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In many cluster randomization studies, cluster sizes are not fixed and may be highly variable. For those studies, sample size estimation assuming a constant cluster size may lead to under-powered studies. Sample size formulas have been developed to incorporate the variability in cluster size for clinical trials with continuous and binary outcomes. Count outcomes frequently occur in cluster randomized studies. In this paper, we derive a closed-form sample size formula for count outcomes accounting for the variability in cluster size. We compare the performance of the proposed method with the average cluster size method through simulation. The simulation study shows that the proposed method has a better performance with empirical powers and type I errors closer to the nominal levels.

Bioactivity-guided fractionation of Streptomyces avermitilis NEAU1069 fermentation broth was used to isolate and determine the chemical identity of bioactive constituents with acaricidal and nemotocidal activity. The structures of novel compounds 1 and 2 were determined on the basis of spectroscopic analysis, including 1D and 2D NMR as well as HRESI-MS, ESI-MS of spectrometry analysis, UV and IR spectroscopic analyses, and comparison with data from the literature. The acaricidal activities of the isolated compounds against adult mites and mite eggs were evaluated by mortality and unhatched eggs. The nematocidal activity of the isolated compounds against Caenorhabditis elegans was calculated according to the immobilized rates against the total number of tested nematodes. The results indicated that compounds 1 and 2 exhibited potent acaricidal activity against adult mites, with a mortality of >90% at a concentration of 30 microg/mL. However, compounds 1 and 2 showed only weak acaricidal activity against mite eggs, with unhatched mite egg rates of <60% at a concentration of 100 microg/mL. Compound 2, a hydroxylated derivative at C-23 of 1, possessed a high nematocidal activity against C. elegans, with an immobility of >90% at a concentration of 10 microg/mL. These results demonstrate that compounds 1 and 2, especially compound 2, have potential as pesticides with acaricidal and nematocidal activity.

The diastolic blood pressure response to rhythmic dynamic handgrip exercise under ischemic conditions was demonstrated to be correlated with insulin resistance-related factors in nondiabetic older adults. This finding provides important insight to the prescription of exercise in this particular patient population as the blood pressure response to exercise, especially under ischemic conditions, could be exaggerated to nonsafe levels.