Asymptotic distribution of an index for disease clustering

Tango (1984, Biometrics 40, 15-26) proposed an index for disease clustering in time, applicable to grouped data with the assumption that the population at risk remains fairly uniform over the study period. However, the asymptotic distribution of the index derived under the hypothesis of no clustering was rather complex for simple use. Recently, Whittemore and Keller (1986, Biometrics 42, 218) and Whittemore et al. (1987, Biometrika 74, 631-635) proved that the distribution of the index is asymptotically normal. The present paper indicates that their approximation may be poor for moderately large sample sizes and suggests a central chi-square distribution as a better approximation to the asymptotic distribution of this index.     

Disease clustering in time

Tango (1984, Biometrics 40, 15-26) proposed a clustering index for testing for clusters of disease in time. A test based on this clustering index was shown to compare favourably with other statistical tests. In this article we show that Pearson's X2 and its components perform well in testing for clusters of disease in time. The rth of these components identifies a departure from uniformity in moments up to the rth and so helps describe the alternative, if any, to uniformity.     

Detecting genomic clustering of risk variants from sequence data: cases versus controls

As the ability to measure dense genetic markers approaches the limit of the DNA sequence itself, taking advantage of possible clustering of genetic variants in, and around, a gene would benefit genetic association analyses, and likely provide biological insights. The greatest benefit might be realized when multiple rare variants cluster in a functional region. Several statistical tests have been developed, one of which is based on the popular Kulldorff scan statistic for spatial clustering of disease. We extended another popular spatial clustering method—Tango’s statistic—to genomic sequence data. An advantage of Tango’s method is that it is rapid to compute, and when single test statistic is computed, its distribution is well approximated by a scaled χ ² distribution, making computation of p values very rapid. We compared the Type-I error rates and power of several clustering statistics, as well as the omnibus sequence kernel association test. Although our version of Tango’s statistic, which we call “Kernel Distance” statistic, took approximately half the time to compute than the Kulldorff scan statistic, it had slightly less power than the scan statistic. Our results showed that the Ionita-Laza version of Kulldorff’s scan statistic had the greatest power over a range of clustering scenarios.     

Testing for simple independent action between two factors for dichotomous response data

This paper compares three statistics for testing simple independent action between two dichotomous factors with respect to the occurrence of a dichotomous outcome. Sizes and powers are examined for the statistics proposed, under a variety of model parameterizations. The results suggest that a test based on the ratio of the nonresponse probability estimates [considered originally by Wahrendorf, Zentgraf, and Brown (1981, Biometrics 37, 45-54)] has proper size and acceptable power, and is recommended for use in this setting.     

A score test for the possible presence of recessive alleles in generalized ABO-like genetic systems

In generalized ABO-like genetic systems, particularly for certain human leukocyte antigen (HLA) loci, it is quite likely, even for large sample sizes, that no double recessives (or 'double blanks') may be found. It has been suggested that all such data should be analyzed as if the true recessive gene frequency were 0. We derive an easily computed score [or C(alpha)] statistic which tests for the possibility that, in such instances, this frequency may exceed 0. An associated point estimator is suggested. The methods are applied to the data analyzed by Smouse and Williams (1982, Biometrics 38, 757-768).     

Selecting a screening cut-off point or diagnostic criterion for comparing prevalences of disease

Comparisons of population prevalences of disease or of inadequate nutriture, across locations or over time (as in monitoring to detect a change in prevalence) are important activities in epidemiology and public health. The data collected are often counts based on a dichotomy of a continuous indicator variable, and performance of the test procedure depends on the cut-off point used. This cut-off may be chosen to optimize performance, on the assumption that the indicator has a mixed normal distribution with unknown mixing proportion corresponding to the unknown prevalence of disease. Results of James (1978, Biometrics 34, 265-275) are applied and extended to the context of monitoring. Charts are presented to facilitate determination of the optimal cut-off, and examples are given for several indicators of nutritional status.     

Augmented cross-sectional studies with abbreviated follow-up for estimating HIV incidence

Cross-sectional HIV incidence estimation based on a sensitive and less-sensitive test offers great advantages over the traditional cohort study. However, its use has been limited due to concerns about the false negative rate of the less-sensitive test, reflecting the phenomenon that some subjects may remain negative permanently on the less-sensitive test. Wang and Lagakos (2010, Biometrics 66, 864-874) propose an augmented cross-sectional design that provides one way to estimate the size of the infected population who remain negative permanently and subsequently incorporate this information in the cross-sectional incidence estimator. In an augmented cross-sectional study, subjects who test negative on the less-sensitive test in the cross-sectional survey are followed forward for transition into the nonrecent state, at which time they would test positive on the less-sensitive test. However, considerable uncertainty exists regarding the appropriate length of follow-up and the size of the infected population who remain nonreactive permanently to the less-sensitive test. In this article, we assess the impact of varying follow-up time on the resulting incidence estimators from an augmented cross-sectional study, evaluate the robustness of cross-sectional estimators to assumptions about the existence and the size of the subpopulation who will remain negative permanently, and propose a new estimator based on abbreviated follow-up time (AF). Compared to the original estimator from an augmented cross-sectional study, the AF estimator allows shorter follow-up time and does not require estimation of the mean window period, defined as the average time between detectability of HIV infection with the sensitive and less-sensitive tests. It is shown to perform well in a wide range of settings. We discuss when the AF estimator would be expected to perform well and offer design considerations for an augmented cross-sectional study with abbreviated follow-up.     

Spatial Aspects of Foot-Pad Dermatitis in Swedish Broilers

This study aimed at analysing spatial and spatio-temporal aspects of foot-pad dermatitis in Swedish broilers. The information on disease prevalence and severity was based on a two-year foot-health surveillance programme where information on producer, breed, feed manufacturer, region, abattoir, date of slaughter and several other variables was recorded. The level of clustering in space was analysed on 2-digit zipcode level using Moran's I test which measures similarity of location. The level of clustering in space was also analysed using the Ipop test, which takes the population at risk into consideration. The examination of time-space interaction was carried out using the Barton method and the Knox method. We found a significant (p<0.001) clustering of regions with respect to foot-pad dermatitis score using Moran's I test, and a significant (p<0.0001) clustering in space also when related to the number of flocks delivered from each region. The flocks with very high prevalence of foot-pad dermatitis were significantly (p<0.05) clustered in both time and space, i.e. the flocks with high prevalence of lesions came from the same geographic area during the same time periods. This information will permit us to focus the control efforts within the foot-health surveillance programme on specific regions in specific time periods, thus making the programme more effective.     

Nonparametric estimation of the concordance correlation coefficient under univariate censoring

Assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects. Lin's (1989, Biometrics 45, 255-268) concordance correlation coefficient (CCC) has become a popular measure of agreement for correlated continuous outcomes. However, commonly used estimation methods for the CCC do not accommodate censored observations and are, therefore, not applicable for survival outcomes. In this article, we estimate the CCC nonparametrically through the bivariate survival function. The proposed estimator of the CCC is proven to be strongly consistent and asymptotically normal, with a consistent bootstrap variance estimator. Furthermore, we propose a time-dependent agreement coefficient as an extension of Lin's (1989) CCC for measuring the agreement between survival times among subjects who survive beyond a specified time point. A nonparametric estimator is developed for the time-dependent agreement coefficient as well. It has the same asymptotic properties as the estimator of the CCC. Simulation studies are conducted to evaluate the performance of the proposed estimators. A real data example from a prostate cancer study is used to illustrate the method.     

Some goodness-of-fit methods for the Poisson plus added zeros distribution

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.     

Some goodness-of-fit methods for the Poisson plus added zeros distribution.

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.     

General ranked set sampling with cost considerations

Nahhas, Wolfe, and Chen (2002, Biometrics58, 964-971) considered optimal set size for ranked set sampling (RSS) with fixed operational costs. This framework can be very useful in practice to determine whether RSS is beneficial and to obtain the optimal set size that minimizes the variance of the population estimator for a fixed total cost. In this article, we propose a scheme of general RSS in which more than one observation can be taken from each ranked set. This is shown to be more cost-effective in some cases when the cost of ranking is not so small. We demonstrate using the example in Nahhas, Wolfe, and Chen (2002, Biometrics58, 964-971), by taking two or more observations from one set even with the optimal set size from the RSS design can be more beneficial.     

Dynamic light scattering study of muscle F-actin

By use of digital autocorrelation and fast Fourier methods, dynamic light-scattering studies of in vitro reconstituted muscle F-actin were made over a wide range of concentrations, 0.01-2 mg/ml F-actin. Measurements of correlation function [g1(t)]2 showed that a transition from a dilute to a semidilute regime for the Brownian motions of filaments occurred at around 0.3 mg/ml F-actin. Beyond this concentration, profiles of successively measured [g1(t)]2 showed very poor reproducibility. This resulted from the existence of very slow components, which could not be measured with a high statistical accuracy even for a measuring time of 3600 s/run. On the other hand, subtraction of these components automatically by an electronic circuit, [g-1(t)]2, or by computer processing, [g1(t)]2, resulted in a fairly good reproducibility of the profiles. The decay characteristics of [g1(t)]2 (and [g-1(t)]2) were very similar to those of [g1(t)]2 for dilute solutions. A theoretical model will be discussed which could account for the above situation. The time sequence [n(t,T)] of photoelectron counts at a sampling time T of light scattered from semidilute solutions of F-actin was stored on magnetic tapes, and both power spectra S(f) and correlation functions [g-1(t)]2 were computed by taking the ensemble average over many short records with duration 1024T. Since both S(f) and [g-1(t)]2 lacked frequency components lower than 1/(2048T) Hz, their profiles were highly reproducible. An analysis of S(f) confirmed our earlier results which had shown an apparent contradiction to later results by a correlation method. A comparison of S(f) and [g-1(t)]2 based on the same [n(t,T)] clarified the reasons why the bandwidth gamma of S(f) largely differed from the bandwidth gamma of [g1(t)]2 and [g-1(t)]2. The temperature dependence of gamma suggested that F-actin would be flexible and that the flexibility parameter would change with temperature.     

Applications and extensions of Chao's moment estimator for the size of a closed population

This article revisits Chao's (1989, Biometrics45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model M(h)). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (M(th)) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for M(th). Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment.     

Confidence interval estimation of the intraclass correlation coefficient for binary outcome data

We obtain closed-form asymptotic variance formulae for three point estimators of the intraclass correlation coefficient that may be applied to binary outcome data arising in clusters of variable size. Our results include as special cases those that have previously appeared in the literature (Fleiss and Cuzick, 1979, Applied Psychological Measurement 3, 537-542; Bloch and Kraemer, 1989, Biometrics 45, 269-287; Altaye, Donner, and Klar, 2001, Biometrics 57, 584-588). Simulation results indicate that confidence intervals based on the estimator proposed by Fleiss and Cuzick provide coverage levels close to nominal over a wide range of parameter combinations. Two examples are presented.     

A note on sliced inverse regression with regularizations

Summary .   In Li and Yin (2008, Biometrics 64, 124–131), a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least-squares algorithm. This methodology reveals good performance in practice. In this note, we focus on the theoretical properties of the estimator. It is shown that the minimization problem is degenerated in the sense that only two situations can occur: Either the ridge SIR estimator does not exist or it is zero.     

Reducing mean squared error in the analysis of stratified epidemiologic studies

Kalish (1990, Biometrics 46, 493-499) proposed an approximately optimal estimator of a common odds ratio for pair-matched case-control studies. His approach is easily extended to general stratified studies. For unmatched stratified studies, the form of the approximately optimal estimator is very simple, and may often correspond to no more than a small correction to the ordinary stratified estimator.     

On estimating standardized risk differences from odds ratios.

An estimator proposed by Greenland and Holland (1991, Biometrics 47, 319-322) for a standardized risk difference parameter is shown to be a maximum likelihood estimator if the consistent estimator of the common odds ratio is appropriately chosen. The statistical problem under consideration is reparameterized. Likelihood equations are derived.     

Leishmania (Leishmania) major-infected rhesus macaques (Macaca mulatta) develop varying levels of resistance against homologous re-infections

Seven rhesus macaques were infected intradermally with 10(7) promastigotes of Leishmania (Leishmania) major. All monkeys developed a localized, ulcerative, self-healing nodular skin lesion at the site of inoculation of the parasite. Non-specific chronic inflammation and/or tuberculoid-type granulomatous reaction were the main histopathological manifestations of the disease. Serum Leishmania-specific antibodies (IgG and IgG1) were detected by ELISA in all infected animals; immunoblot analyses indicated that numerous antigens were recognized. A very high degree of variability was observed in the parasite-specific cell-mediated immune responses [as detected by measuring delayed-type hypersensitivity (DTH) reaction, in vitro lymphocyte proliferation, and gamma interferon (IFN-gamma) production] for individuals over time post challenge. From all the recovered monkeys (which showed resolution of the lesions after 11 weeks of infection), 57.2% (4/7) and 28.6% (2/7) animals remained susceptible to secondary and tertiary infections, respectively, but the disease severity was altered (i.e. lesion size was smaller and healed faster than in the primary infection). The remaining monkeys exhibited complete resistance (i.e. no lesion) to each rechallenge. Despite the inability to consistently detect correlates of cell-mediated immunity to Leishmania or correlation between resistance to challenge and DTH, lymphocyte transformation or IFN-gamma production, partial or complete acquired resistance was conferred by experimental infection. This primate model should be useful for measuring vaccine effectiveness against the human disease.     

Procedures for two-sample comparisons with multiple endpoints controlling the experimentwise error rate

Clinical trials are often concerned with the comparison of two treatment groups with multiple endpoints. As alternatives to the commonly used methods, the T2 test and the Bonferroni method, O'Brien (1984, Biometrics 40, 1079-1087) proposes tests based on statistics that are simple or weighted sums of the single endpoints. This approach turns out to be powerful if all treatment differences are in the same direction [compare Pocock, Geller, and Tsiatis (1987, Biometrics 43, 487-498)]. The disadvantage of these multivariate methods is that they are suitable only for demonstrating a global difference, whereas the clinician is further interested in which specific endpoints or sets of endpoints actually caused this difference. It is shown here that all tests are suitable for the construction of a closed multiple test procedure where, after the rejection of the global hypothesis, all lower-dimensional marginal hypotheses and finally the single hypotheses are tested step by step. This procedure controls the experimentwise error rate. It is just as powerful as the multivariate test and, in addition, it is possible to detect significant differences between the endpoints or sets of endpoints.