The Gompertz equation as a predictive tool in demography

The Gompertz demographic model describes rates of aging and age-independent mortality with the parameters and A, respectively. Estimates of these parameters have traditionally been based on the assumption that mortality rates are constant over short to moderate time periods. This assumption is questionable even for very large samples assayed over short time intervals. In this article, we compare several methods for estimating the Gompertz parameters, including some that do not assume constant mortality rates. A maximum likelihood method that does not assume constant mortality rates is shown to be best, based on the bias and variance of the Gompertz parameter estimates. Moreover, we show how the Gompertz equation can then be used to predict mean longevity and the time of the n_th percentile of mortality. Methods are also developed that assign confidence intervals to such estimates. In some cases, these statistics may be estimated accurately from only the early deaths of a large cohort, thus providing an opportunity to estimate longevity on long-lived organisms quickly.     

Variance estimation for clustered recurrent event data with a small number of clusters

Often in biomedical studies, the event of interest is recurrent and within-subject events cannot usually be assumed independent. In semi-parametric estimation of the proportional rates model, a working independence assumption leads to an estimating equation for the regression parameter vector, with within-subject correlation accounted for through a robust (sandwich) variance estimator; these methods have been extended to the case of clustered subjects. We consider variance estimation in the setting where subjects are clustered and the study consists of a small number of moderate-to-large-sized clusters. We demonstrate through simulation that the robust estimator is quite inaccurate in this setting. We propose a corrected version of the robust variance estimator, as well as jackknife and bootstrap estimators. Simulation studies reveal that the corrected variance is considerably more accurate than the robust estimator, and slightly more accurate than the jackknife and bootstrap variance. The proposed methods are used to compare hospitalization rates between Canada and the U.S. in a multi-centre dialysis study. Copyright (c) 2005 John Wiley & Sons, Ltd.     

Predicting geographic variation in cutaneous leishmaniasis, Colombia

Approximately 6,000 cases of cutaneous leishmaniasis are reported annually in Colombia, a greater than twofold increase since the 1980s. Such reports certainly underestimate true incidence, and their geographic distribution is likely biased by local health service effectiveness. We investigated how well freely available environmental data explain the distribution of cases among 1,079 municipalities. For each municipality, a unique predictive logistic regression model was derived from the association among remaining municipalities between elevation, land cover (preclassified maps derived from satellite images), or both, and the odds of at least one case being reported. Land cover had greater predictive power than elevation; using both datasets improved accuracy. Fitting separate models to different ecologic zones, reflecting transmission cycle diversity, enhanced the accuracy of predictions. We derived measures that can be directly related to disease control decisions and show how results can vary, depending on the threshold selected for predicting a disease-positive municipality. The results identify areas where disease is most likely to be underreported.     

Estimating equations for association structures

This paper investigates generalized estimating equations for association parameters, which are frequently of interest in family studies, with emphasis on covariance estimation. Separate link functions are used to connect the mean, the scale, and the correlation to linear predictors involving possibly different sets of covariates, and separate estimating equations are proposed for the three sets of parameters. Simulations show that the robust 'sandwich' variance estimator and the jackknife variance estimator for the correlation parameters are generally close to the empirical variance for the sample size of 50 clusters. The results contradict Ziegler et al. and Kastner and Ziegler, where the 'sandwich' estimator obtained from the software MAREG was shown to be unsuitable for practical usage. The problem appears to arise because the MAREG variance estimator does not account for variability in estimation of the scale parameters, but may be valid with fixed scale. We also find that the formula for the approximate jackknife variance estimator in Ziegler et al. is deficient, resulting in systematic deviations from the fully iterated jackknife variance estimator. A general jackknife formula is provided and performs well in numerical studies. Data from a study on the genetics of alcoholism is used to illustrate the importance of reliable variance estimation in biomedical applications.     

How many raters are needed for a reliable diagnosis?

If each of a sample of patients is evaluated by enough raters and is independently diagnosed as either positive or negative, we can evaluate the reliability (kappa coefficient and corresponding confidence interval) of each consensus of 2, 3, 4 … M raters. We can select the optimal consensus, and demonstrate an increase in reliability with multiple diagnoses. Results indicate that the majority rule (for example, two out of three, three out of five raters) does not always yield the highest reliability, nor does any other single rule, which leaves determination of the optimal consensus to empirical evaluation. The kappa coefficient and the confidence intervals are calculated using a jackknife technique for these cases and the optimal consensus is determined. Copyright © 2001 Whurr Publishers Ltd.     

Comparison of variance estimation approaches in a two-state Markov model for longitudinal data with misclassification

We examine the behaviour of the variance-covariance parameter estimates in an alternating binary Markov model with misclassification. Transition probabilities specify the state transitions for a process that is not directly observable. The state of an observable process, which may not correctly classify the state of the unobservable process, is obtained at discrete time points. Misclassification probabilities capture the two types of classification errors. Variance components of the estimated transition parameters are calculated with three estimation procedures: observed information, jackknife, and bootstrap techniques. Simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation. The three approaches generally provide similar variance estimates for large samples and moderate misclassification. In these situations, the resampling methods are reasonable alternatives when programming partial derivatives is not appealing. With smaller chains or higher misclassification probabilities, the bootstrap method appears to be the best choice.     

A comparison of the variance estimation methods for heteroscedastic nonlinear models

Heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice. We discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances, and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters. The simulation study suggests that when the true variance is a function of the mean model, the power of the mean variance function estimation method and the transform‐both‐sides method are the best choices for estimating the standard errors of the estimated model parameters. In general, the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias, especially when the heterogeneity is nonsystematic across values of the covariate. Furthermore, we note that the two modified sandwich estimators are appealing choices in practice, considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform‐both‐sides approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of evidence for linkage from different analytic methods

In a randomly chosen replicate of extended pedigrees from GAW10, we conducted robust multipoint genome scans for linkage using a dense marker map. For analysis of the quantitative traits, we selected sibships from the pedigrees, and for analysis of disease status, small families of affected relatives were selected. Lod-score likelihood analyses were conducted in the full pedigrees and in the affected relative families for selected regions. We located a flanking marker for MG1 on chromosome 5, and identified marker regions including MG2, MG4, and MG5 on chromosomes 8 and 9. The analytic methods were consistent for the major gene with a strong effect; false positive errors on chromosomes 1 and 10 could have been eliminated by requiring evidence from more than one method. © 1997 Wiley-Liss, Inc.     

Laparoscopic-assisted abdominoperineal resection in the prone position

With the introduction of laparoscopic-assisted abdominoperineal resection (LAPR), the traditional Lloyd-Davies position with the Mayo two-team combined approach is being adapted. The Lloyd-Davies position allows two teams of surgeons to work simultaneously, minimizing operating time. The conditions required for laparoscopy restrict a simultaneous procedure. Since LAPR is typically performed as a two-stage procedure, we introduce an alternative position which facilitates the perineal dissection. We review the results and technique of LAPR in the prone position in three patients who were suitable candidates for this procedure. Three patients underwent LAPR. No operative or postoperative complications were encountered and the procedures were in keeping with oncologic principles of resection. Total anesthesia times were less than 3.5 h for these initial patients. No hemodynamic problems were encountered due to the choice of patient positioning. The prone jackknife position greatly increases visualization of deep structures, reduces blood loss, enhances dissection, and reduces the technical demands of the laparoscopic portion of the procedure. Received: 23 October 1995/Accepted: 5 August 1996     

Comparing two correlated C indices with right‐censored survival outcome: a one‐shot nonparametric approach

The area under the receiver operating characteristic curve is often used as a summary index of the diagnostic ability in evaluating biomarkers when the clinical outcome (truth) is binary. When the clinical outcome is right‐censored survival time, the C index, motivated as an extension of area under the receiver operating characteristic curve, has been proposed by Harrell as a measure of concordance between a predictive biomarker and the right‐censored survival outcome. In this work, we investigate methods for statistical comparison of two diagnostic or predictive systems, of which they could either be two biomarkers or two fixed algorithms, in terms of their C indices. We adopt a U‐statistics‐based C estimator that is asymptotically normal and develop a nonparametric analytical approach to estimate the variance of the C estimator and the covariance of two C estimators. A z‐score test is then constructed to compare the two C indices. We validate our one‐shot nonparametric method via simulation studies in terms of the type I error rate and power. We also compare our one‐shot method with resampling methods including the jackknife and the bootstrap. Simulation results show that the proposed one‐shot method provides almost unbiased variance estimations and has satisfactory type I error control and power. Finally, we illustrate the use of the proposed method with an example from the Framingham Heart Study. Copyright © 2014 John Wiley & Sons, Ltd.