Abdulkadir Hussein

Risk comparison of some shrinkage M-estimators in linear models

The problem of robust estimation of a (linear) regression parameter (vector), in the presence of nuisance scale parameter, is considered when it is a priori suspected that the regression could be restricted to a linear subspace. Asymptotic properties of variants of Stein-rule M-estimators (including the positive-rule shrinkage M-estimators) are studied. Under an asymptotic distributional quadratic risk criterion, their relative dominance picture is explored, analytically as well as by simulation. An extensive sampling experiment is used to examine the small sample characteristics of the proposed estimators over a wide-range of data sampling designs and distributions. Our simulation experiments have provided strong evidence that corroborates with the asymptotic theory. Two examples are provided to illustrate the performance of the estimators in real-life situations.

Robust weighted likelihood estimation of exponential parameters

The problem of estimating the parameter of an exponential distribution when a proportion of the observations are outliers is quite important to reliability applications. The method of weighted likelihood is applied to this problem, and a robust estimator of the exponential parameter is proposed. Interestingly, the proposed estimator is an /spl alpha/-trimmed mean type estimator. The large-sample robustness properties of the new estimator are examined. Further, a Monte Carlo simulation study is conducted showing that the proposed estimator is, under a wide range of contaminated exponential models, more efficient than the usual maximum likelihood estimator in the sense of having a smaller risk, a measure combining bias & variability. An application of the method to a data set on the failure times of throttles is presented.

Child Restraint Use in Canadian Provinces With and Without Legislation in 2010

Objectives: When used correctly, child safety seats reduce the risk of injury to a child passenger compared to seat belts. The objectives of this study are to (1) describe restraint use among Canadian children ages 4–8 years in 2010; (2) compare child safety seat use between provinces with new legislation (post-2006), old legislation (pre-2006), and without legislation; and (3) compare child safety seat use rates from 2006 to 2010. Methods: Roadside observational surveys of child restraint use were performed in 2006 and 2010 using a nationally representative stratified sample. Proportions of restraint use, correct use (i.e., child safety seats and booster seats) in 4- to 8-year-old children was examined between 3 groups: provinces with new legislation (i.e., child safety seat legislation that included implementation of specific legislation for booster seat use for child passengers ages 4–8 years), old legislation, and no legislation. Results: There were 4048 children observed as passengers in motor vehicles. In provinces with new legislation, 84 percent (95% confidence interval [CI], 72.2–90.8) of children were restrained compared to 94.9 percent (95% CI, 93.0–96.7) in provinces with old legislation, and 81.8 percent (95% CI, 77.3–86.3) in provinces without legislation. Correct use of child restraint was 54.1 percent (95% CI, 48.0–60.3) in provinces with new legislation, 29.5 percent (95% CI, 25.9–33.2) in provinces with old legislation, and 52.0 percent (43.0–61.0) in provinces without legislation in 2010. Conclusion: The findings from this study suggest that child safety seat legislation has an impact on restraint use in Canada. Despite the increase in rates of child safety seat use in provinces with new legislation and stable rates in provinces with old legislation, use rates remain low. Injury prevention strategies including further surveillance, interventions, and enforcement of restraint use in children are important to decrease motor vehicle related injury and death.

Monitoring binary outcomes using risk‐adjusted charts: a comparative study

Monitoring binary outcomes when evaluating health care performance has recently become common. Classical statistical methodologies such as cumulative sum (CUSUM) charts have been refined and used for this purpose. For instance, the risk-adjusted CUSUM chart (RA-CUSUM) for monitoring binary outcomes was proposed for monitoring 30-day mortality following cardiac surgery. The RA-CUSUM inherits optimality properties of the original CUSUM charts in the sense of signaling early when there is change. However, although the RA-CUSUM is a powerful monitoring tool, it will always eventually signal a change with probability 1 even when there is no real change. In other words, the probability of a type I error for the RA-CUSUM is 1. It also turns out that, because of the skewed distribution of the run lengths of the RA-CUSUM, the median is often well below the mean, and as a consequence more than half of all its false alarms occur before the designed average run length. In addition, when the change to be detected occurs at a later time in the series of observations being monitored, the rate of false alarms increases, and the RA-CUSUM may not be appropriate. Therefore, if the price of false alarms is high, it is preferable to use methods that control the rate of false alarms. In this paper, we propose alternative sequential curtailed and risk-adjusted charts that control the type I error rate in the context of monitoring 30-day mortality following cardiac surgery. We explore the merits of each of these methodologies in terms of average run lengths as well as in terms of type I error probabilities, and we compare them to the RA-CUSUM chart. We illustrate the methodologies by using data on monitoring performance of seven surgeons from a medical center.

Group sequential testing of homogeneity in genetic linkage analysis

Human genetic linkage studies have the objective of testing whether disease genes are linked to genetic markers based on family genetic data. Sometimes, these studies require many years of recruiting informative families and large amount of funds. One way to reduce the required sample size for such studies is to use sequential testing procedures. In this paper, we investigate two group sequential tests for homogeneity in binomial mixture models that are commonly used in genetic linkage analysis. We conduct Monte Carlo simulations to examine the performance of the group sequential procedures. The results show that the proposed group sequential procedures can save, on average, substantial sample size and detect linkage with almost the same power as their nonsequential counterparts.

Gamma Mixture: Bimodality, Inflexions and L-Moments

We study some characteristics of the mixture of two gamma distributions. Specifically, we characterize regions of the parameter space where the mixture density is bimodal and/or has four inflexion points and further, we provide formulae for the L-moments of such mixtures. These characteristics may be useful in density and parameter estimation methods, as well as in analytical and graphical modality testing procedures. With a simple example, we illustrate the estimation of the parameters of the gamma mixture by the method of L-moments. Such estimators are in some circumstances more efficient than those based on the conventional method of moments.

Parametric estimation of mixtures of two uniform distributions

In this paper, we consider a mixture of two uniform distributions and derive L-moment estimators of its parameters. Three possible ways of mixing two uniforms, namely with neither overlap nor gap, with overlap, and with gap, are studied. The performance of these L-moment estimators in terms of bias and efficiency is compared to that obtained by means of the conventional method of moments (MM), modified maximum likelihood (MML) method and the usual maximum likelihood (ML) method. These intensive simulations reveal that MML estimators are the best in most of the cases, and the L-moment estimators are less subject to bias in estimation for some mixtures and more efficient in most of the cases than the conventional MM estimators. The L-moment estimators are, in some cases, more efficient than the ML and MML estimators.

Sequential Comparison of Two Treatments Using Weighted Wald-Type Statistics

ABSTRACT A weighted Wald-type statistic is proposed for sequential testing of two-sided composite hypothesis comparing two treatments (populations) and allowing random treatment allocation. The large sample behavior of the test statistic is approximated by means of a Bessel process and approximate monitoring boundaries are derived. Examples of normal and binomial populations are given along with Monte Carlo simulations assessing power and average sample number of the tests.

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

ABSTRACT Monitoring health care performance outcomes such as post-operative mortality rates has recently become more common, spurring new statistical methodologies designed for this purpose. One such methodology is the Risk-adjusted Cumulative Sum chart (RA-CUSUM) for monitoring binary outcomes such as mortality after cardiac surgery. When building RA-CUSUMs, independence and model correctness are assumed. We carry out a simulation study to examine the effect of violating these two assumptions on the charts performance.

Sequential testing of process capability indices

A Process Capability Index (PCI) is a numeric summary that compares the behaviour of a product or process characteristics with engineering specifications. We propose a sequential procedure for testing whether two processes are equally capable by using the PCI (C pm). We employ a non-sequential Wald-type statistic and provide its sequential version by Brownian motion approximations. We point out that, as a byproduct, the non-sequential Wald-type statistic used here provides an easily computable alternative to Boyels’ approximate F-test [Boyels, The Taguchi Capability Index, J. Quality Technol. 23 (1991), pp. 17–26]. We give an algorithm for conducting the sequential test and we examine its performance by using Monte Carlo simulations. Finally, we illustrate the method by testing capability improvement of an industrial process before and after calibration based on published data.