Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

Le médecin face aux inégalités sociales de santé: quel pouvoir d'action [General practitioners facing social inequalities in health: which power to act?].

The link between social inequalities and health has been known for many years, as attested by Villermé's work on the "mental and physical status of the working class" (1840). We have more and more insight into the nature of this relationship, which embraces not only material deprivation, but also psychological mechanisms related to social and interpersonal problems. Defining our possible role as physicians to fight against these inequalities has become a public health priority. Instruments and leads, which are now available to help us in our daily practice, are presented here.

Maximal aerobic power during running and cycling in obese and non-obese children.

The maximal aerobic capacity while running and cycling was measured in 22 prepubertal children (mean age +/- SD 9.5 +/- 0.8 years): 14 obese (47.3 +/- 10 kg) and 8 non-obese (31.1 +/- 6.1 kg). Oxygen consumption (VO2) and carbon dioxide production were measured by an open circuit method. Steady state VO2 was determined at different levels of exercise up to the maximal power on the cycloergometer (92 W in obese and 77 W in non-obese subjects) and up to the maximal running speed on the treadmill at a 2% slope (8.3 km/h in obese and 9.0 km/h in lean children). Expressed in absolute values, the VO2max in obese children was significantly higher than in controls (1.55 +/- 0.29 l/min versus 1.23 +/- 0.22 l/min, p < 0.05) for the treadmill test and comparable in the two groups (1.4 +/- 0.2 l/min versus 1.16 +/- 0.2 l/min, ns) for the cycloergometer test. When VO2max was expressed per kg fat free mass, the difference between the two groups disappeared for both tests. These data suggest that obese children had no limitation of maximal aerobic power. Therefore, the magnitude of the workload prescribed when a physical activity program is intended for the therapy of childhood obesity, it should be designed to increase caloric output rather than to improve cardiorespiratory fitness.

A program for the computation of power and determination of sample size in hierarchical experimental designs.

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

Comparison of the power spectral changes of the voluntary surface electromyogram and M wave during intermittent maximal voluntary contractions.

INTRODUCTION: To compare the power spectral changes of the voluntary surface electromyogram (sEMG) and of the compound action potential (M wave) in the vastus medialis and vastus lateralis muscles during fatiguing contractions. METHODS: Interference sEMG and force were recorded during 48 intermittent 3-s isometric maximal voluntary contractions (MVC) from 13 young, healthy subjects. M waves and twitches were evoked using supramaximal femoral nerve stimulation between the successive MVCs. Mean frequency (F mean), and median frequency were calculated from the sEMG and M waves. Muscle fiber conduction velocity (MFCV) was computed by cross-correlation. RESULTS: The power spectral shift to lower frequencies was significantly greater for the voluntary sEMG than for the M waves (P < 0.05). Over the fatiguing protocol, the overall average decrease in MFCV (~25 %) was comparable to that of sEMG F mean (~22 %), but significantly greater than that of M-wave F mean (~9 %) (P < 0.001). The mean decline in MFCV was highly correlated with the mean decreases in both sEMG and M-wave F mean. CONCLUSIONS: The present findings indicated that, as fatigue progressed, central mechanisms could enhance the relative weight of the low-frequency components of the voluntary sEMG power spectrum, and/or the end-of-fiber (non-propagating) components could reduce the sensitivity of the M-wave spectrum to changes in conduction velocity.

Measurement of the mechanical power of walking by satellite positioning system (GPS).

PURPOSE: This descriptive article illustrates the application of Global Positioning System (GPS) professional receivers in the field of locomotion studies. The technological challenge was to assess the external mechanical work in outdoor walking. METHODS: Five subjects walked five times during 5 min on an athletic track at different imposed stride frequency (from 70-130 steps x min(-1)). A differential GPS system (carrier phase analysis) measured the variation of the position of the trunk at 5 Hz. A portable indirect calorimeter recorded breath-by-breath energy expenditure. RESULTS: For a walking speed of 1.05 +/- 0.11 m x s(-1), the vertical lift of the trunk (43 +/- 14 mm) induced a power of 46.0 +/- 20.4 W. The average speed variation per step (0.15 +/- 0.03 m x s(-1)) produced a kinetic power of 16.9 +/- 7.2 W. As compared with commonly admitted values, the energy exchange (recovery) between the two energy components was low (39.1 +/- 10.0%), which induced an overestimated mechanical power (38.9 +/- 18.3 W or 0.60 W x kg(-1) body mass) and a high net mechanical efficiency (26.9 +/- 5.8%). CONCLUSION: We assumed that the cause of the overestimation was an unwanted oscillation of the GPS antenna. It is concluded that GPS (in phase mode) is now able to record small body movements during human locomotion, and constitutes a promising tool for gait analysis of outdoor unrestrained walking. However, the design of the receiver and the antenna must be adapted to human experiments and a thorough validation study remains to be conducted.