Randomized response technique in a National Survey

In order to produce estimates of the number of women having abortions during a 12-month period in the conterminous United States, the randomized response technique was used in the 1973 National Survey of Family Growth. The model applied used 2 unrelated questions in separate half-samples, with a coin as the randomizing device. The randomized response technique resulted in a higher estimate for the number of women with abortions that has previously been obtained through direct questions or reporting systems. The overall estimated proportion who had abortions among women who had been married or who had their own children in the household is 3.0% with a standardized error of 0.8 percentage points; however, there is a wide variation in the half-sample estimates of abortion. Differences between the 2 half-samples led to an examination of possible measurement error. 3 types of errors in measurement which may affect the estimate based on the randomized response technique are: 1) error in the answer to the sensitive question on abortion under the randomized response conditions; 2) error in the answer to the innocuous question under randomized response conditions; and 3) error in the answer to the innocuous question when asked directly. Comparisons between data from the different sources for currently married women suggest that all differences are not due to measurement error and that a large number of women had an unreported and/or illegal abortion in 1973. Although the randomized response models have been in use for at least 10 years, there continues to be a need for work on the field administration and subsequent analysis of these models.     

An approximation to percentiles of a variable of the bivariate normal distribution when the other variable is truncated,with applications

A Cornish-Fisher expansion is used to approximate the per-centiles of a variable of the bivariate normal distribution when the other variable is truncated. The expression is in terms of the bivariate cumulants of a singly truncated bivariate normal distribution. The percentiles are useful in the problem of personnel selection where we use a screening variable to screen applicants for employment and a correlated performance variable to screen employees for rehiring. This paper provides a bivariate cumulants table for determining the cutoff score of the performance variable. The following two problems are also con¬sidered: (1) determine the proportion of applicants who would have been successful had no screening been applied, and (2) determine the proportion of individuals being rejected byscreening who would have been successful had they been hired, The variable that is used to measure job performance and the variable that measures the outcome of an aptitude test are assumed to be jointly normally distributed with correlation ρ     

Control of type 1 error in a hybrid complete two‐period vaccine efficacy trial

A complete two‐period experimental design has been defined as one in which subjects are randomized to treatment, observed for the occurrence of an event of interest, re‐randomized, and observed again for the event in a second period. A 4‐year vaccine efficacy trial was planned to compare a high‐dose vaccine with a standard dose vaccine. Subjects would be randomized each year, and subjects who had participated in a previous year would be allowed to re‐enroll in a subsequent year and would be re‐randomized. A question of interest is whether positive correlation between observations on subjects who re‐enrolled would inflate the variance of test statistics. The effect of re‐enrollment and correlation on type 1 error in a 4‐year trial is investigated by simulation. As conducted, the trial met its power requirements after two years. Subjects therefore included some who participated for a single year and others who participated in both years. Those who participated in both years constituted a complete two‐period design. An algebraic expression for the variance of the treatment difference in a complete two‐period design is derived. It is shown that under a ‘no difference’ null, correlation does not result in variance inflation in this design. When there is a treatment difference, there is variance inflation but it is small. In the vaccine efficacy trial, the effect of correlation on the statistical inference was negligible. Copyright © 2014 John Wiley & Sons, Ltd.     

Data-Informed Collection Decisions Using R

ABSTRACT

Collection decisions can seem daunting to a librarian who is new to the job. In charge of many new-to-her subject fund codes, the author wanted to understand what had been previously purchased using these funds and how to effectively manage a custom ebook collection. The author used the R programming language to clean and merge purchase and usage data. This article will provide an overview of tasks in R that can be leveraged for making data-informed collection decisions and for sharing information with colleagues.     

Imputation of MĀori Descent for Electoral Calculations in New Zealand

The New Zealand Government Statistician decided that, for electoral purposes, Statistics New Zealand should impute Māori–descent status for individuals not responding Yes or No to theMāori–descent question in the 1996 Census of Population and Dwellings. Imputation provides a sounder basis for calculating electoral populations than the approach used in 1994, when all who had not answered clearly Yes or No in the 1991 Census were effectively allocated to non–Māori descent. For the purposes of imputation, the key variables related to the Māori–descent variable were identified using a statistical technique called CHAID (Chisquared Automatic Interaction Detector). Subgroups were created by cross–classification across five variables—island, iwi, Māori ethnic group, Māori–descent composition of the rest of the household, and age group. Within each subgroup, the proportion who responded Yes or No for Māori descent was used to allocate the remainder to Yes or No. The imputation increased the proportion allocated to Māori descent from 16.0% to 17.4% of the total population. However, the proportion of the population imputed to Māori descent was smaller than the proportion who specified Māori descent originally.     

Business and industrial statistics: the early years

Before his death in July 2002, George Barnard had started writing a sketch of the history of business and industrial statistics in the first 50 years of the twentieth century. The piece was never finished, but it is nonetheless a valuable memoir of the early development of the discipline, from someone who knew those involved.     

Nursing Research Journals

Abstract

Recent discussions concerning the mission and direction of graduate programs in library and information science (LIS) have become heated. In a response to a call for greater communication between practitioners and LIS educators, eight librarians who are relatively recent graduates of LIS graduate programs offer their views on what they wish their programs had taught them about serials. All are either working in serials or have serials experience. Serials Review 2003; 29:26–35.     

The mathematics of Benford’s law: a primer

This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid researchers who are interested in applying Benford’s law, and need to understand general principles clarifying when to expect the appearance of Benford’s law in real-life data and when not to expect it. A second main target audience is students of statistics or mathematics, at all levels, who are curious about the mathematics underlying this surprising and robust phenomenon, and may wish to delve more deeply into the subject. This survey of the fundamental principles behind Benford’s law includes many basic examples and theorems, but does not include the proofs or the most general statements of the theorems; rather it provides precise references where both may be found.

     

A joint latent class changepoint model to improve the prediction of time to graft failure

Summary.  The reciprocal of serum creatinine concentration, RC, is often used as a biomarker to monitor renal function. It has been observed that RC trajectories remain relatively stable after transplantation until a certain moment, when an irreversible decrease in the RC levels occurs. This decreasing trend commonly precedes failure of a graft. Two subsets of individuals can be distinguished according to their RC trajectories: a subset of individuals having stable RC levels and a subset of individuals who present an irrevocable decrease in their RC levels. To describe such data, the paper proposes a joint latent class model for longitudinal and survival data with two latent classes. RC trajectories within latent class one are modelled by an intercept-only random-effects model and RC trajectories within latent class two are modelled by a segmented random changepoint model. A Bayesian approach is used to fit this joint model to data from patients who had their first kidney transplantation in the Leiden University Medical Center between 1983 and 2002. The resulting model describes the kidney transplantation data very well and provides better predictions of the time to failure than other joint and survival models.     

Slope Estimation for Bivariate Longitudinal Outcomes Adjusting for Informative Right Censoring Using Discrete Survival Model: Application to the Renal Transplant Cohort

Patients undergoing renal transplantation are prone to graft failure which causes lost of follow-up measures on their blood urea nitrogen and serum creatinine levels. These two outcomes are measured repeatedly over time to assess renal function following transplantation. Loss of follow-up on these bivariate measures results in informative right censoring, a common problem in longitudinal data that should be adjusted for so that valid estimates are obtained. In this study, we propose a bivariate model that jointly models these two longitudinal correlated outcomes and generates population and individual slopes adjusting for informative right censoring using a discrete survival approach. The proposed approach is applied to the clinical dataset of patients who had undergone renal transplantation. A simulation study validates the effectiveness of the approach.     

A case–control study relating railroad worker mortality to diesel exhaust exposure using a threshold regression model

A case–control study of lung cancer mortality in U.S. railroad workers in jobs with and without diesel exhaust exposure is reanalyzed using a new threshold regression methodology. The study included 1256 workers who died of lung cancer and 2385 controls who died primarily of circulatory system diseases. Diesel exhaust exposure was assessed using railroad job history from the US Railroad Retirement Board and an industrial hygiene survey. Smoking habits were available from next-of-kin and potential asbestos exposure was assessed by job history review. The new analysis reassesses lung cancer mortality and examines circulatory system disease mortality. Jobs with regular exposure to diesel exhaust had a survival pattern characterized by an initial delay in mortality, followed by a rapid deterioration of health prior to death. The pattern is seen in subjects dying of lung cancer, circulatory system diseases, and other causes. The unique pattern is illustrated using a new type of Kaplan–Meier survival plot in which the time scale represents a measure of disease progression rather than calendar time. The disease progression scale accounts for a healthy-worker effect when describing the effects of cumulative exposures on mortality.     

career story: The importance of being ERNIE

ERNIE is the Electronic Random Number Indicator Equipment that caused huge interest in 1957 when it began selecting prize-winners for the new Premium Bonds, the first government-sponsored gamble in Britain in modern times. Stephanie Shirley was a young statistician working on ERNIE. Today, as Steve Shirley or Dame Stephanie , she is one of the wealthiest women in Britain—not through winning on Premium Bonds herself, but through the pioneering software company she formed which, for the first time, gave female-friendly employment to women programmers (and statisticians) who had children and dependants at home to care for. She is now a major philanthropist and a driving force for research into the social effects of the Internet and into autism. She has given more than £50 million to charities in those fields. Julian Champkin interviews her.     

Seasonal patterns of fertility measures: theory and data

The distribution of births by month exhibits a seasonal pattern in most populations. The monthly marital fertility rate for an area of Bangladesh provides a good example of the seasonal periodicity. Seasonal patterns of measures of reproduction in a population of married women are considered. Equations are developed that predict the seasonal patterns of these alternative measures under the assumption that the fertility rate (R) follows a trigonometric curve. This is followed by an empirical analysis of the measures in a Bangladesh population that has a pronounced seasonal fertility. The investigation is intended both to validate the theoretical framework developed in the 1st part of the paper as well as to determine whether seasonal variation in actual populations is sufficiently large to affect the alternative measures significantly. 4 measures are considered: pregnancy prevalence (PP)--the proportion of married women who are pregnant at the survey date; mean open birth interval (MOI)--the time from the last live birth to the date of the survey for parous women and from the time of marriage to the date of the survey for nulliparous women; mean closed interval-birth (MCIB)--the mean interval between the last 2 live births for married women who have a birth in the period immediately preceding the survey date; and mean closed interval-woman (MCIW)--the mean interval between the last 2 live births for women who have had at least 2 children by the time of the survey. It is assumed that the seasonal pattern of the fertility rate of a population follows a cosine curve and that there is no trend in annual fertility from year to year. The lag and relative variability of the other measures are considered in comparison with the fertility rate curve. The predictions from this theoretical effort, when compared with observed patterns and trigonometric regression results for each measure in data from Bangladesh, are shown to be quite accurate. The figure and regression results show that R, PP, and MOI have definite seasonal periodicity, but MCIB and MCIW do not display any seasonal patterns. If there is a secular trend in fertility in addition to seasonality, these relationships between the seasonal patterns of the measures may no longer hold. There is a disadvantage to using closed interval measures, for they are unable to detect effects of limiting of childbearing in a population since they are based only on information from women who have births.     

A multilevel analysis of longitudinal ordinal data: evaluation of the level of physical performance of women receiving adjuvant therapy for breast cancer

Longitudinal health-related quality-of-life (QOL) data are often collected as part of clinical studies. Here two analyses of QOL data from a prospective study of breast cancer patients evaluate how physical performance is related to factors such as age, menopausal status and type of adjuvant treatment. The first analysis uses summary statistic methods. The same questions are then addressed using a multilevel model. Because of the structure of the physical performance response, regression models for the analysis of ordinal data are used. The analyses of base-line and follow-up QOL data at four time points over two years from 257 women show that reported base-line physical performance was consistently associated with later performance and that women who had received chemotherapy in the month before the QOL assessment had a greater physical performance burden. There is a slight power gain of the multilevel model over the summary statistic analysis. The multilevel model also allows relationships with time-dependent covariates to be included, highlighting treatment-related factors affecting physical performance that could not be considered within the summary statistic analysis. Checking of the multilevel model assumptions is exemplified.     

Structurally consistent probabilities of selecting answers

This paper offers a procedure for specifying probabilities for students to select answers on a multiple-choice test that, unlike previous procedures, satisfies all three of the following structural consistency conditions: (1) for any student, the sum over questions of the probabilities that the student will use the correct answers is the student's score on the test; (2) for any student, the sum over possible answers of the probabilities of using the answers is 1.0; and (3) for any answer to any question, the sum over students of the probabilities of using that answer is the number of students who used that answer. When applied to an exam, these fully consistent probabilities had the same power to identify cheaters as the probabilities proposed by Wesolowsky, and noticeably better power than the probabilities suggested by Frary et al.     

财产损失分布建模与实证分析研究

一、引言财产损失分布建模 ,是精算师的一项极为重要的工作。一般来说 ,不同保险标的财产损失具有不同的分布模型 ,即便是同一种保险标的在不同的保险环境下 ,其损失分布也没有可遵循的具体原则。因此 ,我们渴望研究一种简便、科学、实用、快捷的损失分布建模方法 ,针对具体险种的历史损失数据 ,选择损失分布形态并达到最好的拟合。这就是要选择理论模型 ,然后再利用实际数据进行参数估计和拟合检验。从整个过程来看 ,是一般统计建模的程序 ,但是 ,又存在着很大的不同 ;我们知道在大多数统计建模的教科书和相关的文献中都是预先给出所研究的…     

THE CONTRIBUTION OF W. H. ARCHER TO VITAL STATISTICS IN THE COLONY OF VICTORIA

William Henry Archer, as Assistant Registrar General, was responsible for implementing the 1854 Registration Act in the colony of Victoria, and thereby helped establish the framework for official statistics in Australia. Eminently suitable for this role, having served his apprenticeship as an actuary and statistician in London prior to emigration in 1852, his career paralleled that of Dr. William Farr, the famous vital statistician. The greatest contribution Archer made to statistics in Australia was to put the lessons learnt by the statisticians of early Victorian England to advantage and place government statistical practices on a sound footing. Archer had a special interest in infant and childhood mortality, then accounting for one-half of all deaths in the new colony, and showed that a major factor was the extent of dysentery and diarrhoea during the warmer part of the year. Despite the high prevalence, Archer calculated the incidence of infant mortality to be less than in Europe at the time. Had he established links with the medical profession or with persons in the Social sciences who could have appreciated the valuable information being collected in the new government records, as in England where the sanitary reformers made great use of data collected by Farr for their own ends, Archer could have had a far greater impact on the intellectual and medical life of Victoria. Instead he was deflected into an administrative career which ended prematurely for political and religious reasons.     

Tagging and deportation: who gets it right?

The Home Office in England suffered major embarrassment this year over its failure to deport foreign nationals who had served prison sentences. It could not even supply statistics on how many there were, or what crimes they may have committed after release. Scotland, in contrast, could answer such questions with ease. Sheila Bird investigates English failure and Scottish solutions.     

Combined survival analysis of cardiac patients by a Cox PH model and a Markov chain

The control and treatment of dyslipidemia is a major public health challenge, particularly for patients with coronary heart diseases. In this paper we propose a framework for survival analysis of patients who had a major cardiac event, focusing on assessment of the effect of changing LDL-cholesterol level and statins consumption on survival. This framework includes a Cox PH model and a Markov chain, and combines their results into reinforced conclusions regarding the factors that affect survival time. We prospectively studied 2,277 cardiac patients, and the results show high congruence between the Markov model and the PH model; both evidence that diabetes, history of stroke, peripheral vascular disease and smoking significantly increase hazard rate and reduce survival time. On the other hand, statin consumption is correlated with a lower hazard rate and longer survival time in both models. The role of such a framework in understanding the therapeutic behavior of patients and implementing effective secondary and primary prevention of heart diseases is discussed here.     

On the measurement and analysis of asymmetry with applications to facial modelling

Summary.  Asymmetry is a feature of shape which is of particular interest in a variety of applications. With landmark data, the essential information on asymmetry is contained in the degree to which there is a mismatch between a landmark configuration and its relabelled and matched reflection. This idea is explored in the context of a study of facial shape in infants, where particular interest lies in identifying changes over time and in assessing residual deformity in children who have had corrective surgery for a cleft lip or cleft lip and palate. Interest lies not in whether the mean shape is asymmetric but in comparing the degrees of asymmetry in different populations. A decomposition of the asymmetry score into components that are attributable to particular features of the face is proposed. A further decomposition allows different sources of asymmetry due to position, orientation or intrinsic asymmetry to be identified for each feature. The methods are also extended to data representing anatomical curves across the face.