Increase in Power through Multivariate Analyses

Power to detect genetic and environmental influences increases not only with sample size but also with the number of measurements through longitudinal and/or multivariate designs, if those measurements correlate with each other. Power simulations are presented for uni- through quadrivariate cases, with differing genetic and environmental parameters. Even though subject attrition is a problem for most longitudinal studies, the gain in power available may more than make up for this shortcoming in many situations. In terms of planning studies to examine genetic and environmental influences, power calculations should not only consider sample size but number of measurements on particular phenotypes and their intercorrelations.     

Numerical comparisons of two formulations of the logistic regressive models with the mixed model in segregation analysis of discrete traits.

Segregation analysis of discrete traits can be conducted by the classical mixed model and the recently introduced regressive models. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affected persons have a liability exceeding a threshold. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype effects, the phenotypes of older relatives, and other covariates. A formulation of the regressive models, based on an underlying liability model, has been recently proposed. The regression coefficients on antecedents are expressed in terms of the relevant familial correlations and a one-to-one correspondence with the parameters of the mixed model can thus be established. Computer simulations are conducted to evaluate the fit of the two formulations of the regressive models to the mixed model on nuclear families. The two forms of the class D regressive model provide a good fit to a generated mixed model, in terms of both hypothesis testing and parameter estimation. The simpler class A regressive model, which assumes that the outcomes of children depend solely on the outcomes of parents, is not robust against a sib-sib correlation exceeding that specified by the model, emphasizing testing class A against class D. The studies reported here show that if the true state of nature is that described by the mixed model, then a regressive model will do just as well. Moreover, the regressive models, allowing for more patterns of family dependence, provide a flexible framework to understand gene-environment interactions in complex diseases.     

Evaluation of hypothesis testing for comparing two populations using NONMEM analysis

In a simulation study of inference on population pharmacokinetic parameters, two methods of performing tests of hypotheses comparing two populations using NONMEM were evaluated. These two methods are the test based upon 95% confidence intervals and the likelihood ratio test. Data were simulated according to a monoexponential model and, in that context, power curves for each test were generated for (i)the ratio of mean clearance and (ii)the ratio of the population standard deviations of clearance. To generate the power curves, a range of these parameters was employed; other pharmacokinetic parameters were selected to reflect the variability typically present in a Phase II clinical trial. For tests comparing the means, the confidence interval tests had approximately the same power as the likelihood ratio tests and were consistently more faithful to the nominal level of significance. For comparison of the standard deviations, and when the volume of information available was relatively small, however, the likelihood ratio test was more able to detect differences between the two groups. These results were then compared to results on parameter estimation in order to gain insight into the question of power. As an example, the nonnormality of estimates of the ratio of standard deviations plays an important role in explaining the low power for the confidence interval tests. We conclude that, except for the situation of modeling standard deviations with only sparse information, NONMEM produces tests of significance that are effective at detecting clinically significant differences between two populations.Partial support from the Upjohn Company, NIH-BRSG SO RR 07066, and the Burroughs Wellcome Foundation.     

Nonlinear excitation profiles for three-dimensional inflow MR angiography

An RF excitation pulse for three-dimensional (3D) time-of-flight (TOP) MR angiography (MRA) with a nonlinear excitation profile was numerically calculated under the condition of uniform vessel signal across the excitation volume (slab), and the superiority of the optform pulse as compared with conventional RF pulses and TONE pulses was demonstrated. For this purpose we acquired MRA of the lower leg and of the carotid and vertebral arteries in a 30-year-old healthy volunteer. Although the flow velocity ranges in these two anatomic locations are different by about a factor of 10, in both cases the corresponding optform pulse provided the best signal homogeneity at the highest level.     

Time-frequency analysis of heart murmurs. Part II: Optimisation of time-frequency representations and performance evaluation

The basic parameters of the spectrogram, the Choi-Williams, and the Bessel distributions are adjusted to provide the best time-frequency representations (TFRs) of the simulated murmur signals of mitral stenosis, mitral regurgitation, aortic stenosis, aortic regurgitation, and of two musical murmurs. The initial adjustment of the parameters of each TFR technique is performed by computing and minimising the relative averaged absolute error between the frequency contours at −3dB and −10dB of each TFR of the simulated murmurs and those of the theoretical distribution of the same signals. The results show that the spectrogram generally provides very good to excellent performance in representing the TFRs of stenotic and regurgitant murmurs. Improvements provided by the Choi-Williams and the Bessel distributions are minor but not systematic for the two signal-to-noise ratios tested (0 and 30 dB) and for the two frequency contours estimated. The Bessel and the Choi-Williams distributions provide the best performance for the musical murmurs. The study shows that although a single technique cannot be optimal for all six murmurs, the spectrogram using a Hamming window of 30 ms is an acceptable compromise to detect the six simutated heart murmurs.     

The unit impulse response procedure for the pharmacokinetic evaluation of drug entry into the central nervous system

The unit impulse response theory has been adapted to characterize the transport profile of drugs into the central nervous system (CNS). From the obtained input function, the cumulative plasma volume (V) cleared by transport into the CNS in time can be calculated. Simulation studies demonstrated that transport governed by passive diffusion resulted in a linear relationship between V and time, while the slope of the line, the blood- brain barrier (BBB) clearance, proved to be an adequate and model independent parameter to characterize drug transport into the CNS. The error in the result of the numerical procedure could be limited to less than 10% of the theoretically predicted value. Superposition of 5 or 10% random noise on simulated data did not result in significant differences between the calculated and theoretically predicted clearance values. Simulations of carrier-mediated transport resulted in nonlinear transport curves; the degree of nonlinearity, and thus the detectability, was dependent on the initial degree of saturation of the system, the rate of desaturation, as caused by drug elimination processes and the noise level on the data. In vivoexperiments in the rat were performed, using atenolol, acetaminophen, and antipyrine as model drugs. Linear transport relationships were obtained for all drugs, indicating that transport was dependent on passive diffusion or a low affinity carrier system. BBB- clearance values were 7±1 l/min for atenolol, 63±7 ul/min for acetaminiphen and 316±25 l/min for antipyrine. These experiments validate the applicability of the presented technique in in vivostudies.     

Changes in tissue optical properties due to radio-frequency ablation of myocardium

The optical properties of pig heart tissue were measured after in vivo ablation therapy had been performed during open-heart surgery. In vitro samples of normal and ablated tissue were subjected to measurements with an optically integrating sphere set-up in the region 470–900 nm. Three independent measurements were made: total transmittance, total reflectance and collimated transmittance, which made it possible to extract the absorption and scattering coefficients and the scattering anisotropy factor g, using an inverse Monte Carlo model. Between 470 and 700 nm, only the reduced scattering coefficient and absorption could be evaluated. The absorption spectra were fitted to known tissue chromophore spectra, so that the concentrations of haemoglobin and myoglobin could be estimated. The reduced scattering coefficient was compared with Mie computations to provide Mie equivalent average radii. Most of the absorption was from myoglobin, whereas haemoglobin absorption was negligible. Metmyoglobin was formed in the ablated tissue, which could yield a spectral signature to distinguish the ablated tissue with a simple optical probe to monitor the ablation therapy. The reduced scattering coefficient increased by, on average, 50% in the ablated tissue, which corresponded to a slight decrease in the Mie equivalent radius.     

Quaternion-based strap-down integration method for applications of inertial sensing to gait analysis

The proposed strap-down integration method exploits the cyclical nature of human gait: during the gait swing phase, the quaternion-based attitude representation is integrated using a gyroscope from initial conditions that are determined during stance by an accelerometer. Positioning requires double time integration of the gravity-compensated accelerometer signals during swing. An interpolation technique applied to attitude quaternions was developed to improve the accuracy of orientation and positioning estimates by accounting for the effect of sensor bias and scale factor drifts. A simulation environment was developed for the analysis and testing of the proposed algorithm on a synthetic movement trajectory. The aim was to define the true attitude and positioning used in the computation of estimation errors. By thermal modelling, the changes of bias and scale factor of the inertial sensors, calibrated at a single reference temperature, were analysed over a range of ±10°C, for measurement noise standard deviations up to σ_g = 2.5° s⁻¹ (gyroscope) and σ_a = 0.05 m s⁻¹ (accelerometer). The compensation technique reduced the maximum root mean square errors (RMSEs) to: RMSE_θ=14.6° (orientation) and RMSE_d=17.7 cm (positioning) for an integration interval of one gait cycle (an improvement of 3° and 7 cm); RMSE_θ=14.8° and RMSE_d=30.0 cm for an integration interval of two gait cycles (an improvement of 11° and 262 cm).     

Do bilineal pedigrees represent a problem for linkage analysis? basic principles and simulation results for single-gene diseases with no heterogeneity

Some investigators have expressed concern--especially for psychiatric disorders--that bilineal pedigrees should not be included in linkage studies. This study compares the "informativeness" of bilineal and unilineal families for a homogeneous single-gene disorder. Three approaches were used: (1) simulation studies of three-generation pedigrees, (2) calculation of expected lod scores (ELODs) in nuclear families, and (3) calculation of Fisher's information number I(theta) in nuclear families. The simulation studies in (1) permitted a realistic comparison between bilineal datasets and purely unilineal ones. The calculations in nuclear families in (2) and (3) then made it possible to analyze the sources of information loss in bilineal families. Overall, in datasets of five three-generation pedigrees each, the drop in mean maximum lod score was approximately 50% from purely unilineal datasets to extremely bilineal ones. In less-extreme bilineal datasets, which are closer to most real data than the extremely bilineal ones, the drops in lod score were very small--less than 10% in some, and practically zero in others. The details will vary, depending on size and structure of the pedigree, genetic model, true value of the recombination fraction, and informativeness of the marker. However, these results imply that the information loss due to bilineality is not necessarily very great. The nuclear-family calculations showed that for phase-known matings there is relatively little information loss in bilineal families, but for phase-unknown matings there the loss is much greater. In conclusion, for single-gene disorders with no genetic heterogeneity, whereas bilineal families can be less informative than comparable unilineal families, they are not so much less informative that they should automatically be discarded from linkage datasets. The implications of bilineal pedigrees for linkage studies of heterogeneous disorders are also discussed.     

The effects of noise in cardiac diffusion tensor imaging and the benefits of averaging complex data

There is growing interest in cardiac diffusion tensor imaging (cDTI), but, unlike other diffusion MRI applications, there has been little investigation of the effects of noise on the parameters typically derived. One method of mitigating noise floor effects when there are multiple image averages, as in cDTI, is to average the complex rather than the magnitude data, but the phase contains contributions from bulk motion, which must be removed first. The effects of noise on the mean diffusivity (MD), fractional anisotropy (FA), helical angle (HA) and absolute secondary eigenvector angle (E2A) were simulated with various diffusion weightings (b values). The effect of averaging complex versus magnitude images was investigated. In vivo cDTI was performed in 10 healthy subjects with b = 500, 1000, 1500 and 2000 s/mm². A technique for removing the motion‐induced component of the image phase present in vivo was implemented by subtracting a low‐resolution copy of the phase from the original images before averaging the complex images. MD, FA, E2A and the transmural gradient in HA were compared for un‐averaged, magnitude‐ and complex‐averaged reconstructions. Simulations demonstrated an over‐estimation of FA and MD at low b values and an under‐estimation at high b values. The transition is relatively signal‐to‐noise ratio (SNR) independent and occurs at a higher b value for FA (b = 1000–1250 s/mm²) than MD (b ≈ 250 s/mm²). E2A is under‐estimated at low and high b values with a transition at b ≈ 1000 s/mm², whereas the bias in HA is comparatively small. The under‐estimation of FA and MD at high b values is caused by noise floor effects, which can be mitigated by averaging the complex data. Understanding the parameters of interest and the effects of noise informs the selection of the optimal b values. When complex data are available, they should be used to maximise the benefit from the acquisition of multiple averages. The combination of complex data is also a valuable step towards segmented acquisitions. Copyright © 2016 John Wiley & Sons, Ltd.