An Examination of Discrepancies in Multiple Imputation Procedures Between SAS® and SPSS®

Multiple imputation (MI) has become a feasible method to replace missing data due to the rapid development of computer technology over the past three decades. Nonetheless, a unique issue with MI hinges on the fact that different software packages can give different results. Even when one begins with the same random number seed, conflicting findings can be obtained from the same data under an identical imputation model between SAS® and SPSS®. Consequently, as illustrated in this article, a predictor variable can be claimed both significant and not significant depending on the software being used. Based on the considerations of multiple imputation steps, including result pooling, default selection, and different numbers of imputations, practical suggestions are provided to minimize the discrepancies in the results obtained when using MI. Features of Stata® are briefly reviewed in the Discussion section to broaden the comparison of MI computing across widely used software packages.     

Standard statistical tools for the breed allocation problem

Modern technologies are frequently used in order to deal with new genomic problems. For instance, the STRUCTURE software is usually employed for breed assignment based on genetic information. However, standard statistical techniques offer a number of valuable tools which can be successfully used for dealing with most problems. In this paper, we investigated the capability of microsatellite markers for individual identification and their potential use for breed assignment of individuals in seventy Lidia breed lines and breeders. Traditional binomial logistic regression is applied to each line and used to assign one individual to a particular line. In addition, the area under receiver operating curve (AUC) criterion is used to measure the capability of the microsatellite-based models to separate the groups. This method allows us to identify which microsatellite loci are related to each line. Overall, only one subject was misclassified or a 99.94% correct allocation. The minimum observed AUC was 0.986 with an average of 0.997. These results suggest that our method is competitive for animal allocation and has some interpretative advantages and a strong relationship with methods based on SNPs and related techniques.     

An extension of parametric ROC analysis for calculating diagnostic accuracy when underlying distributions are mixture of Gaussian

The semiparametric LABROC approach of fitting binormal model for estimating AUC as a global index of accuracy has been justified (except for bimodal forms), while for estimating a local index of accuracy such as TPF, it may lead to a bias in severe departure of data from binormality. We extended parametric ROC analysis for quantitative data when one or both pair members are mixture of Gaussian (MG) in particular for bimodal forms. We analytically showed that AUC and TPF are a mixture of weighting parameters of different components of AUCs and TPFs of a mixture of underlying distributions. In a simulation study of six configurations of MG distributions:{bimodal, normal} and {bimodal, bimodal} pairs, the parameters of MG distributions were estimated using the EM algorithm. The results showed that the estimated AUC from our proposed model was essentially unbiased, and that the bias in the estimated TPF at a clinically relevant range of FPF was roughly 0.01 for a sample size of n=100/100. In practice, with severe departures from binormality, we recommend an extension of the LABROC and software development for future research to allow for each member of the pair of distributions to be a mixture of Gaussian that is a more flexible parametric form.     

Bayesian approach to the inverse problem in a light scattering application

In this article, static light scattering (SLS) measurements are processed to estimate the particle size distribution of particle systems incorporating prior information obtained from an alternative experimental technique: scanning electron microscopy (SEM). For this purpose we propose two Bayesian schemes (one parametric and another non-parametric) to solve the stated light scattering problem and take advantage of the obtained results to summarize some features of the Bayesian approach within the context of inverse problems. The features presented in this article include the improvement of the results when some useful prior information from an alternative experiment is considered instead of a non-informative prior as it occurs in a deterministic maximum likelihood estimation. This improvement will be shown in terms of accuracy and precision in the corresponding results and also in terms of minimizing the effect of multiple minima by including significant information in the optimization. Both Bayesian schemes are implemented using Markov Chain Monte Carlo methods. They have been developed on the basis of the Metropolis–Hastings (MH) algorithm using Matlab^® and are tested with the analysis of simulated and experimental examples of concentrated and semi-concentrated particles. In the simulated examples, SLS measurements were generated using a rigorous model, while the inversion stage was solved using an approximate model in both schemes and also using the rigorous model in the parametric scheme. Priors from SEM micrographs were also simulated and experimented, where the simulated ones were obtained using a Monte Carlo routine. In addition to the presentation of these features of the Bayesian approach, some other topics will be discussed, such as regularization and some implementation issues of the proposed schemes, among which we remark the selection of the parameters used in the MH algorithm.     

Optimization of parameters for the fabrication of gelatin nanoparticles by the Taguchi robust design method

The Taguchi method is a statistical approach to overcome the limitation of the factorial and fractional factorial experiments by simplifying and standardizing the fractional factorial design. The objective of this study was to optimize the fabrication of gelatin nanoparticles by applying the Taguchi design method. Gelatin nanoparticles have been extensively studied in our previous works as an appropriate carrier for drug delivery, since they are biodegradable, non-toxic, are not usually contaminated with pyrogens and possess relatively low antigenicity. Taguchi method with L₁₆ orthogonal array robust design was implemented to optimize experimental conditions of the purpose. Four key process parameters – temperature, gelatin concentration, agitation speed and the amount of acetone – were considered for the optimization of gelatin nanoparticles. As a result of Taguchi analysis in this study, temperature and amount of acetone were the most influencing parameters of the particle size. For characterizing the nanoparticle sample, atomic force microscope and scanning electron microscope were employed. In this study, a minimum size of gelatin nanoparticles was obtained at 50 °C temperature, 45 mg/ml gelatin concentration, 80 ml acetone and 700 rpm agitation speed. The nanoparticle size at the determined condition was less than 174 nm.     

Implementation of Kolmogorov–Smirnov P-value computation in Visual Basic®: implication for Microsoft Excel® library function

This paper investigates methodologies for evaluating the probabilistic value (P-value) of the Kolmogorov–Smirnov (K–S) goodness-of-fit test using algorithmic program development implemented in Microsoft® Visual Basic® (VB). Six methods were examined for the one-sided one-sample and two methods for the two-sided one-sample cumulative sampling distributions in the investigative software implementation that was based on machine-precision arithmetic. For sample sizes n≤2000 considered, results from the Smirnov iterative method found optimal accuracy for K–S P-values≥0.02, while those from the SmirnovD were more accurate for lower P-values for the one-sided one-sample distribution statistics. Also, the Durbin matrix method sustained better P-value results than the Durbin recursion method for the two-sided one-sample tests up to n≤700 sample sizes. Based on these results, an algorithm for Microsoft Excel® function was proposed from which a model function was developed and its implementation was used to test the performance of engineering students in a general engineering course across seven departments.     

Generalized Confidence Interval Estimation for the Difference in Paired Areas Under the ROC Curves in the Absence of a Gold Standard

Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard (GS) test on the true disease status is required to estimate the AUC. However, a GS test may be too expensive or infeasible. In many medical researches, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, we propose a heuristic method of estimating confidence intervals for the difference in paired AUCs of two diagnostic tests in the absence of a GS reference. This heuristic method is a three-stage method by combining the expectation-maximization (EM) algorithm, bootstrap method, and an estimation based on asymptotic generalized pivotal quantities (GPQs) to construct generalized confidence intervals for the difference in paired AUCs in the absence of a GS. Simulation results show that the proposed interval estimation procedure yields satisfactory coverage probabilities and expected interval lengths. The numerical example using a published dataset illustrates the proposed method.     

Binary quantile regression and variable selection: A new approach

In this paper, we propose a new estimation method for binary quantile regression and variable selection which can be implemented by an iteratively reweighted least square approach. In contrast to existing approaches, this method is computationally simple, guaranteed to converge to a unique solution and implemented with standard software packages. We demonstrate our methods using Monte-Carlo experiments and then we apply the proposed method to the widely used work trip mode choice dataset. The results indicate that the proposed estimators work well in finite samples.     

The diagnostic accuracy of a composite index increases as the number of partitions of the components increases and when specific weights are assigned to each component

The aim of this work was to evaluate whether the number of partitions of index components and the use of specific weights for each component influence the diagnostic accuracy of a composite index. Simulation studies were conducted in order to compare the sensitivity, specificity and area under the ROC curve (AUC) of indices constructed using equal number of components but different number of partitions for all components. Moreover, the odds ratio obtained from the univariate logistic regression model for each component was proposed as potential weight. The current simulation results showed that the sensitivity, specificity and AUC of an index increase as the number of partitions of components increases. However, the rate that the diagnostic accuracy increases is reduced as the number of partitions increases. In addition, it was found that the diagnostic accuracy of the weighted index developed using the proposed weights is higher compared with that of the corresponding un-weighted index. The use of large-scale index components and the use of effect size measures (i.e. odds ratios, ORs) of index components as potential weights are proposed in order to obtain indices with high diagnostic accuracy for a particular binary outcome.     

Regression coefficient analysis for correlated binomial outcomes

At present, the generalized estimating equation (GEE) and weighted least-squares (WLS) regression methods are the most widely used methods for analyzing correlated binomial data; both are easily implemented using existing software packages. We propose an alternative technique, i.e. regression coefficient analysis (RCA), for this type of data. In RCA, a regression equation is computed for each of n individuals; regression coefficients are averaged across the n equations to produce a regression equation, which predicts marginal probabilities and which can be tested to address hypotheses of different slopes between groups, slopes different from zero, different intercepts, etc. The method is computationally simple and can be performed using standard software. Simulations and examples are used to compare the power and robustness of RCA with those of the standard GEE and WLS methods. We find that RCA is comparable with the GEE method under the conditions tested, and suggest that RCA, within specified limitations, is a viable alternative to the GEE and WLS methods in the analysis of correlated binomial data.     

Extension of two-sided test to multiple treatment trials

In a two-treatment trial, a two-sided test is often used to reach a conclusion, Usually we are interested in doing a two-sided test because of no prior preference between the two treatments and we want a three-decision framework. When a standard control is just as good as the new experimental treatment (which has the same toxicity and cost), then we will accept both treatments. Only when the standard control is clearly worse or better than the new experimental treatment, then we choose only one treatment. In this paper, we extend the concept of a two-sided test to the multiple treatment trial where three or more treatments are involved. The procedure turns out to be a subset selection procedure; however, the theoretical framework and performance requirement are different from the existing subset selection procedures. Two procedures (exclusion or inclusion) are developed here for the case of normal data with equal known variance. If the sample size is large, they can be applied with unknown variance and with the binomial data or survival data with random censoring.     

Approximating Symmetric Distributions via Sampling and Coefficient of Variation

Abstract

The Coefficient of Variation is one of the most commonly used statistical tool across various scientific fields. This paper proposes a use of the Coefficient of Variation, obtained by Sampling, to define the polynomial probability density function (pdf) of a continuous and symmetric random variable on the interval [a, b]. The basic idea behind the first proposed algorithm is the transformation of the interval from [a, b] to [0, b-a]. The chi-square goodness-of-fit test is used to compare the proposed (observed) sample distribution with the expected probability distribution. The experimental results show that the collected data are approximated by the proposed pdf. The second algorithm proposes a new method to get a fast estimate for the degree of the polynomial pdf when the random variable is normally distributed. Using the known percentages of values that lie within one, two and three standard deviations of the mean, respectively, the so-called three-sigma rule of thumb, we conclude that the degree of the polynomial pdf takes values between 1.8127 and 1.8642. In the case of a Laplace (μ, b) distribution, we conclude that the degree of the polynomial pdf takes values greater than 1. All calculations and graphs needed are done using statistical software R.     

Multi-factor prediction of water flooding efficiency based on a time-varying system

ABSTRACT

The neural network prediction method gets good historical matching between prediction indices and influence factor indices, while the differential simulation prediction method can reflect the changing trend of prediction indices; considering these new traits, a new multi-factor prediction method is proposed to organically combine these two prediction methods. At first, the input–output relation between water flooding efficiency in ultra-high water cut stage and their influence factors is viewed as a time varying system, then the BP neural network is introduced in parameter identification of differential simulation to obtain a new multi-factor prediction method of functional simulation based on the time varying system. This new prediction model has got good self-adaptability since its parameters change by time. Moreover, it has better results in the mid-long-term water flooding efficiency prediction because the non convergence problem appeared in the coupling process can be overcome in the training process of the neural network by variable learning rates. In the end, practical output prediction cases in two different oilfield blocks in China are given. The computational results show that the prediction results obtained using the new multi-factor prediction method are in good agreement with the reality, even much better than the results obtained by other prediction methods.     

A Simulation Based Study for Comparing Tests Associated With Receiver Operating Characteristic (ROC) Curves

Receiver Operating Characteristic curves and the Area Under Curve (AUC) are widely used to evaluate the predictive accuracy of diagnostic tests. The parametric methods of estimating AUCs are well established while nonparametric methods, such as Wilcoxon's method, lack proper research. This study considered three standard error techniques, namely, Hanley and McNeil, Hanley and Tilaki, and DeLong methods. Several parameters were considered, while measuring the predictor on a binary scale. The normality and type I error rate was violated for Hanley and McNeil's method while asymptotically DeLong's method performed better. Hanley and Tilaki's Jackknife method and DeLong's method performed equally well.     

Bioequivalence and the pharmaceutical industry

Since the early 1990s, average bioequivalence (ABE) studies have served as the international regulatory standard for demonstrating that two formulations of drug product will provide the same therapeutic benefit and safety profile when used in the marketplace. Population (PBE) and individual (IBE) bioequivalence have been the subject of intense international debate since methods for their assessment were proposed in the late 1980s and since their use was proposed in United States Food and Drug Administration guidance in 1997. Guidance has since been proposed and finalized by the Food and Drug Administration for the implementation of such techniques in the pioneer and generic pharmaceutical industries. The current guidance calls for the use of replicate design and of cross‐over studies (cross‐overs with sequences TRTR, RTRT, where T is the test and R is the reference formulation) for selected drug products, and proposes restricted maximum likelihood and method‐of‐moments techniques for parameter estimation. In general, marketplace access will be granted if the products demonstrate ABE based on a restricted maximum likelihood model. Study sponsors have the option of using PBE or IBE if the use of these criteria can be justified to the regulatory authority. Novel and previously proposed SAS^®‐based approaches to the modelling of pharmacokinetic data from replicate design studies will be summarized. Restricted maximum likelihood and method‐of‐moments modelling results are compared and contrasted based on the analysis of data available from previously performed replicate design studies, and practical issues involved in the application of replicate designs to demonstrate ABE are characterized. It is concluded that replicate designs may be used effectively to demonstrate ABE for highly variable drug products. Statisticians should exercise caution in the choice of modelling procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

Sensitivity,specificity and ROC-curves in multiple reader diagnostic trials—A unified,nonparametric approach

In diagnostic trials, the performance of a product is most frequently measured in terms such as sensitivity, specificity and the area under the ROC-curve (AUC). In multiple-reader trials, correlated data appear in a natural way since the same patient is observed under different conditions by several readers. The repeated measures may have quite an involved correlation structure. Even though sensitivity, specificity and the AUC are all assessments of diagnostic ability, a unified approach to analyze all such measurements allowing for an arbitrary correlation structure does not exist. Thus, a unified approach for these three effect measures of diagnostic ability will be presented in this paper. The fact that sensitivity and specificity are particular AUCs will serve as a basis for our method of analysis. As the presented theory can also be used in set-ups with correlated binomial random-variables, it may have a more extensive application than only in diagnostic trials.     

A mixed effects model for analyzing area under the curve of longitudinally measured biomarkers with missing data

A simple approach for analyzing longitudinally measured biomarkers is to calculate summary measures such as the area under the curve (AUC) for each individual and then compare the mean AUC between treatment groups using methods such as t test. This two-step approach is difficult to implement when there are missing data since the AUC cannot be directly calculated for individuals with missing measurements. Simple methods for dealing with missing data include the complete case analysis and imputation. A recent study showed that the estimated mean AUC difference between treatment groups based on the linear mixed model (LMM), rather than on individually calculated AUCs by simple imputation, has negligible bias under random missing assumptions and only small bias when missing is not at random. However, this model assumes the outcome to be normally distributed, which is often violated in biomarker data. In this paper, we propose to use a LMM on log-transformed biomarkers, based on which statistical inference for the ratio, rather than difference, of AUC between treatment groups is provided. The proposed method can not only handle the potential baseline imbalance in a randomized trail but also circumvent the estimation of the nuisance variance parameters in the log-normal model. The proposed model is applied to a recently completed large randomized trial studying the effect of nicotine reduction on biomarker exposure of smokers.     

Equilibrium,affinity, dissociation constants,IC5O: Facts and fantasies

The interaction between ligands and receptors is often described in terms of 50% inhibitory concentrations (IC50). However, IC50 values do not accurately reflect the dissociation constants (Kd), and the domain of application and precision of proposed approximations for Kd estimation are unclear. The effect of affinity and of experimental conditions on the differences between IC50 and Kd has been assessed from exact mass action law calculations and from computer simulations. Competitions between [¹¹¹In]DTPA‐indium and a few metal‐DTPA complexes for binding to a specific antibody are discussed as a practical example. Exact calculations of competition assays have been implemented in Microsoft Excel and performed for a variety of concentrations of receptor, tracer, and competitor. The results are identical to those of software packages. IC50 is found larger than Kd by less than 20% only when tracer concentration is small compared with Kd and to the receptor concentration and when this receptor concentration is small compared with Kd. Otherwise, Kd and IC50 may be very different and approximations proposed in the literature to obtain Kd values from graphically derived IC50 are not acceptable as soon as the concentrations of tracer or of receptor approach Kd. Under most experimental conditions, IC50 values do not reflect Kd values. Using available software packages to determine and report Kd values would allow for more meaningful comparisons of results obtained under different experimental conditions.     

Combined multiple testing by censored empirical likelihood

We propose a new procedure for combining multiple tests in samples of right-censored observations. The new method is based on multiple constrained censored empirical likelihood where the constraints are formulated as linear functionals of the cumulative hazard functions. We prove a version of Wilks’ theorem for the multiple constrained censored empirical likelihood ratio, which provides a simple reference distribution for the test statistic of our proposed method. A useful application of the proposed method is, for example, examining the survival experience of different populations by combining different weighted log-rank tests. Real data examples are given using the log-rank and Gehan-Wilcoxon tests. In a simulation study of two sample survival data, we compare the proposed method of combining tests to previously developed procedures. The results demonstrate that, in addition to its computational simplicity, the combined test performs comparably to, and in some situations more reliably than previously developed procedures. Statistical software is available in the R package ‘emplik’.     

Issues in the assessment of non-inferiority: perspectives drawn from case studies

Superiority claims for improved efficacy are the backbone of clinical development of new therapies. However, not every new therapy in development allows for such a claim. Some therapies per se do not try to improve efficacy further but concentrate on important aspects in safety or convenience. Such improvements can be equally important to patients, and development strategies should be available for such compounds. A three-arm design with placebo, active control and experimental treatment may be viewed as the golden standard for such compounds; however, it may be difficult if not impossible to add a placebo arm in certain diseases. In such situations, non-inferiority designs are the only development option left. This paper will highlight some of the key issues with such designs in practice and will report experience from two studies from different therapeutic areas intended for regulatory submission.