Broadband frequency dependence of respiratory impedance in rats.

Past studies in humans and other species have revealed the presence of resonances and antiresonances, i.e., minima and maxima in respiratory system impedance (Zrs), at frequencies much higher than those commonly employed in clinical applications of the forced oscillation technique (FOT). To help understand the mechanisms behind the first occurrence of antiresonance in the Zrs spectrum, the frequency response of the rat was studied by using FOT at both low and high frequencies. We measured Zrs in both Wistar and PVG/c rats using the wave tube technique, with a FOT signal ranging from 2 to 900 Hz. We then compared the high-frequency parameters, i.e., the first antiresonant frequency (far,1) and the resistive part of Zrs at that frequency [Rrs(far,1)], with parameters obtained by fitting a modified constant-phase model to low-frequency Zrs spectra. The far,1 was 570 +/- 43 (SD) Hz and 456 +/- 16 Hz in Wistar and PVG/c rats, respectively, and it did not shift with respiratory gases of different densities (air, heliox, and a mixture of SF(6)). The far,1 and Rrs(far,1) were relatively independent of methacholine-induced bronchoconstriction but changed significantly with increasing transrespiratory pressures up to 20 cmH(2)O, in the same way as airway resistance but independently of changes to tissue parameters. These results suggest that, unlike the human situation, the first antiresonance in the rat is not primarily dependent on the acoustic dimensions of the respiratory system and can be explained by interactions between compliances and inertances localized to the airways, but this most likely does not include airway wall compliance.     

基于空间结构调查的林分密度估计

利用林分空间结构抽样调查技术,采用测量抽样点到其第k株最近相邻木的距离(距离法)进行密度估计,分别选取k=4和k=6两种距离调查方法进行分析,并对Prodan、Persson、Thompson 3种不同密度估计方法的预估能力进行检验.结果表明：不同预估方法的预估能力受林木水平分布格局影响.Prodan法在均匀分布的林分中有较强的预估能力,随着分布格局聚集性增加会产生越来越大的偏差;Persson计算法在均匀及随机分布的林分中产生正偏差,但随着分布格局聚集性增加产生的相对误差接近0,预估能力增强;Thompson计算法对随机或接近随机分布的林分有较强的预估能力,而在均匀分布和聚集分布的格局中分别产生正偏差和负偏差.抽样点为49个时,选择6株木与4株木预估能力无显著差异,因此,密度估计可与选取4株相邻木的空间结构参数调查整合在一起.     

Some comments on anderson and pospahala's correction of bias in line transect sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we show that the ANDERSON-POSPAHALA estimator is optimal in the sense of being the (unique) best linear unbiased estimator within the class of estimators which are linear combinations of cell frequencies, provided certain assumptions are met.     

A pairwise relatedness estimator for polyploids

Studies in genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. Many diploid estimators have been developed using either method‐of‐moments or maximum‐likelihood estimates. However, there are no relatedness estimators for polyploids. The development of a moment estimator for polyploids with polysomic inheritance, which simultaneously incorporates the two‐gene relatedness coefficient and various ‘higher‐order’ coefficients, is described here. The performance of the estimator is compared to other estimators under a variety of conditions. When using a small number of loci, the estimator is biased because of an increase in ill‐conditioned matrices. However, the estimator becomes asymptotically unbiased with large numbers of loci. The ambiguity of polyploid heterozygotes (when balanced heterozygotes cannot be distinguished from unbalanced heterozygotes) is also considered; as with low numbers of loci, genotype ambiguity leads to bias. A software, PolyRelatedness , implementing this method and supporting a maximum ploidy of 8 is provided.     

Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.     

Mean and variance of ratio estimators used in fluorescence ratio imaging

BACKGROUND: The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS: The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed. RESULTS: We tested the three estimators on simulated data, real-world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real-world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators. CONCLUSIONS: We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators.     

A Class of Almost Unbiased Estimators for Finite Populations Mean Using Two Auxiliary Variables

For estimating finite population mean -Y₀ of study character y₀, a class of almost unbiased estimators applying jackknife technique envisaged by Quenouille (1956) is derived. Optimum unbiased estimator (OUE) is also investigated with its variance formula. An empirical study is carried out to demonstrate the performance of the constructed estimator over the usual unbiased estimator, Srivastava (1965), Singh (1967), Singh and Biradar (1992), Tracy , Singh , and Singh (1996) and other almost unbiased estimators.     

Influence of upper airway shunt on total respiratory impedance in infants.

When input impedance is determined by means of the forced oscillation technique, part of the oscillatory flow measured at the mouth is lost in the motion of the upper airway wall acting as a shunt. This is avoided by applying the oscillations around the subject's head (head generator) rather than at the mouth (conventional technique). In seven wheezing infants, we compared both techniques to estimate the importance of the upper airway wall shunt impedance (Zuaw) for the interpretation of the conventional technique results. Computation of Zuaw required, in addition, estimation of nasal impedance values, which were drawn from previous measurements (K. N. Desager, M. Willemen, H. P. Van Bever, W. De Backer, and P. A. Vermeire. Pediatr. Pulmonol. 11: 1-7, 1991). Upper airway resistance and reactance at 12 Hz ranged from 40 to 120 and from 0 to -150 hPa. l(-1). s, respectively. Varying nasal impedance within the range observed in infants did not result in major changes in the estimates of Zuaw or lung impedance (ZL), the impedance of the respiratory system in parallel with Zuaw. The conventional technique underestimated ZL, depending on the value of Zuaw. The head generator technique slightly overestimated ZL, probably because the pressure gradient across the upper airway was not completely suppressed. Because of the need to enclose the head in a box (which is not required with the conventional technique), the head generator technique is difficult to perform in infants.     

Model misspecification and bias for inverse probability weighting estimators of average causal effects

Commonly used semiparametric estimators of causal effects specify parametric models for the propensity score (PS) and the conditional outcome. An example is an augmented inverse probability weighting (IPW) estimator, frequently referred to as a doubly robust estimator, because it is consistent if at least one of the two models is correctly specified. However, in many observational studies, the role of the parametric models is often not to provide a representation of the data-generating process but rather to facilitate the adjustment for confounding, making the assumption of at least one true model unlikely to hold. In this paper, we propose a crude analytical approach to study the large-sample bias of estimators when the models are assumed to be approximations of the data-generating process, namely, when all models are misspecified. We apply our approach to three prototypical estimators of the average causal effect, two IPW estimators, using a misspecified PS model, and an augmented IPW (AIPW) estimator, using misspecified models for the outcome regression (OR) and the PS. For the two IPW estimators, we show that normalization, in addition to having a smaller variance, also offers some protection against bias due to model misspecification. To analyze the question of when the use of two misspecified models is better than one we derive necessary and sufficient conditions for when the AIPW estimator has a smaller bias than a simple IPW estimator and when it has a smaller bias than an IPW estimator with normalized weights. If the misspecification of the outcome model is moderate, the comparisons of the biases of the IPW and AIPW estimators show that the AIPW estimator has a smaller bias than the IPW estimators. However, all biases include a scaling with the PS-model error and we suggest caution in modeling the PS whenever such a model is involved. For numerical and finite sample illustrations, we include three simulation studies and corresponding approximations of the large-sample biases. In a dataset from the National Health and Nutrition Examination Survey, we estimate the effect of smoking on blood lead levels.     

Conditional Maximum Likelihood Estimation Following a Group Sequential Test

We consider estimation after a group sequential test. An estimator that is unbiased or has small bias may have substantial conditional bias (Troendle and Yu, 1999, Coburger and Wassmer, 2001). In this paper we derive the conditional maximum likelihood estimators of both the primary parameter and a secondary parameter, and investigate their properties within a conditional inference framework. The method applies to both the usual and adaptive group sequential test designs. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust estimation of parasite component community richness.

The performance of 2 nonparametric estimators of species richness, the bootstrap (S(B)) and kth-order jackknife (S(Jk)), are compared using simulated parasite communities. The parameters of the simulation match those of an earlier comparison that favored S(B) as an estimator but did not include S(Jk). S(Jk) is the least biased of the 2 estimators. Whereas the bias of S(B) is significantly affected by true species richness and the proportion of rare species, the bias of S(Jk) is relatively insensitive to changes in these parameters, and is, therefore, recommended as a robust estimator of species richness.     

Analysis of longitudinal marginal structural models

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), proposed by Robins (2000), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator of Robins et al. (2000) is used as an initial estimator and forms the basis for an improved, one-step estimator that is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County. A simulation study demonstrates the bias of naive estimators in the presence of time-dependent confounders and also shows the efficiency gain of the IPTW estimator, even in the absence such confounding. The efficiency gain of the improved, one-step estimator is demonstrated through simulation.     

Effect of upper airway shunt and series properties on respiratory impedance measurements

Because of the contradictory statements published about the influence of the shunt properties of the upper airway on the measurements of the respiratory impedence by means of the forced oscillation technique, this influence has been reevaluated. In healthy adults and children and in patients with obstructive lung disease, the total respiratory impedance was measured by applying oscillations at the mouth (conventional technique) or around the head (head generator technique), with the cheeks either supported by the hands or not. In healthy adults the two techniques (conventional cheeks supported and head generator) yield similar results for respiratory resistance (Rrs) and a more pronounced increase of respiratory reactance (Xrs) with frequency with the head generator. In children and in patients with moderate airway obstruction, the negative frequency dependence of Rrs observed with the conventional technique tends to disappear with the head generator. This is not observed in patients with severe airway obstruction. The differences between the two techniques can be explained by the influence of the shunt impedance of the upper airway on Rrs and Xrs. Correction for this influence by subtracting the impedance measured during a Valsalva maneuver is not satisfactory, since the Valsalva maneuver itself modifies the upper airway shunt. The head generator technique reduces the influence of the upper airway shunt but does not suppress it altogether; the residual error is small, however.     

Uniformly minimum variance unbiased estimation of gene diversity

Gene diversity is an important measure of genetic variability in inbred populations. The survival of species in changing environments depends on, among other factors, the genetic variability of the population. In this communication, I have derived the uniformly minimum variance unbiased estimator of gene diversity. The proposed estimator of gene diversity does not assume that the inbreeding coefficient is known. I have also provided the approximate variance of this estimator according to Fisher's method. In addition, I have developed a numerical resampling-based method for obtaining variances and confidence intervals based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. Efficiency in estimation of the gene diversity based on these two estimators is discussed. In accordance with the simulation results, I found that the uniformly minimum variance estimator developed in this report is more accurate for estimation of gene diversity than the maximum likelihood estimator.     

Homoplasy corrected estimation of genetic similarity from AFLP bands,and the effect of the number of bands on the precision of estimation

AFLP is a DNA fingerprinting technique, resulting in binary band presence–absence patterns, called profiles, with known or unknown band positions. We model AFLP as a sampling procedure of fragments, with lengths sampled from a distribution. Bands represent fragments of specific lengths. We focus on estimation of pairwise genetic similarity, defined as average fraction of common fragments, by AFLP. Usual estimators are Dice (D) or Jaccard coefficients. D overestimates genetic similarity, since identical bands in profile pairs may correspond to different fragments (homoplasy). Another complicating factor is the occurrence of different fragments of equal length within a profile, appearing as a single band, which we call collision. The bias of D increases with larger numbers of bands, and lower genetic similarity. We propose two homoplasy- and collision-corrected estimators of genetic similarity. The first is a modification of D, replacing band counts by estimated fragment counts. The second is a maximum likelihood estimator, only applicable if band positions are available. Properties of the estimators are studied by simulation. Standard errors and confidence intervals for the first are obtained by bootstrapping, and for the second by likelihood theory. The estimators are nearly unbiased, and have for most practical cases smaller standard error than D. The likelihood-based estimator generally gives the highest precision. The relationship between fragment counts and precision is studied using simulation. The usual range of band counts (50–100) appears nearly optimal. The methodology is illustrated using data from a phylogenetic study on lettuce.     

On Estimating Stratified PH Model with Single Covariate from Sparse Data with Application to Brain Metastases Study

The estimation of the unknown parameters in the stratified Cox's proportional hazard model is a typical example of the trade‐off between bias and precision. The stratified partial likelihood estimator is unbiased when the number of strata is large but suffer from being unstable when many strata are non‐informative about the unknown parameters. The estimator obtained by ignoring the heterogeneity among strata, on the other hand, increases the precision of estimates although pays the price for being biased. An estimating procedure, based on the asymptotic properties of the above two estimators, serving to compromise between bias and precision is proposed. Two examples in a radiosurgery for brain metastases study provide some interesting demonstration of such applications.     

Edge-corrected Estimators for the Reduced Second Moment Measure of Point Processes

A new edge-corrected estimator is proposed for the second moment cumulative function K(t) introduced by Ripley (1977, Journal of the Royal Statistical Society, Series B 39, 172–212). This new estimator is compared by simulation methods with existing edge-corrected estimators in the context of both K(t) and L(t) functions which are used to study point patterns. The results of the simulation study suggests that the new estimator provides almost unbiased estimates of K(t) and L(t) and has a smaller mean squared error than its predecessors.     

Shrinkage and Pretest Nonparametric Estimation of Regression Parameters from Censored Data with Multiple Observations at Each Level of Covariate

A simple linear regression model is considered where the independent variable assumes only a finite number of values and the response variable is randomly right censored. However, the censoring distribution may depend on the covariate values. A class of noniterative estimators for the slope parameter, namely, the noniterative unrestricted estimator, noniterative restricted estimator and noniterative improved pretest estimator are proposed. The asymptotic bias and mean squared errors of the proposed estimators are derived and compared. The relative dominance picture of the estimators is investigated. A simulation study is also performed to asses the properties of the various estimators for small samples.     

Interval Estimation of Simple Difference in Dichotomous Data with Repeated Measurements

When comparing two treatments, we often use the simple difference between the probabilities of response to measure the efficacy of one treatment over the other. When the measurement of outcome is unreliable or the cost of obtaining additional subjects is high relative to that of additional measurements from the obtained subjects, we may often consider taking more than one measurement per subject to increase the precision of an interval estimator. This paper focuses discussion on interval estimation of simple difference when we take repeated measurements per subject. This paper develops four asymptotic interval estimators of simple difference for any finite number of measurements per subject. This paper further applies Monte Carlo simulation to evaluate the finite‐sample performance of these estimators in a variety of situations. Finally, this paper includes a discussion on sample size determination on the basis of both the average length and the probability of controlling the length of the resulting interval estimate proposed elsewhere.