Large Strata Research Articles

A revised Little Ice Age chronology of the Franz Josef Glacier, Westland, New Zealand

A reassessed Little Ice Age chronology of the Franz Josef Glacier is presented. Diameter at breast height of 1340 southern rata (Metrosideros umbellata) and kamahi (Weinmannia racemosa) was measured within 50, 150‐m2 quadrats in the Waiho Valley. Age‐size relationships based on 60 tree‐ring counts and associated diameter at breast height measurements were constructed, although the unknown shape of growth curves beyond the realm of tree‐ring data rendered extrapolation unreliable. Thus, the revised chronology is interpreted from mapped tree‐ring counts and measured diameter at breast height of the largest rata and kamahi within moraine limits and trimlines to determine the minimum time elapsed since deglaciation. The Franz Josef Glacier's Little Ice Age (LIA) maximum culminated before AD 1600, when it terminated c. 4.5 km down‐valley of its 2001 position. Subsequent, but lesser magnitude, re‐advances culminated by c. AD 1600 and 1800. This pattern is strongly corroborated by other New Zealand proxy climate data. Evidence from this reassessment provides increasing support for an earlier LIA maximum of the Franz Josef Glacier than is often cited.

The post‐communist transformation: Elite orientations and the emerging Russian state

The simultaneous transitions to democracy market economy and federal decentralisation following change of regime in Russia heavily inflicted upon each other's achievements and almost tore Russia apart. This article asks why the Kremlin reform leadership soon ran into major difficulties.The main argument is that reforms lacking necessary means for implementation soon clashed with the orientations of the large stratum of political, administrative and business elites on national,‐ and regional levels who diligently made use of their newly won democratic and market opportunities in a decentralised federation. The Kremlin leaders became highly dependent on them, a circumstance that eroded Yeltsin's liberal‐istic program and paved the way for Putin's re‐centralisation of the state. Using structured questionnaire interviews, firstly. I am asking how integrated are their orientations, to which extent they are congruent with Kremlin policies and if they have changed from Yeltsin to Putin. Secondly, the question is to which extent the attitudes are shaped by past heritages, new institutions and post‐communist pragmatic ‘learning’. The last part discusses what consequences this culture among important national and regional elites may have for the emerging hybrid‐state in Russia.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent‐deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent‐deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux–time profiles for finite donor volumes and the slope of the terminal log flux–time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount–time and flux–time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum–vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. © 2001 Wiley‐Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504–520, 2001

On mantel-haenszel type estimators in simple nested case-control studies

We are concerned with nested case-control studies in this article. For proportional hazards model, a class of over-all estimators of hazard ratios is presented when simple samples are drawn from risk sets. These estimators have the form of the Mantel-Haenszel estimator of odds ratio, and are consistent not only for large strata, but also for sparse data. Consistent estimators of the variances of the proposed hazard ratio estimators are also developed. An example is given to illustrate the proposed estimators.

A class of permutation tests for stratified survival data.

We propose a class of permutation tests for stratified survival data. The tests are derived using the framework of Fay and Shih (1998, Journal of the American Statistical Association 93, 387-396), which creates tests by permuting scores based on a functional of estimated distribution functions. Here the estimated distribution function for each possibly right-, left-, or interval-censored observation is based on a shrinkage estimator similar to the nonparametric empirical estimator of Ghosh, Lahiri, and Tiwari (1989, Communications in Statistics--Theory and Methods 18, 121-146), and permutation is carried out within strata. The proposed test with a weighted Mann-Whitney functional is similar to the permutation form of the stratified log-rank test when there is a large strata effect or the sample size in each stratum is large and is similar to the permutation form of the ordinary log-rank test when there is little strata effect. Thus, the proposed test unifies the advantages of both the stratified and ordinary log-rank tests. By changing the functional, we may obtain a stratified Prentice-Wilcoxon test or a difference in means test with similar unifying properties. We show through simulations the advantage of the proposed test over existing tests for uncensored and right-censored data.

Estimation and Sample Design in Prevalence Surveys of Dementia

Population prevalence rates of dementia using stratified sampling have previously been estimated using two methods: standard weighted estimates and a logistic model-based approach. An earlier study described this application of the model-based approach and reported a small computer simulation comparing the performance of this estimator to the standard weighted estimator. In this article we use large-scale computer simulations based on data from the recently completed Kame survey of prevalent dementia in the Japanese-American residents of King County, Washington, to describe the performance of these estimators. We found that the standard weighted estimator was unbiased. This estimator performed well for a sample design with proportional allocation, but performed poorly for a sample design that included large strata that were lightly sampled. The logistic model-based estimator performed consistently well for all sample designs considered in terms of the extent of variability in estimation, although some modest bias was observed.

Least Median of Weighted Squares in Logistic Regression with Large Strata

Least Median of Weighted Squares in Logistic Regression with Large Strata

Least median of weighted squares in logistic regression with large strata

One aim of robust regression is to find estimators with high finite sample breakdown points. Although various robust estimators have been proposed in logistic regression models, their breakdown points are not yet known. Here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point, provided the estimator has to fulfill a weak condition. In logistic regression models with large strata however, a modification of Rousseeuw's least median of squares estimator is shown to have a finite sample breakdown point of approximately ½.

Development of monitoring procedures for the herbaceous layer on the Northeastern Transvaal escarpment

A step-wise approach was followed towards the design of a monitoring system for the herbaceous layer on the escarpment of the Drakensberg mountains in the Transvaal, South Africa. The parameter of concern was proportional species composition. In a first phase, the plot size and number of point observations required to achieve a repeatable assessment of a single plot at a predetermined precision level were investigated. The Chapman-Richards three-parameter model was fitted to similarity values obtained from comparisons between successively larger sets of points. This resulted in 140 points being required within a 30 x 30 plot in order to recover 95% of the internal association of the composition data. In a second phase, the number of plots required for a repeatable assessment of a large stratum was determined. Successively larger nested areas were sampled. Monitoring of a large stratum at 95% of asymptotic replicate similarity would require sets of 21 randomly selected plots. The third and final phase was concerned with the development of a procedure for detecting change. A similarity test made it possible to detect change between successive surveys with a known degree of precision. Keywords: botany; composition; drakensberg mountains; herbaceous layer; internal association; model; monitoring; precision; procedure; replicate similarity; sourveld; south africa; species composition; survey; transvaal; wheel-point apparatus African Journal of Range & Forage Science , 10(3): pp. 129-134

Logistic analysis in case-control studies under validation sampling

SUMMARY This paper proposes an analysis of case-control data under a double-sampling scheme, when covariates are missing or measured with error at the first stage of sampling and are validated at the second stage in a subsample. The method combines risk information from both samples. It is derived under the assumptions that (i) the prospective disease incidence model is of logistic form, (ii) the proxy or partial information takes on finitely many values, and (iii) the error is nondifferential. The method of Prentice & Pyke (1979) is extended to a two-sample design to derive an estimating equation for the odds-ratio parameters. It provides an alternative estimator to that given by Breslow & Cain (1988). Consistency and asymptotic normality of the estimates are derived and a variance formula is presented. Parameters can be estimated by use of standard packages for quantalresponse data. The method can easily be extended to the analysis of stratified designs with large strata.

Victimization Revisited: A National Statistical Analysis

After an historical introduction to the problem of violence in society, and a short review of some important socio-juridical developments that took place during the first part of the 20th century, the authors review the crime rate in major United States cities during the past decade. They then present a statistical analysis of the murder rate in eight American cities from 1965 to 1990. The results reveal an appalling increase in the crime rate for that period. The result of this longitudinal analysis confirms that crime is rampant in American cities, that there is an interplay between mobility and crime rate, and that the widespread use of crack-cocaine coincides with the upsurge of the crime rate from 1985 to the present. In their reflections and suggestions the authors analyze socio-psychological factors leading to violent crime and discuss the apparent present impotence of societal agencies, the police, and the courts in dealing with crime. They also offer some of their views regarding the conflicting and counterproductive ways in which present-day society tends to deal with its offenders. They conclude that in order to deal efficiently with the soaring crime in the United States, in addition to a multidisciplinary approach, society and its people should try to address the primary causative factor: the organizational and moral disintegration of the American family unit. The authors believe that the lack of a socially educating, morally cohesive, affectively bound and economically self-sufficient family breeds social incompetence and crime among a large stratum of the population.

Pseudotable methods for the analysis of 2 × 2 tables

Epidemiologists often use the log odds ratio regression model to analyze sets of 2 × 2 tables. The estimation of a common odds ratio is based on this model. The classical estimation procedures for this problem are maximum likelihood, conditional maximum likelihood, and Mantel-Haenszel estimation. This paper proposes new estimators which augment the data by pseudotables of a particular form to reduce the bias and mean squared error of the estimation. The estimators can be motivated by Bayes and empirical Bayes methodology or as penalized likelihood estimators. A simulation study demonstrates that the proposed estimators have improved operating characteristics over large portions of the parameter space compared to the classical estimators. Applications are given to estimating the common odds ration of tumor in two examples, one involving “large strata” and one involving “sparse strata”.

Confidence limits for small proportions in complex samples

Exact upper confidence limits for small proportions in stratified samples are derived. An algorithm for their computation which employs a new normal approximation for the case of infinitely large strata and a finite number of defectives is proposed. Using selected examples it is shown that the usual confidence limits derived from the standard normal approximation can be highly misleading, and that the exact limits are not unacceptably conservative when compared to natural Empirical Bayes and appropriately defined pseudo-Bayes limits. The loss of efficiency of non-proportionate staratified designs, vis-a-vis simple random sampling or proportionate designs for setting confidence limits on small proportions is studied in a variety of examples. Exact upper confidence limits for small proportions are also derived for simple random samples of equal-size clusters, and a similar algorithm for their derivation is presented. These limits are compared to several Bayes credibility limits in selected examples. The los...

Generalized Mantel-Haenszel Estimators for K 2 x J Tables

Mickey and Elashoff (1985, Biometrics 41, 623-635) gave an extension of Mantel-Haenszel estimation to log-linear models for 2 x J x K tables. Their extension yields two generalizations of the Mantel-Haenszel odds ratio estimator to K 2 x J tables. This paper provides variance and covariance estimators for these generalized Mantel-Haenszel estimators that are dually consistent (i.e., consistent in both large strata and sparse data), and presents comparisons of the efficiency of the generalized Mantel-Haenszel estimators.

Information Value and Investor Wealth: The Case of Earnings Announcements

This paper empirically investigates the relation between investor wealth and the value of annual and quarterly earnings announcements as implied by (1) the behavior of mean stock trade transaction sizes at announcement dates, and (2) transaction size-stratified trading activity in postannouncement time periods. Announcement-period mean transaction sizes are found to exceed expected mean transactions sizes estimated from trading activity occurring in nonannouncement periods. This result is attributed to a greater relative trading response to earnings announcements by wealthier investors, consistent with Ohlson's [1975] proposition that information value increases with investor wealth in a security market setting. Further evidence of a positive relation between value and wealth is found when postearnings announcement stock transactions are stratified by share size into three strata, where the first stratum (small stratum) is transactions of 100 and 200 shares, the second stratum (large stratum) is transactions of 300 to 900 shares, and the third stratum (institutional

Variance estimators for attributable fraction estimates consistent in both large strata and sparse data.

A number of variance formulae for the attributable fraction have been presented, but none is consistent in sparse data, such as found in individually matched case-control studies. This paper employs Mantel-Haenszel estimation to derive variance estimators for attributable fractions that are dually consistent, that is, consistent in both sparse data and large strata. The method may also be applied using conditional maximum likelihood. Extensions of these estimators to situations involving effect modification and preventive exposures are also derived. Examples of applications to individually matched case-control studies are given.

Nutrient Concentrations in Foliage of Species Within a New South Wales Sub-Tropical Rainforest

Sub-tropical rainforests in New South Wales are complex, often with more than 30 tree species ha−1. Estimation of nutrient contents involves obtaining information on the range of nutrient concentrations both in different species and in different forest strata. The foliage from the tree and shrub components of an undisturbed forest were analyzed chemically together with the small tree and shrub component of an area logged two years previously. The site had high nutrient availability. All nutrients analyzed (nitrogen, phosphorus, calcium, magnesium, potassium, manganese, aluminium, sodium, zinc, iron, boron and chloride) varied between species. Some individuals accumulated high concentrations of specific nutrients, but an accumulator of one nutrient was not necessarily an accumulator of any other. Assessment of nutrient concentrations on the basis of forest strata showed major differences. Nutrients were accumulated in higher concentrations on a disturbed site than on an undisturbed site. This has been discussed in relation to nutrient conservation mechanisms after disturbance. Within the undisturbed stand, the large shrub stratum had the highest concentrations of nitrogen, phosphorus, potassium and boron. Mean concentrations of aluminium, sodium and chloride were highest in the small shrub stratum, mainly because several species accumulate these elements.

Estimation of a Common Effect Parameter from Sparse Follow-Up Data

Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.

Maximum Likelihood Fitting of General Risk Models to Stratified Data

A recursive algorithm (Howard, 1972; Gail et al., 1981) useful for maximum conditional likelihood fitting of logistic regression models with large strata can be generalized to arbitrary relative risk models. An example is presented which permits comparison between fitting methods vis a vis stratified vs. unstratified analysis, additive vs. multiplicative risk model, and use of expected vs. observed information. On the basis of results from this comparison we suggest that Wald's test and the score test computed with observed information be avoided in non‐standard models. An interactive computer program is available for fitting multiplicative, additive and general risk models to stratified data.

Likelihood calculations for matched case-control studies and survival studies with tied death times

SUMMARY A recursion is presented which permits rapid computation of a conditional likelihood function which arises in matched case-control studies and survival studies with tied death times. An example with seven parameters and ten large strata, the largest of which contains 29 cases and 52 controls, illustrates the feasibility of the conditional maximum likelihood solution. These methods may be specialized to permit rapid calculation of the conditional maximum likelihood estimate of the common odds ratio for several 2 x 2 tables.