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Feasible symptom monitoring was demonstrated when gathering weekly responses of validated questionnaires for depression and mania from bipolar patients [ 20] and when collecting daily outcomes on several symptom dimensions from patients suffering from schizophrenia [ 21].
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However, it is impossible to obtain the daily outcome data for many developing countries.
Simulated daily outcome counts in these data sets were generated based on a Poisson distribution with the daily mean being the scaled daily expected outcome counts.
In the simulation results, increasing time-series length and average daily outcome counts both increased power to a similar extent.
So although our pollutant data are not available on a daily basis, the daily outcome data afford us the ability to examine different single-day lags.
Once data sets with appropriately scaled expected daily outcome counts and the appropriate time-series length had been generated, 2000 data sets were created for each scenario.
Power was estimated by conducting analyses of the association between simulated daily outcome counts and air pollution in 2000 data sets for each scenario.
These analyses demonstrate the similar impact on power of increasing time-series length versus increasing daily outcome counts, which has not previously been reported.
Power calculations were conducted for scenarios chosen to represent a range of pollutant-outcome combinations of interest, various magnitudes of effect, and various time-series lengths and mean daily outcome counts.
To optimize power, one can increase either time-series length (by acquiring data for a longer time period) or the daily outcome counts (e.g., by acquiring data from more hospitals).
The mean daily outcome counts may be limited by the population size in the study area, and increasing the number of hospitals may increase exposure measurement error if the geographic area is substantially expanded.
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