Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

Modeling cumulative evidence for freedom from disease with applications to BSE surveillance trials

This investigation deals with the question of when a particular population can be considered to be disease-free. The motivation is the case of BSE where specific birth cohorts may present distinct disease-free subpopulations. The specific objective is to develop a statistical approach suitable for documenting freedom of disease, in particular, freedom from BSE in birth cohorts. The approach is based upon a geometric waiting time distribution for the occurrence of positive surveillance results and formalizes the relationship between design prevalence, cumulative sample size and statistical power. The simple geometric waiting time model is further modified to account for the diagnostic sensitivity and specificity associated with the detection of disease. This is exemplified for BSE using two different models for the diagnostic sensitivity. The model is furthermore modified in such a way that a set of different values for the design prevalence in the surveillance streams can be accommodated (prevalence heterogeneity) and a general expression for the power function is developed. For illustration, numerical results for BSE suggest that currently (data status September 2004) a birth cohort of Danish cattle born after March 1999 is free from BSE with probability (power) of 0.8746 or 0.8509, depending on the choice of a model for the diagnostic sensitivity.

The importance of body-mass exponent optimization for evaluation of performance capability in cross-country skiing

Introduction Performance in cross-country skiing is influenced by the skier’s ability to continuously produce propelling forces and force magnitude in relation to the net external forces. A surrogate indicator of the “power supply” in cross-country skiing would be a physiological variable that reflects an important performance-related capability, whereas the body mass itself is an indicator of the “power demand” experienced by the skier. To adequately evaluate an elite skier’s performance capability, it is essential to establish the optimal ratio between the physiological variable and body mass. The overall aim of this doctoral thesis was to investigate the importance of body-mass exponent optimization for the evaluation of performance capability in cross-country skiing. Methods In total, 83 elite cross-country skiers (56 men and 27 women) volunteered to participate in the four studies. The physiological variables of maximal oxygen uptake (V̇O2max) and oxygen uptake corresponding to a blood-lactate concentration of 4 mmol∙l-1 (V̇O2obla) were determined while treadmill roller skiing using the diagonal-stride technique; mean oxygen uptake (V̇O2dp) and upper-body power output (Ẇ) were determined during double-poling tests using a ski-ergometer. Competitive performance data for elite male skiers were collected from two 15-km classical-technique skiing competitions and a 1.25-km sprint prologue; additionally, a 2-km double-poling roller-skiing time trial using the double-poling technique was used as an indicator of upper-body performance capability among elite male and female junior skiers. Power-function modelling was used to explain the race and time-trial speeds based on the physiological variables and body mass. Results The optimal V̇O2max-to-mass ratios to explain 15-km race speed were V̇O2max divided by body mass raised to the 0.48 and 0.53 power, and these models explained 68% and 69% of the variance in mean skiing speed, respectively; moreover, the 95% confidence intervals (CI) for the body-mass exponents did not include either 0 or 1. For the modelling of race speed in the sprint prologue, body mass failed to contribute to the models based on V̇O2max, V̇O2obla, and V̇O2dp. The upper-body power output-to-body mass ratio that optimally explained time-trial speed was Ẇ ∙ m-0.57 and the model explained 63% of the variance in speed. Conclusions The results in this thesis suggest that V̇O2max divided by the square root of body mass should be used as an indicator of performance in 15-km classical-technique races among elite male skiers rather than the absolute or simple ratio-standard scaled expression. To optimally explain an elite male skier’s performance capability in sprint prologues, power-function models based on oxygen-uptake variables expressed absolutely are recommended. Moreover, to evaluate elite junior skiers’ performance capabilities in 2-km double-poling roller-skiing time trials, it is recommended that Ẇ divided by the square root of body mass should be used rather than absolute or simple ratio-standard scaled expression of power output.

Optimal V. O2max-to-mass ratio for predicting 15 km performance among elite male cross-country skiers

The aim of this study was 1) to validate the 0.5 body-mass exponent for maximal oxygen uptake (V. O2max) as the optimal predictor of performance in a 15 km classical-technique skiing competition among elite male cross-country skiers and 2) to evaluate the influence of distance covered on the body-mass exponent for V. O2max among elite male skiers. Twenty-four elite male skiers (age: 21.4±3.3 years [mean ± standard deviation]) completed an incremental treadmill roller-skiing test to determine their V. O2max. Performance data were collected from a 15 km classicaltechnique cross-country skiing competition performed on a 5 km course. Power-function modeling (ie, an allometric scaling approach) was used to establish the optimal body-mass exponent for V . O2max to predict the skiing performance. The optimal power-function models were found to be race speed = 8.83⋅(V . O2max m-0.53) 0.66 and lap speed = 5.89⋅(V . O2max m-(0.49+0.018lap)) 0.43e0.010age, which explained 69% and 81% of the variance in skiing speed, respectively. All the variables contributed to the models. Based on the validation results, it may be recommended that V. O2max divided by the square root of body mass (mL⋅min−1 ⋅kg−0.5) should be used when elite male skiers’ performance capability in 15 km classical-technique races is evaluated. Moreover, the body-mass exponent for V . O2max was demonstrated to be influenced by the distance covered, indicating that heavier skiers have a more pronounced positive pacing profile (ie, race speed gradually decreasing throughout the race) compared to that of lighter skiers.

Rotina computacional e equação simplificada para modelar o transporte de sedimentos num Latossolo Vermelho Distrófico

Os objetivos do presente trabalho foram desenvolver rotina computacional para a solução da equação de Yalin e do diagrama de Shields e avaliar uma equação simplificada para modelar a capacidade de transporte de sedimento num Latossolo Vermelho Distrófico que possa ser utilizada no Water Erosion Prediction Project - WEPP, assim como em outros modelos de predição da erosão do solo. A capacidade de transporte de sedimento para o fluxo superficial foi representada como função-potência da tensão cisalhante, a qual revelou ser aproximação da equação de Yalin. Essa equação simplificada pôde ser aplicada em resultados experimentais oriundos de topografia complexa. A equação simplificada demonstrou acuracidade em relação à equação de Yalin, quando calibrada utilizando-se da tensão média cisalhante. Testes de validação com dados independentes demonstraram que a equação simplificada foi eficiente para estimar a capacidade de transporte de sedimento.

Funções psicofísicas para área percebida, inferida e relembrada: o efeito da idade

O objetivo deste trabalho foi verificar o efeito da idade no expoente da função-potência nas Condições experimentais Perceptiva, Memória e Inferência. Para cada Condição, as faixas etárias dos sujeitos variaram de 17 a 34 anos (I), 38 a 57 anos (II) e 58 a 77 anos de idade (III). Os sujeitos estimaram áreas dos Estados do Brasil, utilizando o método psicofísico de estimação de magnitude. Os resultados obtidos pelas três Faixas etárias não diferiram para cada Condição experimental, com exceção da Condição Memória (24 horas). A análise entre as Condições experimentais e Faixas etárias evidenciou uma diferença da Condição Perceptiva em relação às demais, não havendo diferenças entre as Condições Memória e Inferência. Os dados apresentados sugerem que no processo de relembrar, não há perda da informação em função da idade.

Comparison of cheliped weight and growth in two species of crabs of the genus Callinectes (Brachyura, Portunidae)

A comparison of the cheliped's weight in two species of the genus Callinectes was accomplished. The species C. danae e C. ornatus were collected by two otter trawl in Ubatuba bay (23 degrees 26' S and 45 degrees 02' W). The allometric constants obtained from the regression adjusted to a power function (Y = aX(b)) were analyzed. These species presented different allometry degrees for each sex considered. The relation Pe x PC presented positive allometry for sex of both species, but male presented higher positive allometry than female. C. danae presented higher positive allometry for chelipeds than C. ornatus. We suggest here that C. danae could be indicated to be submitted to grow out in ponds since it reaches higher size and bigger chelipeds.

Relação peso/largura da carapaça e fator de condição em Dilocarcinus pagei Stimpson (Crustacea, Trichodactylidae), em São José do Rio Preto, São Paulo, Brasil

A biologia de caranguejos de água doce tem sido pouco enfocada na literatura carcinológica, especialmente em relação à Dilocarcinus pagei Stimpson, 1861. Este estudo visa analisar a relação peso/tamanho e variações temporais/sazonais do fator de condição, comparando com a biologia da espécie. Os exemplares foram coletados mensalmente na Represa Municipal de São José do Rio Preto (São Paulo), durante um período bianual (outubro/1994 a setembro/1996). Foram obtidos 962 espécimes (534 machos e 428 fêmeas), que foram mensurados (LC = largura do cefalotórax) e pesados (PE = peso úmido total). Os pontos empíricos da relação PE/LC foram analisados para cada sexo e submetidos à análise de regressão pela função potência (y = ax b) e representadas por: PE Machos = 0,0002LC3,º8 e PE Fêmeas = 0,0005LC2,82. O fator de condição foi calculado mensal e sazonalmente, sendo o das fêmeas cerca de 2,5 maior que o dos machos, possivelmente devido ao maior tamanho/peso das gônadas. de modo geral o verão foi caracterizado pela menor média de fator de condição (época reprodutiva), contrastando com a maior verificada no inverno (reorganização gonadal). Os resultados obtidos são enfocados pela primeira vez na literatura carcinológica, sendo de grande valia no manejo populacional e preservação desta espécie, que vem sendo intensamente explorada e usada como isca na pesca esportiva.

Fractal concepts in relation to soil water diffusivity

Fractal geometry would appear to offer promise for new insight on water transport in unsaturated soils, This study was conducted to evaluate possible fractal influence on soil water diffusivity, and/or the relationships from which it arises, for several different soils, Fractal manifestations, consisting of a time-dependent diffusion coefficient and anomalous diffusion arising out of fractional Brownian motion, along with the notion of space-filling curves were gleaned from the literature, It was found necessary to replace the classical Boltzmann variable and its time t(1/2) factor with the basic fractal power function and its t(n) factor, For distinctly unsaturated soil water content theta, exponent n was found to be less than 1/2, but it approached 1/2 as theta approached its sated value, This function n = n(theta), in giving rise to a time-dependent, anomalous soil water diffusivity D, was identified with the Hurst exponent H of fractal geometry, Also, n approaching 1/2 at high water content is a behavior that makes it possible to associate factal space filling with soil that approaches water saturation, Finally, based on the fractally interpreted n = n(theta), the coalescence of both D and 8 data is greatly improved when compared with the coalescence provided by the classical Boltzmann variable.

Selection and shell relationship in Isocheles-sawayai forest and Saint-laurent, 1967 (crustacea, anomura, diogenidae)

A populational sample of Isocheles sawayai Forest & Saint Laurent, 1967 was analysed in order to detect the validity of the shell aperture size as a parameter in the gastropod shell selection. The gastropods genus occupied by this hermit crab were: Thais, Buccinanops, Olivancillaria, Polinices and Cymatium. The power function (y = a.x(b)) was the best equation to represent biologically the regression analyses carried out among the measured parameters.

RELATIVE GROWTH OF THE SPECKLED SWIMMING CRAB ARENAEUS-CRIBRARIUS (LAMARCK, 1818) (BRACHYURA, PORTUNIDAE), NEAR UBATUBA, STATE OF SAO-PAULO, BRAZIL

Arenaeus cribrarius is a mainly tropical crab that occurs in the Western Atlantic Ocean, Brazil being its type-locality. The species ranges from Vinevard Sound, Massachusetts, USA to La Paloma, Uruguay. Information about this species is scarce. The relative growth of A. cribrarius was analyzed, based on some morphometric relations, where the carapace width, excluding lateral spines (CW), was used as an independent variable. A total of 403 specimens (189 males and 214 females), was collected in Ubatuba, State of São Paulo, Brazil, with otter-trawls. The animals were sexed and sorted to maturation phase (juvenile or adult). Some measurements were made: carapace (length and width excluding lateral spines), abdomen (greatest width of the fifth somite in females and the sixth in males) and major chela (greatest length, width and height, dactylus length). This study was made by the application of the power function (y=a.x(b)) which was fitted to the data and the pattern of growth established for each parameter by the ''b''-value (constant of allometry), as positive allometry (b>1), negative allometry (b<1) or isometry (b=1). The morphometric relations of the carapace showed a tendency to isometry. In females, the abdominal width grew in positive allometry, higher in juveniles (b=1.33) than in adults (b=1.18). In this case, an overlap and discontinuity was noticed between the phases over a carapace width range of 55 to 70 mm, where the puberty molt occurs. The majority of relationships showed that the major chela of the males grew in positive allometry, however, the greatest allometric difference between the phases was observed towards the propodus length with 1.09 as juvenile and 1.26 as adult ''b''values. In the males, this variable showed an inflection between the CW range of 45' to 55 mm, where the transition to the maturation phase occurs. The relative growth of this species is similar to those of previously studied species. This indicates, that the propodus length and the abdominal width are the morphometric variables most appropriate to estimate the size of the beginning of the sexual maturity for males and females of this species, respectively.

Biometric relationship analysis of the wet weight by carapace width to the swimming crab Arenaeus-cribrarius (Lamarck, 1818) (Crustacea, Brachyura, Portunidae)

The biometric relationship between the weigth and the carapace width in the swimming crab A. cribrarius was compared with the results from other portunid crabs studied previously. During November/1988 to October/1989, a total of 403 specimens (189 males and 214 females) were collected with otter-trawl nets in north coast of the São Paulo State, Brazil. The animals were measured (carapace width excluding lateral spines = LC! and weighed (wet weight = PE). The empiric points of this relation were fit according to the power function (Y = a.X(b)) for each sex, maturation phases and total of individuals. The relation PE x LC indicates that the mole's growth changes during the ontogenesys from isometric (in juvenile phase) to allometric positive (in adult phase). For the females the growth is isometric in the two phases. The weight grows in a higher proportion than the carapace width variable (allometric positive growth). The data can be grouped in a single equation (PE = 7.85.10(-5).LC(3.14)) for the convertion between the variables there was a greater similarity between the equations obtained far each sex. In spite of this, the males present the fattening grade value (''a'') slightly higher than that of the females, possibly because of the greater size reached in its devellopment. The mean weight of the males is greater than the females one (p < 0.01). In the range 80 proves 90mm the males were more abundant, probably due to the females terminal ecdysis is near this size. The females only have the mean weight greater than the males in the 60 proves 70mm range (p < 0.01) when the puberty molt occurs and they present morphological changes in their reproductive system.

Relative growth of spider crab Acanthonyx scutiformis (Dana, 1851) (Crustacea, Decapoda, Majidae)

The dimensions of chelar propodus and abdomen were utilized for the morphometric analysis about the relative growth studies of Acanthonyx scutiformis (Dana, 1851). A total of 297 specimens (114 males and 183 females), was collected in Ubatuba, State of São Paulo, Brazil. The animals were sexed and soarted to maturation phase (immature and mature). The following measurements were made: carapace (length and width), abdomen width and chelar propodus (length and height). In this study was applicated the power function (y= a.x(b)), in which the growth was considered positive allometric with isometric with b=1, and negative allometric with b<1. The alometry becomes isometric, when the results concerning immature and mature females and males are analysed. In the Brachyura male chelipeds are utilized in territorial defense, fight, display and courtship and female abdomens are utilized as a chamber that protect and incubate the eggs.

Influence of temperature on larval survival, development and respiration in Chasmagnathus granulata (Crustacea, Decapoda)

Larvae of an estuarine grapsid crab Chasmagnathus granulata Dana 1851, from temperate and subtropical regions of South America, were reared in seawater (32 ‰) at five different constant temperatures (12, 15, 18, 21, 24 °C). Complete larval development from hatching (Zoea I) to metamorphosis (Crab I) occurred in a range from 15 to 24 °C. Highest survival (60% to the first juvenile stage) was observed at 18°C, while all larvae reared at 12°C died before metamorphosis. The duration of development (D) decreased with increasing temperature (T). This relationship is described for all larval stages as a power function (linear regressions after logarithmic transformation of both D and T). The temperature-dependence of the instantaneous developmental rate (D-1) is compared among larval stages and temperatures using the Q10 coefficient (van't Hoff's equation). Through all four zoeal stages, this index tends to increase during development and to decrease with increasing T (comparing ranges 12-18, 15-21, 18-24 °C). In the Megalopa, low Q10 values were found in the range from 15 to 24 °C. In another series of experiments, larvae were reared at constant 18°C and their dry weight (W) and respiratory response to changes in T were measured in all successive stages during the intermoult period (stage C) of the moulting cycle. Both individual and weight-specific respiration (R, QO2) increased exponentially with increasing T. At each temperature, R increased significantly during growth and development through successive larval stages. No significantly different QO2 values were found in the first three zoeal stages, while a significant decrease with increasing W occurred in the Zoea IV and Megalopa. As in the temperature-dependence of D, the respiratory response to changes in temperature (Q10) depends on both the temperature range and the developmental stage, however, with different patterns. In the zoeal stages, the respiratory Q10 was minimum (1.7-2.2) at low temperatures (12-18 °C), but maximum (2.2-3.0) at 18-24 °C. The Megalopa, in contrast, showed a stronger metabolic response in the lower than in the upper temperature range (Q10 = 2.8 and 1.7, respectively). We interpret this pattern as an adaptation to a sequence of temperature conditions that should typically be encountered by C. granulata larvae during their ontogenetic migrations: hatching in and subsequent export from shallow estuarine lagoons, zoeal development in coastal marine waters, which are on average cooler, return in the Megalopa stage to warm lagoons. We thus propose that high metabolic sensitivity to changes in temperature may serve as a signal stimulating larval migration, so that the zoeae should tend to leave warm estuaries and lagoons, whereas the Megalopa should avoid remaining in the cooler marine waters and initiate its migration towards shallow coastal lagoons.

Comparação do peso dos quelípodos e crescimento em duas espécies de sirís do gênero Callinectes (Brachyura, Portunidae)

A comparison of the cheliped's weight in two species of the genus Callinectes was accomplished. The species C. danae e C. ornatus were collected by two otter trawl in Ubatuba bay (23°26' S and 45°02' W). The allometric constants obtained from the regression adjusted to a power function (Y = aXb) were analyzed. These species presented different allometry degrees for each sex considered. The relation PQ x PC presented positive allometry for sex of both species, but male presented higher positive allometry than female. C. danae presented higher positive allometry for chelipeds than C. ornatus. We suggest here that C. danae could be indicated to be submitted to grow out in ponds since it reaches higher size and bigger chelipeds. © 1998, Paraná Institute of Technology Publication.