Sampling Grain Shipments To Detect Genetically Modified Seed

When food manufacturers specify a maximum limit for the amount of foreign material (FM) in the lot, handlers estimate the true percent FM in a commercial lot by measuring FM in a small sample taken from the lot before shipment to a food manufacturer. Because of the uncertainty (variability) in FM among samples taken from the same lot, it is difficult to obtain a precise estimate of the true FM in the lot. The objectives of this study were to (1) measure the variability and FM distribution among sample test results when estimating the true lot proportion of FM in a lot of shelled peanuts, (2) compare the measured variability and FM distribution among sample test results to that predicted by the binomial distribution, (3) develop a computer model, based upon the binomial distribution, to evaluate the performance (buyer's risk and seller's risk) of sampling plan designs used to estimate FM in a bulk lot of shelled peanuts, and (4) demonstrate with the model the effect of increasing sample size to reduce misclassification of lots. Eighty-eight samples, 9 kg (20 lb) each, were selected at random from each of six commercial lots of shelled medium runner peanuts. The percent FM (PFM), based upon number of kernels was determined for each sample. The mean, variance, and distribution among the 88 sample test results were calculated for each of the six lots. Results indicated that the variance and distribution among the 88 sample test results are very similar to that predicted by the binomial distribution. The performance of various sampling plan designs was demonstrated using the binomial distribution.

StarLink is a genetically modified corn that produces an insecticidal protein, Cry9C. Studies were conducted to determine the variability and Cry9C distribution among sample test results when Cry9C protein was estimated in a bulk lot of corn flour and meal. Emphasis was placed on measuring sampling and analytical variances associated with each step of the test procedure used to measure Cry9C in corn flour and meal. Two commercially available enzyme-linked immunosorbent assay kits were used: one for the determination of Cry9C protein concentration and the other for % StarLink seed. The sampling and analytical variances associated with each step of the Cry9C test procedures were determined for flour and meal. Variances were found to be functions of Cry9C concentration, and regression equations were developed to describe the relationships. Because of the larger particle size, sampling variability associated with cornmeal was about double that for corn flour. For cornmeal, the sampling variance accounted for 92.6% of the total testing variability. The observed sampling and analytical distributions were compared with the Normal distribution. In almost all comparisons, the null hypothesis that the Cry9C protein values were sampled from a Normal distribution could not be rejected at 95% confidence limits. The Normal distribution and the variance estimates were used to evaluate the performance of several Cry9C protein sampling plans for corn flour and meal. Operating characteristic curves were developed and used to demonstrate the effect of increasing sample size on reducing false positives (seller's risk) and false negatives (buyer's risk).

BackgroundDifferent colorectal cancer (CRC) studies rarely report overlapping prognostic genes. This study aimed to investigate the effects of sample size on prognostic genes analysis in CRC.MethodsWe included 418 CRC cases detected by whole-exome sequencing (WES) in the TCGA PanCancer cohort and 931 CRC cases detected by targeted sequencing in the MSK cohort. Prognostic genes analysis was repeated 200 times at each sample size level using a random resampling method.ResultsFor WES data, the number of prognostic genes increased in a power-law with increasing sample size in CRC cases with stage III and IV. This pattern also applied to CRC patients with stage II after the removal of patients with MSI-H or POLE mutations. However, for targeted sequencing data, the number of prognostic genes increased linearly with increasing sample size in CRC cases with stage III and IV. About 550 cases were required for stage IV CRC to reach the plateau of prognostic genes. In both cohorts, the proportion of true prognostic genes relative to sample size was consistent with a binomial distribution, indicating a significant effect of sample size on the reliability of prognostic genes. At the same sample size level, the number of prognostic genes from the WES data was higher than that from the targeted sequencing data, while the reliability of prognostic genes from the WES data was lower.ConclusionThis study shows the relationship between the number of prognostic genes and sample size in CRC and how mutation data affects this relationship. This will contribute to the trial design for prognostic genetic analysis in CRC.

Bayesian methods allow borrowing of historical information through prior distributions. The concept of prior effective sample size (prior ESS) facilitates quantification and communication of such prior information by equating it to a sample size. Prior information can arise from historical observations; thus, the traditional approach identifies the ESS with such a historical sample size. However, this measure is independent of newly observed data, and thus would not capture an actual "loss of information" induced by the prior in case of prior-data conflict. We build on a recent work to relate prior impact to the number of (virtual) samples from the current data model and introduce the effective current sample size (ECSS) of a prior, tailored to the application in Bayesian clinical trial designs. Special emphasis is put on robust mixture, power, and commensurate priors. We apply the approach to an adaptive design in which the number of recruited patients is adjusted depending on the effective sample size at an interim analysis. We argue that the ECSS is the appropriate measure in this case, as the aim is to save current (as opposed to historical) patients from recruitment. Furthermore, the ECSS can help overcome lack of consensus in the ESS assessment of mixture priors and can, more broadly, provide further insights into the impact of priors. An R package accompanies the paper.

Hulson, P-J. F., Hanselman, D. H., and Quinn, T. J. II. 2011. Effects of process and observation errors on effective sample size of fishery and survey age and length composition using variance ratio and likelihood methods. – ICES Journal of Marine Science, 68: 1548–1557. Observations of age or length composition from fisheries or research surveys are modelled frequently with the multinomial distribution. Violations of multinomial assumptions in data collection usually cause overdispersion of observations and consequent underestimation of uncertainty. This has led to the adoption of an effective sample size less than the actual sample size to approximate the likelihood function for age or length composition better in, for example, fishery stock assessment models. The behaviour of effective sample size is examined under different scenarios for population age distribution and sampling design. Effective sample size was approximated with three approaches: (i) the ratio of multinomial to empirical variance; (ii) sampling estimation; and (iii) the Dirichlet likelihood. The most significant changes in effective sample size were attributable to process error involving aggregation of ages within schools. In terms of observation error, effective sample size can be increased by increasing the number of tows from which samples are obtained for age or length composition, then, because of the reduced uncertainty in effective sample size, the Dirichlet likelihood can be integrated into the objective function of fishery stock assessment models to estimate the effective sample size in future assessments.

The primary focus of the paper is to establish both numerical and experimental methods to control the concentration of samples in a microreactor well. The concentration of the reacting samples is controlled by varying the initial sample size and electric field. Further, the paper numerically investigates the feasibility of mixing and reacting nanoliter samples with a wide variation in reaction rates in the microreactor driven by electro-osmotic pumping. Two discrete samples are measured and transported to the microreactor simultaneously by electro-osmotic pinching and switching. The transported samples are mixed in the microreactor and floated for 4.5 s for reaction to occur. It is seen that the normalized concentration of the product increases from 0.25 to 0.45 during that period. Also the effects of sample size and applied electric field on sample concentration during the switching process are studied. It is found that the normalized final sample concentration increases from 0.03 to 0.11 with an increase in sample size from 60 to 150 µm, at a constant electric field. Further, by increasing the electric field from 100 to 1000 V cm−1, at a constant sample size, there is a significant decrease in the final concentration of the sample from 0.14 to 0.04. Our studies also show that the normalized product concentration depends on the reaction rate and increases from 0.28 to 0.48 as the reaction rate increases from 10 L mol−1 s−1 to 105 L mol−1 s−1. However, the increase in the reaction rate beyond 105 L mol−1 s−1 does not influence the product concentration for the present design of the microreactor. Our microreactor with improved mixing can be used for assessing reactions of biological samples. The optimized sample size along with a controlled electric field for sample injection forms the basis for developing a prototype of a microreactor device for high throughput drug screening.

Log Pearson III distribution — Effect of dependence, distribution parameters and sample size on peak annual flood estimates

The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model, and principal axes factor analyses were performed. The results indicated that when the population congruence coefficient is zero, the sampling distribution of the congruence coefficient is relatively stable and is similar to the sampling distribution of the correlation coefficient. The congruence coefficient was found to be positively biased for values of psi from .10 to .40 and negatively biased for the following values of psi: .50, .60, .90, and .99. The amount of bias (a) depends on the sample size and the number of variables used and (b) tends to decrease as sample size increases.

Indoor positioning system has been an essential work to substitute the Global Positioning System (GPS). GPS utilizing Global Navigation Satellite Systems (GNSS) cannot provide an accurate positioning in the indoor due to the multipath effect and shadow fading. Fingerprinting method with Wi-Fi technology is a promising system to solve this issue. However, there are several problems with the fingerprinting method. The fingerprinting database collected has different sample sizes where the previous researcher does not indicate any standard for the sample size to be used. In this paper, the effect of the sample sizes in fingerprinting database for Wi-Fi technology has been discussed deeply. The statistical analyzation for different sample sizes has been analyzed. Furthermore, two methods which are K- Nearest Neighbor (KNN) and Deep Neural Network (DNN) are being used to examine the effect of the sample sizes in term of accuracy and distance error. The discussion in this paper will contribute to the better sample size selection depending on the method taken by the user. The result shows that sample sizes are an important metrics in developing the indoor positioning system as it effects the result of the location estimation.

The identification of prognostic genes can help in the clinical management of non-small cell lung cancer (NSCLC). However, there is little overlap in the prognostic genes identified in different NSCLC studies. One reason for this may be the inadequate sample size. Here, the effect of sample size on prognostic genes analysis was investigated based on 515 stage II/III NSCLC cases from two cohorts detected by whole-exome sequencing. Prognostic genes analysis was repeatedly performed 100 times for each sample size level using random resampling methods. In stage II lung adenocarcinoma (LUAD) and lung squamous cell carcinoma (LUSC) cases from the TCGA Pan-Lung Cancer cohort, the number of statistically significant prognostic genes first increased with sample size in a power law, then fluctuated steadily, and finally decreased slightly. The power law growth curves were also observed in stage III LUAD and LUSC cases from the TCGA Pan-Lung Cancer cohort and stage III Chinese LUAD cases from the OncoSG cohort. The correlation R2 of the fitted power law growth curves were all greater than 0.99. In addition, at the sample size level where the number of prognostic genes peaked, the mean proportion of true prognostic genes in patients with stage II LUAD and LUSC was 28.32% and 23.12%, which could partly explain the little overlap in prognostic genes between reports. In conclusion, the number of prognostic genes takes a power law growth with the sample size in NSCLC, independent of histopathological subtype, race, and stage. These results also show how sample size affects the reliability of prognostic genes and will aid trial design for genomic mutation-based prognostic studies in NSCLC.

P-values are misunderstood, but do not confound

Although smouldering ignition of upholstery items remains a leading cause of residential fire deaths, relatively little research is conducted on the topic. An experimental investigation of the effect of sample size on the ignition and spread of smouldering and flaming in polyurethane foam under natural flow conditions is reported here. Polyurethane foam samples are used because this is a common material in modern, residential environments and one for which there exists significant quantities of previous experimental data in the literature. Samples of different square cross-section size and a fixed height of 150 mm are insulated on all sides except the top which is exposed to a radiant heat flux and is open to the air. Samples with side lengths of 50 mm, 100 mm, and 140 mm are studied. Ignition and spread dynamics are diagnosed using thirteen thermocouples located along the vertical centre line. The onset of smouldering ignition (13 $$\hbox{kW}\, \hbox{m}^{-2}$$ , 8 $$\hbox{kW}\, \hbox{m}^{-2}$$ and $$7\,\hbox{kW}\, \hbox{m}^{-2}$$ for 50 mm, 100 mm and 140 mm sample sizes respectively) is observed at significantly lower heat fluxes that flaming (45 $$\hbox{kW}\,\hbox{m}^{-2}$$ , 32 $$\hbox{kW}\,\hbox{m}^{-2}$$ and $$30\,\hbox{kW}\,\hbox{m}^{-2}$$ respectively). Critical heat fluxes for smouldering and flaming ignition increase with decreasing sample size, with smouldering ignition being significantly more sensitive to sample size than flaming ignition under the size range studied. Smouldering spread rates are measured in the range from 3 $$\hbox{mm}\, \hbox{min}^{-1}$$ to $$25\,\hbox{mm}\, \hbox{min}^{-1}$$ and found to be a strong function of the heat flux and depth of the smoulder front. The effect of sample size on smouldering has been theoretically proposed before but this is the first time that this effect has been demonstrated experimentally for ignition. The fact that large samples result in the lowest critical heat flux could have implications for testing procedures and translation of results from small-scale testing to real-scale in the built environment.

Adequate description of hydraulic variables based on a sample of field measurements is challenging in coarse‐bed streams, a consequence of high spatial heterogeneity in flow properties that arises due to the complexity of channel boundary. By applying a resampling procedure based on bootstrapping to an extensive field data set, we have estimated sampling variability and its relationship with sample size in relation to two common methods of representing flow characteristics, spatially averaged velocity profiles and fitted probability distributions. The coefficient of variation in bed shear stress and roughness length estimated from spatially averaged velocity profiles and in shape and scale parameters of gamma distribution fitted to local values of bed shear stress, velocity, and depth was high, reaching 15–20% of the parameter value even at the sample size of 100 (sampling density 1 m−2). We illustrated implications of these findings with two examples. First, sensitivity analysis of a 2‐D hydrodynamic model to changes in roughness length parameter showed that the sampling variability range observed in our resampling procedure resulted in substantially different frequency distributions and spatial patterns of modeled hydraulic variables. Second, using a bedload formula, we showed that propagation of uncertainty in the parameters of a gamma distribution used to model bed shear stress led to the coefficient of variation in predicted transport rates exceeding 50%. Overall, our findings underscore the importance of reporting the precision of estimated hydraulic parameters. When such estimates serve as input into models, uncertainty propagation should be explicitly accounted for by running ensemble simulations.

Determining the sample size of an experiment can be challenging, even more so when incorporating external information via a prior distribution. Such information is increasingly used to reduce the size of the control group in randomized clinical trials. Knowing the amount of prior information, expressed as an equivalent prior effective sample size (ESS), clearly facilitates trial designs. Various methods to obtain a prior's ESS have been proposed recently. They have been justified by the fact that they give the standard ESS for one-parameter exponential families. However, despite being based on similar information-based metrics, they may lead to surprisingly different ESS for nonconjugate settings, which complicates many designs with prior information. We show that current methods fail a basic predictive consistency criterion, which requires the expected posterior-predictive ESS for a sample of size N to be the sum of the prior ESS and N. The expected local-information-ratio ESS is introduced and shown to be predictively consistent. It corrects the ESS of current methods, as shown for normally distributed data with a heavy-tailed Student-t prior and exponential data with a generalized Gamma prior. Finally, two applications are discussed: the prior ESS for the control group derived from historical data and the posterior ESS for hierarchical subgroupanalyses.

We examine various methods to estimate the effective sample size for construction of confidence intervals for survival probabilities. We compare the effective sample sizes of Cutler and Ederer and Peto et al., as well as a modified Cutler-Ederer effective sample size. We investigate the use of these effective sample sizes in the common situation of many censored observations that intervene between the time point of interest and the last death before this time. We note that there is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric. We recommend the use of the Cutler-Ederer effective sample size in construction of upper confidence intervals and the Peto effective sample size in construction of lower confidence intervals. Two examples with real data demonstrate the differences between confidence intervals formed with different effective sample sizes. This study also illustrates the need for caution in the application of simulation studies to real problems.