Effective sample size for georeferenced and temporally evolving data

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.

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

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.

P-values are misunderstood, but do not confound

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.

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.

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.

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.

Clinical prediction models are estimated using a sample of limited size from the target population, leading to uncertainty in predictions, even when the model is correctly specified. Generally, not all patient profiles are observed uniformly in model development. As a result, sampling uncertainty varies between individual patients' predictions. We aimed to develop an intuitive measure of individual prediction uncertainty. The variance of a patient's prediction can be equated to the variance of the sample mean outcome in hypothetical patients with the same predictor values. This hypothetical sample size can be interpreted as the number of similar patients that the prediction is effectively based on, given that the model is correct. For generalized linear models, we derived analytical expressions for the effective sample size. In addition, we illustrated the concept in patients with acute myocardial infarction. In model development, can be used to balance accuracy versus uncertainty of predictions. In a validation sample, the distribution of indicates which patients were more and less represented in the development data, and whether predictions might be too uncertain for some to be practically meaningful. In a clinical setting, the effective sample size may facilitate communication of uncertainty about predictions. We propose the effective sample size as a clinically interpretable measure of uncertainty in individual predictions. Its implications should be explored further for the development, validation and clinical implementation of prediction models.

The paper describes an investigation of parasite richness in relation to host life history and ecology using data from an extensive survey of helminth parasites (cestodes, trematodes and nematodes) in Soviet birds. Correlates of parasite richness (number of parasite species per host species) were sought among 13 life-history variables, 13 ecological variables and one non-biological variable (number of host individuals examined) across a sample of 158 species of host. A statistical method to control for the effects of phylogenetic association was adopted throughout. Parasite richness correlates positively with the number of hosts examined (sample size) in all three parasite groups. Positive correlations (after controlling for the effects of sample size) were also found between host body weight and parasite richness for trematodes and nematodes, but not for cestodes. A number of ecological variables were associated with parasite richness. However, when the effects of sample size and body weight were controlled for, only a single significant correlation (an association between trematode richness and aquatic habitat) remained. Similarly, a number of significant correlates of parasite richness were found among the life-history variables examined. Though several of these were robust to the confounding effects of sample size, all could be explained by the co-variation between life-history traits and body weight among the host species under investigation.

In their Report “Sample dimensions influence strength and crystal plasticity” (13 Aug., p. [986][1]), M. D. Uchic et al. demonstrate that the dimensions of micrometer-sized metal crystals have dramatic effects on the properties of the crystals. However, they do not mention a critical factor; namely, that oxide films were present on their specimens. All metals oxidize. Therefore, except for short times in ultra-high vacua, they have oxide (or hydroxide) surface films. These films have negligible effects on the behaviors of most macroscopic metals. As sizes decrease, however, they become increasingly important. The necessity for shearing through these films may well account for the increase in jaggedness of the stress-strain curves observed by the authors with decreasing size. Also, this interpretation is consistent with the lack of a “size effect” observed for the nickel-based superalloy, as well as the large glide offsets. # Response {#article-title-2} Gilman points out that a thin surface film (oxide or hydroxide) on a micrometer-sized crystal could affect the sample flow behavior, especially as the sample size decreases. He raises an important point. However, it is not entirely clear to us how a surface film could contribute significantly to the strength under progressively rising stresses, without also leading to severe strain localization. High-resolution scanning electron micrographs of deformed samples generally show slip traces at many points along the sample gage length. One might expect much more slip localization in these samples if oxide films were acting as strong barriers to deformation. The “jaggedness” of the stress-strain response that Gilman mentions may be simply the result of mechanical testing at the micrometer scale. A slip event in a micrometer-sized crystal will be more clearly resolved than if the same event occurred in a millimeter-sized sample. In addition, Gilman indicates that the lack of a “size effect” in nickel-based superalloys is consistent with the interpretation that surface films are affecting the observed mechanical behavior. Although this is open to interpretation, we have recently learned through additional testing that sample size effects of the type discussed in our Report do occur for a nickel-based superalloy at sample sizes that are 5 μm in diameter and smaller ([1][2]). Finally, significant sample size effects have recently been observed in testing of 1-μm-diameter single crystals of pure gold ([2][3]), using the same fabrication and testing methodology. The magnitude of the size-dependent strengthening is similar to the results for pure nickel. However, gold does not form a native oxide. Clearly, more research is needed to positively establish the connection between sample size effects to either changes in deformation mechanisms or extrinsic effects such as surface case hardening. 1. 1.[↵][4] 1. M. D. Uchic, 2. D. M. Dimiduk , in preparation. 2. 2.[↵][5] 1. J. R. Greer, 2. W. C. Oliver, 3. W. D. Nix , presentation at the 2004 Fall Minerals, Metal, and Materials Society Meeting, New Orleans, LA, 26 to 29 Sept. 2004. [1]: /lookup/doi/10.1126/science.1098993 [2]: #ref-1 [3]: #ref-2 [4]: #xref-ref-1-1 View reference 1. in text [5]: #xref-ref-2-1 View reference 2. in text

This paper describes an experimental investigation on the effect of sample size on consolidation characteristics of fissured London Clay. Pore pressure dissipation tests on 38, 100, and 300 mm diameter samples were undertaken in the laboratory. Constant-head in situ permeability tests were conducted in four boreholes at different depths in the clay. Conventional oedometer tests on 76 mm diameter samples recovered from the same depths at which in situ permeability tests were carried out were also undertaken. The results show that both the coefficient of compressibility mv and the coefficient of consolidation determined in the laboratory are not significantly affected by sample size. It is concluded that estimate of in situ coefficient of consolidation can best be made from mv determined in the laboratory, and from in situ permeability measurements. Key words: consolidation, compressibility, fissured clay, permeability, size effect, testing.

Effect of sample size on Case II diffusion of methanol in poly(methyl methacrylate) beads

Effective sample size: Quick estimation of the effect of related samples in genetic case–control association analyses