This parametric study aimed to analyze the effects of increased magnetic field exposure (MFE) on the growth and production of the bioactive compounds of Chlorella (C.) vulgaris. With the intent of studying the effect of an increased MFE, the magnetic field typically experienced by life on Earth was amplified by an order of magnitude. In the increased-MFE environment, six treatments of C. vulgaris with two repetitions for each treatment were exposed to a magnetic field of 5 Gauss (500 µT) about each axis, which was generated in a state-of-the-art Helmholtz cage. The treatments and the control were characterized by the duration of exposure, which was varied from 0 min to 120 min with a step increment of 20 min. The treatments were repeated for six days (TR1) and twelve days (TR2) in two separate experiments. From the first day of the treatment, the specimens in both the experiments were propagated for twenty-one days. For parametric analysis, the overall growth, protein, and beta-carotene content were measured every three days for twenty-one days. For TR1 in general, the samples treated with the increased MFE demonstrated a higher growth rate than the control. Specifically, for the specimen treated with 40 min of the increased MFE, the growth on the 21st day was measured to be 38% higher than the control. For the specimen treated with 120 min of the increased MFE, the protein content on the 15th day was measured to be 15.6% higher than the control. For the specimen treated with 40 min of the increased MFE, the beta-carotene content on the 15th day was measured to be 20.4% higher than the control. For TR2 in general, the results were inferior compared to TR1 but showed higher production than the control specimen. Specifically, for the specimen treated with 80 min of the increased MFE, the protein content on the 21st day was measured to be 4.3% higher than the control. For the specimen treated with 100 min of the increased MFE, the beta-carotene content on the 15th day was measured to be 17.1% higher than the control. For the specimen treated with 100 min of the increased MFE, the growth on the 21st day was measured to be 5% higher than the control. Overall, the treated specimens in TR1 exhibited significantly higher production compared to the control specimen. The treated specimen in TR2 demonstrated some adverse impacts, but still exhibited higher production compared to the control specimen.

Clustered data are a special type of correlated data where units within a cluster are correlated while units between different clusters are independent. The number of units in a cluster can be associated with that cluster’s outcome. This is called the informative cluster size (ICS), which is known to impact clustered data inference. However, when comparing the outcomes from multiple groups of units in clustered data, investigating ICS may not be enough. This is because the number of units belonging to a particular group in a cluster can be associated with the outcome from that group in that cluster, leading to an informative intra-cluster group size or IICGS. This phenomenon of IICGS can exist even in the absence of ICS. Ignoring the existence of IICGS can result in a biased inference for group-based outcome comparisons in clustered data. In this article, we mathematically formulate the concept of IICGS while distinguishing it from ICS and propose a nonparametric bootstrap-based statistical hypothesis-testing mechanism for testing any claim of IICGS in a clustered data setting. Through simulations and real data applications, we demonstrate that our proposed statistical testing method can accurately identify IICGS, with substantial power, in clustered data.

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on the outcomes. However, when potentially important covariate data is available in observational studies, ignoring these covariate effects on the outcomes can result in a flawed inference. In this article, using rank based weighted estimating equations, we propose a robust procedure for covariate effect adjusted comparison of paired outcomes in a clustered data that can also address the issue of informative cluster size. Through simulated scenarios and real-life neuroimaging data, we demonstrate the importance of considering covariate effects during paired testing and robust performances of our proposed method in covariate adjusted paired comparisons in complex clustered data settings.

In cluster‐correlated data, the number of observations in a cluster can be associated with the outcome from that cluster. This phenomenon is known as informative cluster size which can occur in cluster‐randomized clinical trial data. Several studies have found that ignoring the issue of informative cluster size can produce biased results in the analysis of clustered data. Most of the existing methods for addressing informative cluster size are suited to continuous outcomes. However, ordinal outcomes and covariates are often encountered in clustered data obtained from large clinical studies. The existing methods for ordinal association testing in clustered data can produce suboptimal results in the presence of informative cluster size. In this article, we propose a new nonparametric method for testing marginal association between ordinal variables in clustered data that can account for informative cluster size. Through simulated data analyses, we show that our new test outperforms the existing alternatives in accurately identifying significant marginal ordinal associations in the presence of informative cluster size. Even if the cluster size is not informative, the performance of our method is comparable to the existing methods. Additionally, we demonstrate the usefulness of our proposed method through an application to a real‐world cluster‐randomized clinical trial data.

Teen-to-teen (t2t) crisis lines are a special type of crisis service where youth volunteers help their peers. Although prior research has examined the experience of adult crisis line responders, no research has examined the experience of adolescents who do this work. In collaboration with two of the largest t2t lines in the U.S., this pilot study is the first examination of t2t crisis line work. Volunteers (ages 14–20) reported: their primary motivation for joining the crisis lines was to help others and give back to the community; responding to a range of peers’ problems on the t2t crisis line, including high-risk suicide contacts; and a range of ways the crisis line work impacted their lives. Findings provide preliminary information about the experience of adolescents engaging in t2t crisis line work. Additional research is needed in larger and more diverse samples to understand the impact of crisis line work for youth.