three layers according to the three basic geometric structures -- points, lines and polygons. The difference within the layer is small and the difference between layers is large, which conforms to the basic principle of stratification. Then, the proportion of the total number of elements in each layer is taken as the weight to distribute layer by layer, and the sample size of each layer is obtained. (3) Allocation of samples. The spatial property of spatial sampling is mainly reflected in the allocation of samples. Considering the spatial correlation of elements in same layer, Local Moran's I index was used to calculate the correlation degree of a certain attribute between each spatial element and its neighbouring elements. After cluster analysis of elements in each layer, samples were screened by setting a reasonable threshold value. (4) Sample inspection. Each sample was examined against reference information, including images and data. The classification of each sample is judged by the principle of majority judgment. (5) Classification accuracy assessment. The classification accuracy information of samples was obtained by making the confusion matrix of the classification result of samples and the real results. The classification accuracy of experimental data is evaluated according to Kappa index. A case study of Global Core Vector Data of Japan shows the improved method in this paper and process of classification accuracy assessment for regional spatial vector data product. Global Core Vector Data are organized according to the country or region, including three categories of transportation, river system, place names, which are divided into 8 middle categories and 52 small categories. In this paper, 1405 samples of Global Core Vector Data in the experimental area of Japan are selected by spatial stratified sampling in 3 strata. The experimental results show that the proposed improved method is applicable to classification accuracy assessment of regional spatial vector data product and overcomes the disadvantages of type-based spatial stratified sampling that relies on the classification information of all elements. The Kappa coefficient is 0.831, which reflects the result of classification accuracy assessment in the experimental area is good. The proposed improved method provides a reference for the method of classification accuracy assessment classification of following global spatial vector data product.

Optimal Design of Cluster- and Multisite-Randomized Studies Using Fallible Outcome Measures.

Evaluation studies frequently draw on fallible outcomes that contain significant measurement error. Ignoring outcome measurement error in the planning stages can undermine the sufficiency and efficiency of an otherwise well-designed study and can further constrain the evidence studies bring to bear on the effectiveness of programs. We develop simple formulas to adjust statistical power, minimum detectable effect (MDE), and optimal sample allocation formulas for two-level cluster- and multisite-randomized designs when the outcome is subject to measurement error. The resulting adjusted formulas suggest that outcome measurement error typically amplifies treatment effect uncertainty, reduces power, increases the MDE, and undermines the efficiency of conventional optimal sampling schemes. Therefore, achieving adequate power for a given effect size will typically demand increased sample sizes when considering fallible outcomes, while maintaining design efficiency will require increasing portions of a budget be applied toward sampling a larger number of individuals within clusters. We illustrate evaluation planning with the new formulas while comparing them to conventional formulas using hypothetical examples based on recent empirical studies. To encourage adoption of the new formulas, we implement them in the R package PowerUpR and in the PowerUp software.

Associations of Symptomatic Knee Osteoarthritis With Histopathologic Features in Subchondral Bone.

Subchondral bone and the osteochondral junction are thought to contribute to osteoarthritis (OA) knee pain. We undertook this study to identify osteochondral pathologies specifically associated with symptomatic human knee OA. Medial tibial plateau samples from 2 groups of subjects (n = 31 per group) were matched for macroscopic chondropathy scores. The symptomatic chondropathy group had undergone total knee replacement for OA knee pain, at which time specimens of the medial tibial plateau were obtained. The asymptomatic chondropathy group included subjects who died of unrelated illness (specimens were obtained at postmortem examination) and who had not previously sought help for knee pain. OA histopathology, immunoreactivity for nerve growth factor (NGF) and CD68 (macrophages), tartrate-resistant acid phosphatase-positive subchondral osteoclasts, and synovitis were compared between groups. Mankin scores, subchondral bone density, and subchondral CD68-immunoreactive macrophage infiltration were similar between the 2 groups. NGF-like immunoreactivity was found in subchondral mononuclear cells and osteoclasts, as well as in chondrocytes. NGF in osteochondral channels and osteoclast densities in subchondral bone were higher in the symptomatic chondropathy group than in the asymptomatic chondropathy group (P < 0.01 and P = 0.02, respectively), as were synovitis scores (P < 0.01). Osteochondral pathology was not significantly associated with synovitis score. The differences in NGF expression and in osteoclast density remained significant after adjustment for age and synovitis score (P = 0.01 and P = 0.04, respectively). Osteochondral NGF and osteoclast densities, together with synovitis scores, explained ~28% of sample allocation to symptomatic or asymptomatic groups. Subchondral pathology was associated with symptomatic knee OA, independent of chondropathy and synovitis. Increased NGF expression in osteochondral channels and increased osteoclast density appear to be key features associated with bone pain in knee OA.

Performance-Based Nested Surrogate Modeling of Antenna Input Characteristics

Utilization of electromagnetic (EM) simulation tools is mandatory in the design of contemporary antenna structures. At the same time, conducting design procedures that require multiple evaluations of the antenna at hand, such as parametric optimization or yield-driven design, is hindered due to the high cost of accurate EM analysis. To a certain extent, this issue can be addressed using fast replacement models (also referred to as surrogates). Unfortunately, due to curse of dimensionality, traditional data-driven surrogate modeling methods are limited to antenna structures described by a few parameters with relatively narrow parameter ranges. This is by no means sufficient given the complexity of modern designs. In this paper, a novel technique for surrogate modeling of antenna structures is proposed. It involves a construction of two levels of surrogates, both realized as kriging interpolation models. The first model is based on a set of reference designs optimized for selected performance figures. It is used to establish a domain for the final (second level) surrogate. This formulation permits efficient modeling within wide ranges of antenna geometry parameters and wide ranges of performance figures (e.g., operating frequencies). At the same time, it allows uniform allocation of training data samples in a straightforward manner. Our approach is demonstrated using two microstrip antenna examples and is compared with conventional kriging and radial basis function modeling. Application examples for antenna optimization are also provided along with experimental validation.

A practical approach to improve the statistical performance of surface water monitoring networks

The representativeness of aquatic ecosystem monitoring and the precision of the assessment results are of high importance when implementing the EU’s Water Framework Directive that aims to secure a good status of waterbodies in Europe. However, adapting monitoring designs to answer the objectives and allocating the sampling resources effectively are seldom practiced. Here, we present a practical solution how the sampling effort could be re-allocated without decreasing the precision and confidence of status class assignment. For demonstrating this, we used a large data set of 272 intensively monitored Finnish lake, coastal, and river waterbodies utilizing an existing framework for quantifying the uncertainties in the status class estimation. We estimated the temporal and spatial variance components, as well as the effect of sampling allocation to the precision and confidence of chlorophyll-a and total phosphorus. Our results suggest that almost 70% of the lake and coastal waterbodies, and 27% of the river waterbodies, were classified without sufficient confidence in these variables. On the other hand, many of the waterbodies produced unnecessary precise metric means. Thus, reallocation of sampling effort is needed. Our results show that, even though the studied variables are among the most monitored status metrics, the unexplained variation is still high. Combining multiple data sets and using fixed covariates would improve the modeling performance. Our study highlights that ongoing monitoring programs should be evaluated more systematically, and the information from the statistical uncertainty analysis should be brought concretely to the decision-making process.

Strategies for Efficient Experimental Design in Studies Probing 2-1-1 Mediation

When well-implemented, mediation analyses play a critical role in probing theories of action because their results help lay the ground work for the critical development of a treatment and the iterative advancement of theories that are foundational to a discipline. Despite strong interest in designs that incorporate mediation, few studies have developed effective and efficient strategies to plan experiments examining multilevel mediation. We probe several design strategies for cluster-randomized designs and derive sampling plans that maximize power under cost constraints. The results suggest that among the more durable design strategies for mediation is covariance adjustment on variables predictive of the outcome and optimal sample allocation. The statistical power and optimal sample allocation results are implemented in the R package PowerUpR.

Response-adaptive treatment allocation for clinical studies with ordinal responses.

Ordinal responses are common in clinical studies. Although the proportional odds model is a popular option for analyzing ordered-categorical data, it cannot control the type I error rate when the proportional odds assumption fails to hold. The latent Weibull model was recently shown to be a superior candidate for modeling ordinal data, with remarkably better performance than the latent normal model when the data are highly skewed. In clinical trials with ordinal responses, a balanced design is common, with equal sample allocation for each treatment. However, a more ethical approach is to adopt a response-adaptive allocation scheme in which more patients receive the better treatment. In this paper, we propose the use of the doubly adaptive biased coin design to generate treatment allocations that benefit the trial participants. The proposed treatment allocation scheme not only allows more patients to receive the better treatment, it also maintains compatible test power for the comparison of treatment efficiencies. A clinical example is used to illustrate the proposed procedure.

Enhanced uniform data sampling for constrained data‐driven modeling of antenna input characteristics

AbstractData‐driven surrogates are the most popular replacement models utilized in many fields of engineering and science, including design of microwave and antenna structures. The primary practical issue is a curse of dimensionality, which limits the number of independent parameters that can be accounted for in the modeling process. Recently, a performance‐driven modeling technique has been proposed where the constrained domain of the model is spanned by a set of reference designs optimized with respect to selected figures of interest. This approach allows for significant improvement of prediction power of the surrogates without the necessity of reducing the parameter ranges. Yet uniform allocation of the training data samples in the constrained domain remains a problem. Here, a novel design of experiments technique ensuring better sample uniformity is proposed. Our approach involves uniform sampling on the domain‐spanning manifold and linear transformation of the remaining sample vector components onto orthogonal directions with respect to the manifold. Two antenna examples are provided to demonstrate the advantages of the technique, including application case studies (antenna optimization).

Optimal Sample Allocation in Group-Randomized Mediation Studies with a Group-Level Mediator

We derive sample-allocation formulas that maximize the power of several mediation tests in two-level–group-randomized studies under a linear cost structure and fixed budget. The results suggest that the optimal individual sample size is typically smaller than that associated with the detection of a main effect and is frequently less than 10 under parameter values commonly seen in the literature. However, the optimal sample allocation can be heavily influenced by the group-to-individual cost ratio, the ratio of the treatment-mediator to mediator-outcome path coefficients, and the outcome variance structure. We illustrate these findings with a hypothetical group-randomized trial examining a school-discipline reform policy. To encourage utilization of the sample allocation formulas we implement them in the R package PowerUpR and powerupr Shiny application.