Statistical cluster points of sequences in finite dimensional spaces

summary:In this paper we study the set of statistical cluster points of sequences in $m$-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in $m$-dimensional spaces too. We also define a notion of $\Gamma$-statistical convergence. A sequence $x$ is $\Gamma$-statistically convergent to a set $C$ if $C$ is a minimal closed set such that for every $\epsilon > 0$ the set $\lbrace k\:\rho (C, x_k ) \ge \epsilon \rbrace$ has density zero. It is shown that every statistically bounded sequence is $\Gamma$-statistically convergent. Moreover if a sequence is $\Gamma$-statistically convergent then the limit set is a set of statistical cluster points

LID - 10.1016/j.euf.2020.09.010 [doi]

BACKGROUND: Atezolizumab (ATZ) has demonstrated antitumor activity and manageable safety in previous studies in patients with locally advanced or metastatic platinum-resistant urothelial carcinoma. OBJECTIVE: To compare the real-life experience and data of clinical trials on ATZ treatment in metastatic urothelial carcinoma. DESIGN, SETTING, AND PARTICIPANTS: Patients with urothelial cancer treated with ATZ after progression on first-line chemotherapy from an expanded access program were retrospectively studied. Data of patients were obtained from their files and hospital records. Safety was evaluated for patients treated with at least one cycle of ATZ. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: The primary endpoint was objective response rate (ORR). The secondary endpoints are overall survival (OS), progression-free survival (PFS), duration of response, and safety profile of patients. Kaplan-Meier methods were used to calculate median follow-up and estimate PFS and OS. RESULTS AND LIMITATIONS: Data of 115 enrolled patients were analyzed. Most of the patients (92.3%, n = 106) had received chemotherapy regimen only once prior to ATZ. The median follow-up duration was 23.5 mo. The complete response rate, partial response rate, and ORR were 8.7% (n = 10), 20.0% (n = 23), and 28.7% (n = 33), respectively. The median duration of response was 20.4 mo (95% confidence interval [CI], 6.47-28.8). Of the 33 patients who responded to treatment, 60% (n = 20) had an ongoing response at the time of the analysis. PFS and OS with ATZ were 3.8 mo (95% CI, 2.25-5.49) and 9.8 mo (95% CI, 6.7-12.9), respectively. All-cause and any-grade adverse events were observed in 113 (98%) patients. Of the patients, 64% experienced a treatment-related adverse event of any grade and 24 (21.2%) had a grade 3-4 treatment-related adverse event. Limitations of the study included its retrospective design, and determination of treatment response based on clinical notes and local radiographic studies. CONCLUSIONS: In these real-life data, ATZ was effective and well tolerated in patients with metastatic urothelial carcinoma who have progressed with platinum-based first-line chemotherapy. ATZ is an effective and tolerable treatment for patients with locally advanced or metastatic platinum-resistant urothelial carcinoma in our study, similar to previously reported trials. PATIENT SUMMARY: Atezolizumab is effective and well-tolerated in patients with metastatic urothelial cancer who progressed with first-line chemotherapy, consistent with the outcomes of the previous clinical trials in this setting

AgroEcoList 1.0: A checklist to improve reporting standards in ecological research in agriculture.

Many publications lack sufficient background information (e.g. location) to be interpreted, replicated, or reused for synthesis. This impedes scientific progress and the application of science to practice. Reporting guidelines (e.g. checklists) improve reporting standards. They have been widely taken up in the medical sciences, but not in ecological and agricultural research. Here, we use a community-centred approach to develop a reporting checklist (AgroEcoList 1.0) through surveys and workshops with 23 experts and the wider agroecological community. To put AgroEcoList in context, we also assessed the agroecological community's perception of reporting standards in agroecology. A total of 345 researchers, reviewers, and editors, responded to our survey. Although only 32% of respondents had prior knowledge of reporting guidelines, 76% of those that had said guidelines improved reporting standards. Overall, respondents agreed on the need of AgroEcolist 1.0; only 24% of respondents had used reporting guidelines before, but 78% indicated they would use AgroEcoList 1.0. We updated AgroecoList 1.0 based on respondents' feedback and user-testing. AgroecoList 1.0 consists of 42 variables in seven groups: experimental/sampling set-up, study site, soil, livestock management, crop and grassland management, outputs, and finances. It is presented here, and is also available on github (https://github.com/AgroecoList/Agroecolist). AgroEcoList 1.0 can serve as a guide for authors, reviewers, and editors to improve reporting standards in agricultural ecology. Our community-centred approach is a replicable method that could be adapted to develop reporting checklists in other fields. Reporting guidelines such as AgroEcoList can improve reporting standards and therefore the application of research to practice, and we recommend that they are adopted more widely in agriculture and ecology

AgroEcoList 1.0: A checklist to improve reporting standards in ecological research in agriculture.

Many publications lack sufficient background information (e.g. location) to be interpreted, replicated, or reused for synthesis. This impedes scientific progress and the application of science to practice. Reporting guidelines (e.g. checklists) improve reporting standards. They have been widely taken up in the medical sciences, but not in ecological and agricultural research. Here, we use a community-centred approach to develop a reporting checklist (AgroEcoList 1.0) through surveys and workshops with 23 experts and the wider agroecological community. To put AgroEcoList in context, we also assessed the agroecological community's perception of reporting standards in agroecology. A total of 345 researchers, reviewers, and editors, responded to our survey. Although only 32% of respondents had prior knowledge of reporting guidelines, 76% of those that had said guidelines improved reporting standards. Overall, respondents agreed on the need of AgroEcolist 1.0; only 24% of respondents had used reporting guidelines before, but 78% indicated they would use AgroEcoList 1.0. We updated AgroecoList 1.0 based on respondents' feedback and user-testing. AgroecoList 1.0 consists of 42 variables in seven groups: experimental/sampling set-up, study site, soil, livestock management, crop and grassland management, outputs, and finances. It is presented here, and is also available on github (https://github.com/AgroecoList/Agroecolist). AgroEcoList 1.0 can serve as a guide for authors, reviewers, and editors to improve reporting standards in agricultural ecology. Our community-centred approach is a replicable method that could be adapted to develop reporting checklists in other fields. Reporting guidelines such as AgroEcoList can improve reporting standards and therefore the application of research to practice, and we recommend that they are adopted more widely in agriculture and ecology

Same data, different analysts: variation in effect sizes due to analytical decisions in ecology and evolutionary biology

Gould E, Fraser H, Parker T, et al. Same data, different analysts: variation in effect sizes due to analytical decisions in ecology and evolutionary biology. 2023.Although variation in effect sizes and predicted values among studies of similar phenomena is inevitable, such variation far exceeds what might be produced by sampling error alone. One possible explanation for variation among results is differences among researchers in the decisions they make regarding statistical analyses. A growing array of studies has explored this analytical variability in different (mostly social science) fields, and has found substantial variability among results, despite analysts having the same data and research question. We implemented an analogous study in ecology and evolutionary biology, fields in which there have been no empirical exploration of the variation in effect sizes or model predictions generated by the analytical decisions of different researchers. We used two unpublished datasets, one from evolutionary ecology (blue tit, Cyanistes caeruleus, to compare sibling number and nestling growth) and one from conservation ecology (Eucalyptus, to compare grass cover and tree seedling recruitment), and the project leaders recruited 174 analyst teams, comprising 246 analysts, to investigate the answers to prespecified research questions. Analyses conducted by these teams yielded 141 usable effects for the blue tit dataset, and 85 usable effects for the Eucalyptus dataset. We found substantial heterogeneity among results for both datasets, although the patterns of variation differed between them. For the blue tit analyses, the average effect was convincingly negative, with less growth for nestlings living with more siblings, but there was near continuous variation in effect size from large negative effects to effects near zero, and even effects crossing the traditional threshold of statistical significance in the opposite direction. In contrast, the average relationship between grass cover and Eucalyptus seedling number was only slightly negative and not convincingly different from zero, and most effects ranged from weakly negative to weakly positive, with about a third of effects crossing the traditional threshold of significance in one direction or the other. However, there were also several striking outliers in the Eucalyptus dataset, with effects far from zero. For both datasets, we found substantial variation in the variable selection and random effects structures among analyses, as well as in the ratings of the analytical methods by peer reviewers, but we found no strong relationship between any of these and deviation from the meta-analytic mean. In other words, analyses with results that were far from the mean were no more or less likely to have dissimilar variable sets, use random effects in their models, or receive poor peer reviews than those analyses that found results that were close to the mean. The existence of substantial variability among analysis outcomes raises important questions about how ecologists and evolutionary biologists should interpret published results, and how they should conduct analyses in the future