The dilemma of negative analysis of variance estimators of intraclass correlation

Summary At least two common practices exist when a negative variance component estimate is obtained, either setting it to zero or not reporting the estimate. The consequences of these practices are investigated in the context of the intraclass correlation estimation in terms of bias, variance and mean squared error (MSE). For the one-way analysis of variance random effects model and its extension to the common correlation model, we compare five estimators: analysis of variance (ANOVA), concentrated ANOVA, truncated ANOVA and two maximum likelihood-like (ML) estimators. For the balanced case, the exact bias and MSE are calculated via numerical integration of the exact sample distributions, while a Monte Carlo simulation study is conducted for the unbalanced case. The results indicate that the ANOVA estimator performs well except for designs with family size n = 2. The two ML estimators are generally poor, and the concentrated and truncated ANOVA estimators have some advantages over the ANOVA in terms of MSE. However, the large biases may make the concentrated and truncated ANOVA estimators objectionable when intraclass correlation () is small. Bias should be a concern when a pooled estimate is obtained from the literature since <0.05 in many genetic studies.     

Parametric and jackknife confidence interval estimators for two-factor mating design genetic variance ratios

Summary Confidence interval estimators have not been defined for dominance to additive genetic variance () and average degree of dominance () for the nested, factorial, and backcross mating designs. The objective of this paper was to describe interval estimators for these parameters. Approximate F random variables were defined for expected mean square (EMS) ratios for linear models with one environmental effect. Approximate 1– parametric interval estimators were defined for and using these random variables. Random variables defined for linear models with no environmental effects are not approximately distributed as F random variables because common EMS are involved in the numerators and denominators of the EMS ratios. Delete-one jackknife (jackknife) interval estimators were defined for and for linear models with zero or one environmental effect(s); In transformed analysis of variance point estimates were used in pseudovalue estimators.Oregon Agricultural Experiment Station Technical Paper No. 8067     

Confidence interval estimators for heritability for several mating and experiment designs

Summary Confidence interval estimators have not been described for several heritability (H) estimators relevant to recurrent family selection. Previously described H interval estimators do not apply to onefactor mating designs in split-plot in time experiment designs in one or more locations, one-factor mating designs for several experiment designs in two or more locations and years, and two-factor mating designs for several experiment designs in two or more locations or years. Our objective was to derive H interval estimators for these cases. H reduced to a function of constants and a single expected mean square ratio in every case; H=1–E(M)/E(M) where E(M) is a linear function of expected mean squares and E(M) is a single expected mean square. It was shown that F=[M/E(M)]/[M/E(M)] has an approximate F-distribution with df and df degrees of freedom, respectively, where M and M are mean squares corresponding to E(M) and E(M), respectively. H is a function of F, therefore, we used F to define an approximate (1–) interval estimator for H.Oregon Agricultural Experiment Station Technical Paper No. 7923     

Admixture Indicative Interval (AII): a new approach to assess trends in genetic admixture

The genetic admixture is a dynamic and diachronic process, taking place during a great number of generations. Consequently, a sole admixture rate does not represent such an event and several estimates could help to take into account its dynamics. We developed an Admixture Indicative Interval (AII) which gives a mathematical key to avoid this problem by integrating several admixture estimators and their respective accuracy into a single metric and provides a trend in genetic admixture. To illustrate AIIs interests in admixture studies, AII were calculated using seven estimators on two sets of simulated SNPs data generated under two different admixture scenarios and were then calculated from several published admixed population data: a Comorian population and several Puerto-Rican and Colombian populations for recent admixture events as well as European populations representing the Neolithic/Paleolithic admixture for an older event. Our method provides intervals taking properly the variability and accuracy of admixture estimates into account. The AII lays in the intuitive interval in all actual and simulated datasets and is not biased by divergent points by the mean of a double-weighting step. The great quantity of heterogeneous parental contributions is synthesized by a few AII, which turn out to be more manageable and meaningful than aplenty variable point estimates. This offers an improvement in admixture study, allowing a better understanding of migratory flows. Furthermore, it offers a better assessment of admixture than the arithmetic mean, and enhances comparisons between regions, samples, and between studies on same population.     

The Hyper-Negative Binomial Distribution

A generalized family of the negative binomial distribution is introduced in a paper by Srivastava, Yousry and Ahmed (1986). It is a solution of the difference equation and is called the hyper-negative binomial distribution. Certain properties including the moments of the distribution are presented. Moment estimators of the parameters are obtained and goodness of fit is illustrated for chromatid aberration data.     

A Comparison of Biomarker Based Incidence Estimators

Background

Cross-sectional surveys utilizing biomarkers that test for recent infection provide a convenient and cost effective way to estimate HIV incidence. In particular, the BED assay has been developed for this purpose. Controversy surrounding the way in which false positive results from the biomarker should be handled has lead to a number of different estimators that account for imperfect specificity. We compare the estimators proposed by McDougal et al., Hargrove et al. and McWalter & Welte.

Methodology/Principal Findings

The three estimators are analyzed and compared. An identity showing a relationship between the calibration parameters in the McDougal methodology is shown. When the three estimators are tested under a steady state epidemic, which includes individuals who fail to progress on the biomarker, only the McWalter/Welte method recovers an unbiased result.

Conclusions/Significance

Our analysis shows that the McDougal estimator can be reduced to a formula that only requires calibration of a mean window period and a long-term specificity. This allows simpler calibration techniques to be used and shows that all three estimators can be expressed using the same set of parameters. The McWalter/Welte method is applicable under the least restrictive assumptions and is the least prone to bias of the methods reviewed.     

On the Use of Jack‐Knife Techniques in Systematic Sampling

We have proposed two general classes of ratio and product type estimators to estimate an unknown population parameter of a response variable y under systematic sampling strategy. Jack‐Knife technique is employed to make the classes almost/exactly unbiased and sampling variance of the proposed estimators are derived to the first order of approximation. The merits of the proposed estimators over other estimators are discussed in this paper.     

Survival Prediction Based on Compound Covariate under Cox Proportional Hazard Models

Survival prediction from a large number of covariates is a current focus of statistical and medical research. In this paper, we study a methodology known as the compound covariate prediction performed under univariate Cox proportional hazard models. We demonstrate via simulations and real data analysis that the compound covariate method generally competes well with ridge regression and Lasso methods, both already well-studied methods for predicting survival outcomes with a large number of covariates. Furthermore, we develop a refinement of the compound covariate method by incorporating likelihood information from multivariate Cox models. The new proposal is an adaptive method that borrows information contained in both the univariate and multivariate Cox regression estimators. We show that the new proposal has a theoretical justification from a statistical large sample theory and is naturally interpreted as a shrinkage-type estimator, a popular class of estimators in statistical literature. Two datasets, the primary biliary cirrhosis of the liver data and the non-small-cell lung cancer data, are used for illustration. The proposed method is implemented in R package “compound.Cox” available in CRAN at http://cran.r-project.org/.     

On estimating the linkage of marker genes to viability genes controlling inbreeding depression

Statistical properties and extensions of Hedrick and Muona's method for mapping viability alleles causing inbreeding depression are discussed in this paper. Their method uses the segregation ratios among selfed progeny of a marker-locus heterozygote to estimate the viability reduction, s, of an allele and its recombination fraction, c, with the marker. Explicit estimators are derived for c and s, including expressions for their variances. The degree of estimation bias is examined for cases when (1) the viability allele is partially recessive and (2) the marker locus is linked to two viability loci. If linkage or viability reduction is moderate, very large sample sizes are required to obtain reliable estimates of c and s, in part because these estimates show a statistical correlation close to unity. Power is further reduced because alleles causing viability reduction often occur at low frequency at specific loci in a population. To increase power, we present a statistical model for the joint analysis of several selfed progeny arrays selected at random from a population. Assuming a fixed total number of progeny, we determine the optimal number of progeny arrays versus number of progeny per array under this model. We also examine the increase of information provided by a second, flanking marker. Two flanking markers provide vastly superior estimation properties, reducing sample sizes by approximately 95% from those required by a single marker.     

On the accuracy of some mark-recapture estimators

Summary The behaviour of the mark-recapture estimators of Petersen, Bailey (triple catch) and Jolly and Seber are examined theoretically and empirically by means of simulation techniques. The correlation between the parameter and its associated variance is shown to be significant for all the estimators. This correlation makes the estimated variance an insensitive measure of the accuracy of the estimate except at very high sampling intensities. Such sampling intensities are rarely achieved in experimental work and so the method of mark-recapture must be considered of very limited use. At the sampling intensities necessary to give a coefficient of variation of less than 0.05 it does not seem likely that the correlation between and its variance will produce serious underestimation but the minimum confidence limits are recommended.     

Temporal pattern discrimination of impulse sequences in the computer-simulated nerve cells

This paper deals with some properties of temporal pattern discrimination performed by single digital-computer simulated synaptic cells. To clarify these properties, the Shannon's entropy method which is a basic notion in the information theory and a fundamental approach for the design of pattern classification system was applied to input-output relations of the digital computer simulated synaptic cells. We used the average mutual information per symbol as a measure for the temporal pattern sensitivity of the nerve cells, and the average response entropy per symbol as a measure for the frequency transfer characteristics. To use these measures, the probability of a post-synaptic spike as a function of the recent history of pre-synaptic intervals was examined in detail. As the results of such application, it was found that the EPSP size is closely related to the pattern of impulse sequences of the input, and the average mutual information per symbol for EPSP size is given by a bimodal curve with two maximum values. One is a small EPSP size and the other is a large EPSP size. In two maximum points, the structure of the temporal pattern discrimination reverses each other. In addition, the relation between the mean frequency, or the form of impulse sequences of the input, and the average mutual information per symbol has been examined. The EPSP size at one maximum point of average mutual information is in inverse proportion to the magnitude of input mean frequency which relates to the convergence number of input terminal, while that at the other maximum point is proportional to that of the mean frequency. Moreover, the temporal pattern discrimination is affected remarkably by whether successive interspike intervals of the input are independent or not in the statistical sense. Computer experiments were performed by the semi-Markov processes with three typical types of transition matrixes and these shuffling processes. The average mutual informations in the cases of these semi-Markov processes are in contrast to those of the shuffling processes which provide a control case. The temporal structure of successive interspike intervals of the input is thus a significant factor in pattern discrimination at synaptic level.     

Biochemical genetics of chromosome forms of Venezuelan spiny rats of the proechimys guairae and proechimys trinitatis superspecies

Spiny rats from Venezuela show an extensive karyotypic diversification (2n=24 to 2n=62) and little morphological differentiation. This study reports genetic distance, heterozygosity and polymorphism based upon 22 loci in semispecies and allospecies of the Proechimys guairae superspecies from N Central Venezuela, as compared with Proechimys urichi, a member of the Proechimys trinitatis superspecies from eastern Venezuela. Four chromosome forms of the P. guairae complex are included, each characterized by karyotypes of 2n=46 (Fundamental Number=72), 2n=48 (FN=72), 2n=50 (FN=72) and 2n=62 (FN=74). Proechimys urichi has a distinetive karyotype of 2n=62 (FN=88). The overall mean value of Nei's genetic identity index for all pair-wise comparisons is I=0.942±0.011. Mean identity within the P. guairae complex is =0.969±0.033. Mean identity between P. urichi and members of that complex is =0.889±0.011. Within the P. guairae complex, increased genetic divergence is correlated with higher karyotypic divergence. Heterozygosity varies from H=0.059 to H=0.153, with a mean value of H0.059. The mean percent of polymorphic loci is P=18.2±3.9 after the 0,95% polymorphism criterion, and P=20,5±5.2 after the 0.99% criterion. These results are compared with similar data from fossorial and non-fossorial rodents. Spiny rats are non-fossorial, forest-dwelling rodents which have undergone a speciation process with little genetic divergence and extensive chromosome rearrangements.     

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.     

Construction of Prediction Intervals in Location-Scale Families

Let x₁ ≤x₂ ≤x₃ … ≤x_r be the r smallest observations out of n observations from a location-scale family with density $ \frac{1}{\sigma}f\left({\frac{{x - \mu}}{\sigma}} \right) $ where μ and σ are the location and the scale parameters respectively. The goal is to construct a prediction interval of the form $ \left({\hat \mu + k_1 \hat \sigma,\,\hat \mu + k_2 \hat \sigma} \right) $ for a location-scale invariant function, T(Y) = T(Y₁, …, Y_m), of m future observations from the same distribution. Given any invariant estimators $ \hat \mu $ and $ \hat \sigma $, we have developed a general procedure for how to compute the values of k₁ and k₂. The two attractive features of the procedure are that it does not require any distributional knowledge of the joint distribution of the estimators beyond their first two raw moments and $ \hat \mu $ and $ \hat \sigma $ can be any invariant estimators of μ and σ. Examples with real data have been given and extensive simulation study showing the performance of the procedure is also offered.     

Fish production in Lake Kariba,reconsidered

Synopsis Revised total and available production, yield and mean biomass per ha were calculated for each species in Lake Kariba, and for the whole lake. The revision was undertaken because (1) the original value 1 g for W₀ for each species was too high, (2) B_i+1 was occasionally used instead of B_i in the calculation of mean biomass for an interval i to i + 1, and (3) species' contributions to mean parameter values for the whole lake were not weighted according to their mean standing crop. Revised values are, A = 1224, P = 720, Y_A = 400, Y_{Pp, = 202 and B} = 827 kg ha^–1y–1. These correspond to 38.2%, 66.7%, 107.1% and 25.8% respectively of the values calculated initially.     

Occupancy and abundance of wintering birds in a dynamic agricultural landscape

Assessing wildlife management action requires monitoring populations, and abundance often is the parameter monitored. Recent methodological advances have enabled estimation of mean abundance within a habitat using presence–absence or count data obtained via repeated visits to a sample of sites. These methods assume populations are closed and intuitively assume habitats within sites change little during a field season. However, many habitats are highly variable over short periods. We developed a variation of existing occupancy and abundance models that allows for extreme spatio-temporal differences in habitat, and resulting changes in wildlife abundance, among sites and among visits to a site within a field season. We conducted our study in sugarcane habitat within the Everglades Agricultural Area southeast of Lake Okeechobee in south Florida. We counted wintering birds, primarily passerines, within 245 sites usually 5 times at each site during December 2006–March 2007. We estimated occupancy and mean abundance of birds in 6 vegetation states during the sugarcane harvest and allowed these parameters to vary temporally or spatially within a vegetation state. Occupancy and mean abundance of the common yellowthroat (Geothlypis trichas) was affected by structure of sugarcane and uncultivated edge vegetation (occupancy = 1.00 [ = 0.96–1.00] and mean abundance = 7.9 [ = 3.2–19.5] in tall sugarcane with tall edge vegetation versus 0.20 [ = 0.04–0.71] and 0.22 [ = 0.04–1.2], respectively, in short sugarcane with short edge vegetation in one half of the study area). Occupancy and mean abundance of palm warblers (Dendroica palmarum) were constant (occupancy = 1.00, = 0.69–1.00; mean abundance = 18, = 1–270). Our model may enable wildlife managers to assess rigorously effects of future edge habitat management on avian distribution and abundance within agricultural landscapes during winter or the breeding season. The model may also help wildlife managers make similar management decisions involving other dynamic habitats such as wetlands, prairies, and even forested areas if forest management or fires occur during the field season. © 2011 The Wildlife Society.     

Can you trust the parametric standard errors in nonlinear least squares? Yes,with provisos

Background

Questions about the reliability of parametric standard errors (SEs) from nonlinear least squares (LS) algorithms have led to a general mistrust of these precision estimators that is often unwarranted.

Random-Effects,Fixed-Effects and the within-between Specification for Clustered Data in Observational Health Studies: A Simulation Study

Background

When unaccounted-for group-level characteristics affect an outcome variable, traditional linear regression is inefficient and can be biased. The random- and fixed-effects estimators (RE and FE, respectively) are two competing methods that address these problems. While each estimator controls for otherwise unaccounted-for effects, the two estimators require different assumptions. Health researchers tend to favor RE estimation, while researchers from some other disciplines tend to favor FE estimation. In addition to RE and FE, an alternative method called within-between (WB) was suggested by Mundlak in 1978, although is utilized infrequently.

Methods

We conduct a simulation study to compare RE, FE, and WB estimation across 16,200 scenarios. The scenarios vary in the number of groups, the size of the groups, within-group variation, goodness-of-fit of the model, and the degree to which the model is correctly specified. Estimator preference is determined by lowest mean squared error of the estimated marginal effect and root mean squared error of fitted values.

Results

Although there are scenarios when each estimator is most appropriate, the cases in which traditional RE estimation is preferred are less common. In finite samples, the WB approach outperforms both traditional estimators. The Hausman test guides the practitioner to the estimator with the smallest absolute error only 61% of the time, and in many sample sizes simply applying the WB approach produces smaller absolute errors than following the suggestion of the test.

Conclusions

Specification and estimation should be carefully considered and ultimately guided by the objective of the analysis and characteristics of the data. The WB approach has been underutilized, particularly for inference on marginal effects in small samples. Blindly applying any estimator can lead to bias, inefficiency, and flawed inference.     

Robotics versus laparoscopy - an experimental study of the transfer effect in maiden users

Background

Randomized trials comparing VATS lobectomy to open lobectomy are of small size. We analyzed a case-control series using propensity score-weighting to adjust for important covariates in order to compare the clinical outcomes of the two techniques.

Methods

We compared patients undergoing lobectomy for clinical stage I lung cancer (NSCLC) by either VATS or open (THOR) methods. Inverse probability of treatment weighted estimators, with weights derived from propensity scores, were used to adjust cohorts for determinants of perioperative morbidity and mortality including age, gender, preop FEV1, ASA class, and Charlson Comorbidity Index (CCI). Bootstrap methods provided standard errors. Endpoints were postoperative stay (LOS), chest tube duration, complications, and lymph node retrieval.

Results

We analyzed 136 consecutive lobectomy patients. Operative mortality was 1/62 (1.6%) for THOR and 1/74 (1.4%) for VATS, P = 1.00. 5/74 (6.7%) VATS were converted to open procedures. Adjusted median LOS was 7 days (THOR) versus 4 days (VATS), P < 0.0001, HR = 0.33. Adjusted median chest tube duration (days) was 5 (THOR) versus 3 (VATS), P < 0.0001, HR = 0.42. Complication rates were 39% (THOR) versus 34% (VATS), P = 0.61. Adjusted mean number of lymph nodes dissected per patient was 18.1 (THOR) versus 14.8 (VATS), p = 0.17.

Conclusions

After balancing covariates that affect morbidity, mortality and LOS in this case-control series using propensity-weighting, the results confirm that VATS lobectomy is associated with a statistically significant shorter LOS, similar mortality and complication rates and similar rates of lymph node removal in patients with clinical stage I NSCLC.