Variable apparent sample size

They then derive their own binomial model relationships using Horwitz s data with variable apparent sample size. 

Sample sizes for randomized controlled trials in neurology may need to be large, either because treatment effects are relatively small or because the progression of disease is slow. Table 18.3 shows the effect of sample size on the reliability of the result of a trial of a hypothetical neurological treatment that is assumed to reduce the risk of a poor outcome by 20%, from 10% to 8%. The risk of getting the wrong result when a trial has an inadequate sample size is illustrated in Fig. 18.1. In this trial, there was considerable variability in the apparent effect of treatment until several hundred patients had been randomized. If the trial had been small, misleading trends in treatment effect could easily have been reported. 

When a PPK study is designed to detect a difference between two subpopulations or to determine important covariates necessary to explain variability, attention should be paid to the sample size required for such a study. Simulation plays an important role in this situation, and Kowalski and Hutmacher (33) demonstrated the importance of using clinical trial simulations to assess the power to detect subpopulation differences in apparent drug clearance CLIP) and sample size requirements for a PPK substudy (1) of a Phase 3 clinical trial. Two subpopulations were... 

This smoother is one way to improve the signal-to-noise ratio of the data, as shown in Figure 5.4. The original data has some visible random noise and a large spike. The mean smoother with a 3-point window reduces the noise significantly, but does not remove the spike. Witli the largest window size (21 point), the spike is removed but the shape of the peak has changed (broader and lower intensity). The apparent shift in the peak to lower variable number is due to the end effect (i.c., 10 points from each end of the sample vector have been removed). 

The fact that Carson et al. found larger errors for comparable orifice sizes can probably be accounted for by their smaller chamber (approximately one-third in volume). Exact comparison is difficult because of uncertainty in the amount and nature of the sample surface. In any case, considering the experimental variability, the pressure-drop error apparently can be safely neglected (3%) if the orifice is 1 mm. or less in diameter, which was the case for all the work reported here. 

Laser granulometry indicated little variation in the particle size with depth in the trench section, the median size being 12-15 pm. On average the bulk sediments were found to contain approximately 20% clay ( < 2 pm), 70% silt (2-63 pm) and < 10% sand ( > 63 pm). Bulk sediment XRF analyses also showed that the major element proportions are also relatively constant with depth (Figure 7.7). X-ray diffraction (XRD) analyses showed some variability in the relative proportions of clay minerals present in the < 2 pm fraction, but all samples were dominated by illite, smectite, kaolinite and chlorite. The calcium carbonate content was low ( < 1%), much of the detrital material apparently having been dissolved. The sediment pH ranged from 6.2 to 6.7. 

Light can interact with the sample as reflection, refraction, absorption, scattering, diffraction, and transmission. Signal losses from the sample can occur as specular reflection, internal scattering, refraction, complete absorption, transmission loss during reflectance measurements, and trapping losses. Spectral artifacts can also arise as offset or multiplicative errors due to coloration of the sample, variable particle sizes and resultant variability in apparent pathlength, refractive index... 

The absorption rate behavior of crosslinked,water swellable polymers is explained in terms of diffusion of water into the polymer network. The absorption kinetics can be studied over time using a viscosity versus time measurement. Alternately, a one point determination of sorption time can be used to compare various polymers. The limitation of this method is that the polymers tested must have a sufficiently high swelling capacity so that the simplifying equations hold. This limitation can be eliminated by a proper choice of polymer/sallne solution ratio in the vortex test. The variables which control the absorption rate of ail the samples studied are swelling capacity, mesh size of powder particles and the distribution of particle sizes, the specific surface area of the product, and the apparent density of the polymer. 

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