RISK FACTORS ASSOCIATED WITH CULLING AGE IN DAIRY CATTLE: APPLICATIONS OF FRAILTY MODELS

Culling decisions for dairy cattle are an important component of dairy herd management. To investigate risk factors for culling, farms (clusters) constitute the sampling units. Therefore, we believe that ages-at-culling may be correlated within farms. The score test on the null hypothesis of no extra-variation in survival data was not supported by age-at-culling data collected from 72 dairy farms from the province of Ontario, Canada. To correct for the intraherd correlation, three modelling approaches were used to fit the data: Population-Averaged (PA) , cluster-specific (CS), and Random Effects Models (RAEM). The modelling approaches are described and compared using the dairy cow culling data

Copula based prediction models: an application to an aortic regurgitation study

<p>Abstract</p> <p>Background:</p> <p>An important issue in prediction modeling of multivariate data is the measure of dependence structure. The use of Pearson's correlation as a dependence measure has several pitfalls and hence application of regression prediction models based on this correlation may not be an appropriate methodology. As an alternative, a copula based methodology for prediction modeling and an algorithm to simulate data are proposed.</p> <p>Methods:</p> <p>The method consists of introducing copulas as an alternative to the correlation coefficient commonly used as a measure of dependence. An algorithm based on the marginal distributions of random variables is applied to construct the <it>Archimedean </it>copulas. Monte Carlo simulations are carried out to replicate datasets, estimate prediction model parameters and validate them using Lin's concordance measure.</p> <p>Results:</p> <p>We have carried out a correlation-based regression analysis on data from 20 patients aged 17–82 years on pre-operative and post-operative ejection fractions after surgery and estimated the prediction model: Post-operative ejection fraction = - 0.0658 + 0.8403 (Pre-operative ejection fraction); p = 0.0008; 95% confidence interval of the slope coefficient (0.3998, 1.2808). From the exploratory data analysis, it is noted that both the pre-operative and post-operative ejection fractions measurements have slight departures from symmetry and are skewed to the left. It is also noted that the measurements tend to be widely spread and have shorter tails compared to normal distribution. Therefore predictions made from the correlation-based model corresponding to the pre-operative ejection fraction measurements in the lower range may not be accurate. Further it is found that the best approximated marginal distributions of pre-operative and post-operative ejection fractions (using q-q plots) are gamma distributions. The copula based prediction model is estimated as: Post -operative ejection fraction = - 0.0933 + 0.8907 × (Pre-operative ejection fraction); p = 0.00008 ; 95% confidence interval for slope coefficient (0.4810, 1.3003). For both models differences in the predicted post-operative ejection fractions in the lower range of pre-operative ejection measurements are considerably different and prediction errors due to copula model are smaller. To validate the copula methodology we have re-sampled with replacement fifty independent bootstrap samples and have estimated concordance statistics 0.7722 (p = 0.0224) for the copula model and 0.7237 (p = 0.0604) for the correlation model. The predicted and observed measurements are concordant for both models. The estimates of accuracy components are 0.9233 and 0.8654 for copula and correlation models respectively.</p> <p>Conclusion:</p> <p>Copula-based prediction modeling is demonstrated to be an appropriate alternative to the conventional correlation-based prediction modeling since the correlation-based prediction models are not appropriate to model the dependence in populations with asymmetrical tails. Proposed copula-based prediction model has been validated using the independent bootstrap samples.</p

Interval estimation and optimal design for the within-subject coefficient of variation for continuous and binary variables

BACKGROUND: In this paper we propose the use of the within-subject coefficient of variation as an index of a measurement's reliability. For continuous variables and based on its maximum likelihood estimation we derive a variance-stabilizing transformation and discuss confidence interval construction within the framework of a one-way random effects model. We investigate sample size requirements for the within-subject coefficient of variation for continuous and binary variables. METHODS: We investigate the validity of the approximate normal confidence interval by Monte Carlo simulations. In designing a reliability study, a crucial issue is the balance between the number of subjects to be recruited and the number of repeated measurements per subject. We discuss efficiency of estimation and cost considerations for the optimal allocation of the sample resources. The approach is illustrated by an example on Magnetic Resonance Imaging (MRI). We also discuss the issue of sample size estimation for dichotomous responses with two examples. RESULTS: For the continuous variable we found that the variance stabilizing transformation improves the asymptotic coverage probabilities on the within-subject coefficient of variation for the continuous variable. The maximum like estimation and sample size estimation based on pre-specified width of confidence interval are novel contribution to the literature for the binary variable. CONCLUSION: Using the sample size formulas, we hope to help clinical epidemiologists and practicing statisticians to efficiently design reliability studies using the within-subject coefficient of variation, whether the variable of interest is continuous or binary

Comparison of two dependent within subject coefficients of variation to evaluate the reproducibility of measurement devices

<p>Abstract</p> <p>Background</p> <p>The within-subject coefficient of variation and intra-class correlation coefficient are commonly used to assess the reliability or reproducibility of interval-scale measurements. Comparison of reproducibility or reliability of measurement devices or methods on the same set of subjects comes down to comparison of dependent reliability or reproducibility parameters.</p> <p>Methods</p> <p>In this paper, we develop several procedures for testing the equality of two dependent within-subject coefficients of variation computed from the same sample of subjects, which is, to the best of our knowledge, has not yet been dealt with in the statistical literature. The Wald test, the likelihood ratio, and the score tests are developed. A simple regression procedure based on results due to Pitman and Morgan is constructed. Furthermore we evaluate the statistical properties of these methods via extensive Monte Carlo simulations. The methodologies are illustrated on two data sets; the first are the microarray gene expressions measured by two plat- forms; the Affymetrix and the Amersham. Because microarray experiments produce expressions for a large number of genes, one would expect that the statistical tests to be asymptotically equivalent. To explore the behaviour of the tests in small or moderate sample sizes, we illustrated the methodologies on data from computer-aided tomographic scans of 50 patients.</p> <p>Results</p> <p>It is shown that the relatively simple Wald's test (WT) is as powerful as the likelihood ratio test (LRT) and that both have consistently greater power than the score test. The regression test holds its empirical levels, and in some occasions is as powerful as the WT and the LRT.</p> <p>Conclusion</p> <p>A comparison between the reproducibility of two measuring instruments using the same set of subjects leads naturally to a comparison of two correlated indices. The presented methodology overcomes the difficulty noted by data analysts that dependence between datasets would confound any inferences one could make about the differences in measures of reliability and reproducibility. The statistical tests presented in this paper have good properties in terms of statistical power.</p

Estimation problems for some generalized discrete probability distributions

Bibliography: p. 170-175

Families of discrete probability distributions associated with power series expansions

Bibliography; p. 73-76

On the generalization and estimation for the double Poisson distribution

The bivariate forms of many important discrete probability distributions have been studied by many statisticians. The trinomial, the double Poisson, the bivariate negative binomial, and the bivariate logarithmic series distributions are in fact the bivariate generalizations of the well known univariate distributions. A systematic account of various families of distributions of bivariate discrete random variables have been given by Patil and Joshi (11), Johnson and Kotz (4), and Mardia (9) in their books. In this paper we introduce a new generalized form for the double Poisson distribution given by Joshi (5), and we discuss some of its interesting properties and application

Evaluating Aortic Stenosis using the Archimedean copula methodology

Abstract: In modeling and analyzing multivariate data, the conventionally used measure of dependence structure is the Pearson&apos;s correlation coefficient. However use of the correlation as a dependence measure has several pitfalls. Copulas recently have emerged as an alternative measure of the dependence, overcoming most of the drawbacks of the correlation. We discuss Archimedean copulas and their relationships with tail dependence. An algorithm to construct empirical and Archimedean copulas is described. Monte Carlo simulations are carried out to replicate and analyze data sets by identifying the appropriate copula. We apply the Archimedean copula based methodology to assess the accuracy of Doppler echocardiography in determining aortic valve area from the Aortic Stenosis: Simultaneous DopplerCatheter Correlative study carried out at the King Faisal Specialist Hospital and Research Centre, Riyadh, KSA