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Quantification of variability and uncertainty for censored data sets and application to air toxic emission factors.

Many environmental data sets, such as for air toxic emission factors, contain several values reported only as below detection limit. Such data sets are referred to as "censored." Typical approaches to dealing with the censored data sets include replacing censored values with arbitrary values of zero, one-half of the detection limit, or the detection limit. Here, an approach to quantification of the variability and uncertainty of censored data sets is demonstrated. Empirical bootstrap simulation is used to simulate censored bootstrap samples from the original data. Maximum likelihood estimation (MLE) is used to fit parametric probability distributions to each bootstrap sample, thereby specifying alternative estimates of the unknown population distribution of the censored data sets. Sampling distributions for uncertainty in statistics such as the mean, median, and percentile are calculated. The robustness of the method was tested by application to different degrees of censoring, sample sizes, coefficients of variation, and numbers of detection limits. Lognormal, gamma, and Weibull distributions were evaluated. The reliability of using this method to estimate the mean is evaluated by averaging the best estimated means of 20 cases for small sample size of 20. The confidence intervals for distribution percentiles estimated with bootstrap/MLE method compared favorably to results obtained with the nonparametric Kaplan-Meier method. The bootstrap/MLE method is illustrated via an application to an empirical air toxic emission factor data set.

Air↗

Analysis of genetic relationships between 10 cattle breeds with 17 microsatellites.

To guide genetic conservation programmes with objective criteria, general genetic variability has to be taken into account. This study was conducted to determine the genetic variation between 10 cattle breeds by using 17 microsatellite loci and 13 biochemical markers (11 blood groups, the transferrin and beta-casein loci). Microsatellite loci were amplified in 31-50 unrelated individuals from 10 cattle breeds: Charolais, Limousin, Breton Black Pied, Parthenais, Montbéliard, Vosgien, Maine-Anjou, Normande, Jersey and Holstein. Neighbor-joining trees were calculated from genetic distance estimates. The robustness of tree topology was obtained by bootstrap resampling of loci. A total of 210 alleles of the 17 microsatellites were detected in this study and average heterozygosities ranged from 0.53 in the Jersey breed to 0.66 in the Parthenais breed. In general, low bootstrap values were obtained: with the 17 microsatellites, the highest bootstrap values concerned the Holstein/Maine-Anjou grouping with an occurrence of 74%; with the biochemical markers, this node had an occurrence of 79% and the Charolais/Limousin grouping appeared with an occurrence of 74%; when microsatellites and biochemical polymorphism were analysed together, the occurrence of the Holstein/Maine-Anjou grouping was 90% and that of the Charolais/Limousin grouping was 42%. These results suggest that 30 microsatellites, a number currently considered as sufficient to distinguish closely related breeds is, in fact, probably insufficient.

Alleles↗

Population pharmacokinetics of epinastine, a histamine H1 receptor antagonist, in adults and children.

AIMS: Our objective was to develop a population pharmacokinetic (PPK) model for epinastine, a histamine H(1) receptor antagonist, in adults and children and to obtain pharmacokinetic information to support dosing recommendations in children. METHODS: A total of 1510 plasma samples were collected from 62 healthy adult volunteers and 62 paediatric atopic dermatitis patients. The data were analysed using the NONMEM program according to a two-compartment model with first-order absorption. In addition, the final PPK model was evaluated by means of bootstrapping resampling. RESULTS: The oral clearance (CL/F) was found to be associated with body weight, formulation and food status. The volume of distribution of the central compartment (V(1)/F) was related to body weight and food status. An absorption lag time was apparent in fed subjects. On the other hand, other covariates (formulation on V(1)/F, volume of distribution of the peripheral compartment (V(2)/F), first-order absorption rate constant (Ka) and absorption lag time (ALAG); food status on V(2)/F and Ka; body weight on V(2)/F) were not statistically significant. No effect of age on CL/F, V(1)/F or V(2)/F was found. The mean parameter estimates obtained with an additional 200 bootstrap replicates of data were within 90-117% of those obtained with the original data set. These results suggest that the pharmacokinetics of epinastine are similar in adults and in children, except for the effect of the difference of body weight. The result of the application of the PPK model to the clinical trial in paediatric patients, in which dosage was determined based on the body weight (from 14 kg to less than 24 kg; 10 mg dose, 24 kg or more; 20 mg dose), showed that the C(max) and AUC (25.6 +/- 6.9 ng ml(-1) and 246.8 +/- 68.2 ng h ml(-1)) were almost same levels with those of adults after administration of 20 mg (26.9 +/- 9.1 ng ml(-1) and 281.6 +/- 90.5 ng h ml(-1)). CONCLUSIONS: A PPK model for epinastine was established and further evaluation by bootstrapping indicated that this model is stable. The model shows that, if dosage is adjusted based on the body weight, the epinastine exposure in paediatric patients is similar to that in adults.

Adult↗

Population pharmacokinetics of darbepoetin alfa in haemodialysis and peritoneal dialysis patients after intravenous administration.

AIMS: To characterize the pharmacokinetics of darbepoetin alfa and covariate relationships in haemodialysis (HD) and peritoneal dialysis (PD) patients. METHODS: Data were collected from 131 (63 HD and 68 PD) patients who received darbepoetin alfa intravenously. A total of 917 serum concentrations were available. The data were analysed by nonlinear mixed effect modelling using NONMEM with a model including endogenous erythropoietin production. In addition, the final model was evaluated using bootstrap resampling. RESULTS: The selected basic model was a two-compartment model with a combination of additive and the constant coefficient of variation error models. The significant covariates were weight (WT) for clearance (CL) and the volume of central compartment (V(1)), and the dialysis technique (DIA) for V(1). The typical values of CL and V(1) were 0.0807 l h(-1) and 2.51 l, respectively. V(1) in PD patients was 17% higher than in HD patients. With the introduction of WT in CL and WT and DIA in V(1), interindividual variability decreased from 27.1% to 20.6% in CL and from 29.1% to 21.8% in V(1). The mean parameter estimates from the bootstrap datasets were similar to those from the original dataset. Evaluation by bootstrapping showed that the final model was stable. CONCLUSIONS: The results of the present analysis suggest no dosage regimen change is warranted for darbepoetin alfa in HD and PD patients over the range of distribution of covariates included in this study.

Adult↗

Issues in biomedical statistics: comparing means by computer-intensive tests.

In this review there are described two alternatives to classical tests for distinguishing means. These are called computer-intensive because they can only be performed on fast computers. Permutation procedures have the virtue in that they are easy to understand, they can be employed to analyse small sets of experimental data, and under the randomization model of inference (though not the population model) they require no assumptions except that the experimental groups have been constructed by randomization. Bootstrap procedures are designed for use under the population model of inference (though not the randomization model) and are best suited to larger sets of experimental data. Non-parametric bootstrapping requires populations to be sampled randomly, but it depends on no prior assumptions about the distributions of those populations. It is argued that if randomization rather than random sampling has been done, permutation tests are superior to the classical t and F tests for detecting differences between means and therefore should replace them. If random sampling has been done, non-parametric bootstrap techniques may prove to be superior to classical tests for constructing population confidence intervals or testing hypotheses. However, their accuracy, especially for hypothesis-testing and when samples are small, has yet to be firmly established and there is a dearth of commercial software with which they can be executed on personal computers.

Computer Simulation↗

Home-based care after a shortened hospital stay versus hospital-based care postpartum: an economic evaluation.

OBJECTIVES: To compare the cost effectiveness of early postnatal discharge and home midwifery support with a traditional postnatal hospital stay. DESIGN: Cost minimisation analysis within a pragmatic randomised controlled trial. SETTING: The University Hospital of Geneva and its catchment area. POPULATION: Four hundred and fifty-nine deliveries of a single infant at term following an uncomplicated pregnancy. METHODS: Prospective economic evaluation alongside a randomised controlled trial in which women were allocated to either early postnatal discharge combined with home midwifery support (n= 228) or a traditional postnatal hospital stay (n= 231). MAIN OUTCOME MEASURES: Costs (Swiss francs, 2000 prices) to the health service, social services, patients, carers and society accrued between delivery and 28 days postpartum. RESULTS: Clinical and psychosocial outcomes were similar in the two trial arms. Early postnatal discharge combined with home midwifery support resulted in a significant reduction in postnatal hospital care costs (bootstrap mean difference 1524 francs, 95% confidence interval [CI] 675 to 2403) and a significant increase in community care costs (bootstrap mean difference 295 francs, 95% CI 245 to 343). There were no significant differences in average hospital readmission, hospital outpatient care, direct non-medical and indirect costs between the two trial groups. Overall, early postnatal discharge combined with home midwifery support resulted in a significant cost saving of 1221 francs per mother-infant dyad (bootstrap mean difference 1209 francs, 95% CI 202 to 2155). This finding remained relatively robust following variations in the values of key economic parameters performed as part of a comprehensive sensitivity analysis. CONCLUSIONS: A policy of early postnatal discharge combined with home midwifery support exhibits weak economic dominance over traditional postnatal care, that is, it significantly reduces costs without compromising the health and wellbeing of the mother and infant.

Adult↗

The effects of exercise on resting blood pressure in children and adolescents: a meta-analysis of randomized controlled trials.

Resting blood pressure in children and adolescents can track into adulthood. The purpose of this study was to use the meta-analytic approach to examine the effects of exercise on resting systolic and diastolic blood pressure in children and adolescents. Twelve randomized, controlled trials representing 16 outcomes in 1,266 subjects met the inclusion criteria. Reductions in blood pressure were approximately 1% and 3% for resting systolic and diastolic blood pressures, respectively. However, random-effects modeling using 5000 bootstrap confidence intervals revealed that neither result was statistically significant (systolic, x-bar (x);+/-SEM=-1+/-2; 95% bootstrap confidence intervals=-2 to 0 mm Hg; diastolic, x+/-SEM=-2+/-1; 95% bootstrap confidence intervals=-3 to 0 mm Hg). The results of this study suggest that short-term exercise does not appear to reduce resting systolic and diastolic blood pressure in children and adolescents. However, a need exists for additional studies, especially in hypertensive children and adolescents.

Adolescent↗

Cost-utility of selective serotonin reuptake inhibitors for depression in primary care in Catalonia.

OBJECTIVE: To determine the cost-utility of selective serotonin reuptake inhibitors (SSRIs) for treating depressive disorders prescribed in primary care (PC). METHOD: A total of 301 participants beginning antidepressant treatment with an SSRI were enrolled in a prospective 6-month follow-up naturalistic study. Incremental cost-utility ratios (ICUR) were obtained for several comparisons among different SSRIs. To address uncertainty in the ICUR's sampling distribution, non-parametric bootstrapping was carried out. RESULTS: Taking into account adjusted total costs and incremental quality of life gained, fluoxetine dominated paroxetine and citalopram with 63.4% and 79.3% of the bootstrap replications in the dominance quadrant, respectively. Additionally, fluoxetine was cost-effective over sertraline with 83.4% of the bootstrap replications below the threshold of 33,936 US$/quality-adjusted life year (30,000 euro/QALY). CONCLUSION: Fluoxetine seems to be a better cost-utility SSRI option for treating depressive disorders in PC.

Adolescent↗

Ischemia-modified albumin in acute stroke.

BACKGROUND: Ischemia-modified albumin (IMA)is a new biological marker of ischemia. Previous studies have found increased serum IMA levels after myocardial ischemia, but no study has investigated the possibility that stroke modifies IMA blood levels. MATERIALS AND METHODS: We studied 118 consecutive patients presenting within 3 h of the onset of an acute neurological deficit [84 brain infarctions (BI), 18 brain hemorrhages (ICH) and 16 transient ischemic attacks lasting less than 1 h or epileptic seizures]. Serum samples were obtained for all patients at initial presentation and repeated only in patients with stroke at 6, 12 and 24 h. IMA was measured by the albumin-cobalt-binding test (Ischemia Technologies, Denver, Colo., USA). RESULTS: The initial median IMA (bootstrap 95% confidence interval, CI) was 83 U/ml (79-86) and 86 U/ml (75-90) in patients with BI and ICH, respectively (p = 0.76), and was 73 U/ml (58-79) in others (p = 0.003 compared with BI, and p = 0.017 with ICH). Baseline IMA levels correlated with the National Institutes of Health Stroke Scale [Spearman correlation coefficient: 0.34 (p = 0.002) in BI, 0.61 (p = 0.008) in ICH]. During the first 24 h, IMA levels increased in BI patients (median, 9.1%; bootstrap 95% CI, 5.2-11.5), whereas no change was observed in ICH patients (median, 1.2%; bootstrap 95% CI, -7.8 to 6.8). CONCLUSIONS: IMA blood levels may be a biomarker for early identification of acute stroke. Further studies are required to investigate the role of IMA in the early detection of acute stroke.

Acute Disease↗

The impact of visual impairment on functional vision of children in rural South India: the Kariapatti Pediatric Eye Evaluation Project.

PURPOSE: To determine the impact of visual impairment on functional vision of children in a rural population of south India. METHODS: A visual function questionnaire (LVP-VFQ) was administered to 1194 children aged 7 to 15 years identified through a systematic random sampling technique from 144 hamlets of Kariapatti in rural south India as part of a larger population-based project. Visual acuity estimations and clinical examinations for morbidity were performed in these 1194 children. A Rasch analysis was performed to validate the use of the instrument in this population. Bootstrap estimates (95% confidence intervals) of the regression coefficients were used to compare visual function scores between children with normal sight and children with uncorrected monocular and binocular visual impairment. RESULTS: The mean age of children was 10.3 +/- 2.1 years. The reliability estimates were 0.82 for person ability and 0.88 for item difficulty parameters, according to the Rasch analysis. A separation index of 2.15 was obtained for person measures and 2.74 for item measures, and the mean square infit and outfit statistics were 1.03 (Z(STD) 0.1) and 0.99 (Z(STD) -0.1), respectively. Children with monocular visual impairment (bootstrap estimate [95%CI] -0.05 [-0.08 to -0.01]) and binocular visual impairment (bootstrap estimate [95%CI] -0.09 [-0.11 to -0.07]) were more likely to have functional visual deficits than were normally sighted peers. CONCLUSIONS: Monocular or binocular visual impairment impacts on the functional vision of children in this rural population. Further studies are needed to determine the impact of treatment of visual impairment on functional vision in children of this population.

Adolescent↗

Comparison of mode estimation methods and application in molecular clock analysis.

BACKGROUND: Distributions of time estimates in molecular clock studies are sometimes skewed or contain outliers. In those cases, the mode is a better estimator of the overall time of divergence than the mean or median. However, different methods are available for estimating the mode. We compared these methods in simulations to determine their strengths and weaknesses and further assessed their performance when applied to real data sets from a molecular clock study. RESULTS: We found that the half-range mode and robust parametric mode methods have a lower bias than other mode methods under a diversity of conditions. However, the half-range mode suffers from a relatively high variance and the robust parametric mode is more susceptible to bias by outliers. We determined that bootstrapping reduces the variance of both mode estimators. Application of the different methods to real data sets yielded results that were concordant with the simulations. CONCLUSION: Because the half-range mode is a simple and fast method, and produced less bias overall in our simulations, we recommend the bootstrapped version of it as a general-purpose mode estimator and suggest a bootstrap method for obtaining the standard error and 95% confidence interval of the mode.

Ascomycota↗

Concordance between genetic relatedness and phenotypic similarities of Trichomonas vaginalis strains.

BACKGROUND: Despite the medical importance of trichomoniasis, little is known about the genetic relatedness of Trichomonas vaginalis strains with similar biological characteristics. Furthermore, the distribution of endobionts such as mycoplasmas or Trichomonas vaginalis virus (TVV) in the T. vaginalis metapopulation is poorly characterised. RESULTS: We assayed the relationship between 20 strains of T. vaginalis from 8 countries using the Random Amplified Polymorphic DNA (RAPD) analysis with 27 random primers. The genealogical tree was constructed and its bootstrap values were computed using the program FreeTree. Using the permutation tail probability tests we found that the topology of the tree reflected both the pattern of resistance to metronidazole (the major anti-trichomonal drug) (p < 0.01) and the pattern of infection of strains by mycoplasmas (p < 0.05). However, the tree did not reflect pattern of virulence, geographic origin or infection by TVV. Despite low bootstrap support for many branches, the significant clustering of strains with similar drug susceptibility suggests that the tree approaches the true genealogy of strains. The clustering of mycoplasma positive strains may be an experimental artifact, caused by shared RAPD characters which are dependent on the presence of mycoplasma DNA. CONCLUSIONS: Our results confirmed both the suitability of the RAPD technique for genealogical studies in T. vaginalis and previous conclusions on the relatedness of metronidazol resistant strains. However, our studies indicate that testing analysed strains for the presence of endobionts and assessment of the robustness of tree topologies by bootstrap analysis seem to be obligatory steps in such analyses.

Animals↗

Bayesian and maximum likelihood phylogenetic analyses of protein sequence data under relative branch-length differences and model violation.

BACKGROUND: Bayesian phylogenetic inference holds promise as an alternative to maximum likelihood, particularly for large molecular-sequence data sets. We have investigated the performance of Bayesian inference with empirical and simulated protein-sequence data under conditions of relative branch-length differences and model violation. RESULTS: With empirical protein-sequence data, Bayesian posterior probabilities provide more-generous estimates of subtree reliability than does the nonparametric bootstrap combined with maximum likelihood inference, reaching 100% posterior probability at bootstrap proportions around 80%. With simulated 7-taxon protein-sequence datasets, Bayesian posterior probabilities are somewhat more generous than bootstrap proportions, but do not saturate. Compared with likelihood, Bayesian phylogenetic inference can be as or more robust to relative branch-length differences for datasets of this size, particularly when among-sites rate variation is modeled using a gamma distribution. When the (known) correct model was used to infer trees, Bayesian inference recovered the (known) correct tree in 100% of instances in which one or two branches were up to 20-fold longer than the others. At ratios more extreme than 20-fold, topological accuracy of reconstruction degraded only slowly when only one branch was of relatively greater length, but more rapidly when there were two such branches. Under an incorrect model of sequence change, inaccurate trees were sometimes observed at less extreme branch-length ratios, and (particularly for trees with single long branches) such trees tended to be more inaccurate. The effect of model violation on accuracy of reconstruction for trees with two long branches was more variable, but gamma-corrected Bayesian inference nonetheless yielded more-accurate trees than did either maximum likelihood or uncorrected Bayesian inference across the range of conditions we examined. Assuming an exponential Bayesian prior on branch lengths did not improve, and under certain extreme conditions significantly diminished, performance. The two topology-comparison metrics we employed, edit distance and Robinson-Foulds symmetric distance, yielded different but highly complementary measures of performance. CONCLUSIONS: Our results demonstrate that Bayesian inference can be relatively robust against biologically reasonable levels of relative branch-length differences and model violation, and thus may provide a promising alternative to maximum likelihood for inference of phylogenetic trees from protein-sequence data.

Bayes Theorem↗

Comparison of family-based association tests in chromosome regions selected by linkage-based confidence intervals.

We use the Genetic Analysis Workshop 14 simulated data to explore the effectiveness of a two-stage strategy for mapping complex disease loci consisting of an initial genome scan with confidence interval construction for gene location, followed by fine mapping with family-based tests of association on a dense set of single-nucleotide polymorphisms. We considered four types of intervals: the 1-LOD interval, a basic percentile bootstrap confidence interval based on the position of the maximum Zlr score, and asymptotic and bootstrap confidence intervals based on a generalized estimating equations method. For fine mapping we considered two family-based tests of association: a test based on a likelihood ratio statistic and a transmission-disequilibrium-type test implemented in the software FBAT. In two of the simulation replicates, we found that the bootstrap confidence intervals based on the peak Zlr and the 1-LOD support interval always contained the true disease loci and that the likelihood ratio test provided further strong confirmatory evidence of the presence of disease loci in these regions.

Chromosomes, Human↗

Sample size and power estimation for studies with health related quality of life outcomes: a comparison of four methods using the SF-36.

We describe and compare four different methods for estimating sample size and power, when the primary outcome of the study is a Health Related Quality of Life (HRQoL) measure. These methods are: 1. assuming a Normal distribution and comparing two means; 2. using a non-parametric method; 3. Whitehead's method based on the proportional odds model; 4. the bootstrap. We illustrate the various methods, using data from the SF-36. For simplicity this paper deals with studies designed to compare the effectiveness (or superiority) of a new treatment compared to a standard treatment at a single point in time. The results show that if the HRQoL outcome has a limited number of discrete values (< 7) and/or the expected proportion of cases at the boundaries is high (scoring 0 or 100), then we would recommend using Whitehead's method (Method 3). Alternatively, if the HRQoL outcome has a large number of distinct values and the proportion at the boundaries is low, then we would recommend using Method 1. If a pilot or historical dataset is readily available (to estimate the shape of the distribution) then bootstrap simulation (Method 4) based on this data will provide a more accurate and reliable sample size estimate than conventional methods (Methods 1, 2, or 3). In the absence of a reliable pilot set, bootstrapping is not appropriate and conventional methods of sample size estimation or simulation will need to be used. Fortunately, with the increasing use of HRQoL outcomes in research, historical datasets are becoming more readily available. Strictly speaking, our results and conclusions only apply to the SF-36 outcome measure. Further empirical work is required to see whether these results hold true for other HRQoL outcomes. However, the SF-36 has many features in common with other HRQoL outcomes: multi-dimensional, ordinal or discrete response categories with upper and lower bounds, and skewed distributions, so therefore, we believe these results and conclusions using the SF-36 will be appropriate for other HRQoL measures.

Algorithms↗

Postoperative nomogram for 12-year sarcoma-specific death.

PURPOSE: Few published studies have analyzed risk factors for sarcoma-specific death. We developed and internally validated a nomogram that combines the factors to predict the probability of 12-year sarcoma-specific death using a database of 2,136 prospectively followed adult patients treated at a single institution. PATIENTS AND METHODS: Nomogram predictor variables included age at diagnosis, tumor size (< or = 5, 5 to 10, or > 10 cm), histologic grade (high or low), histologic subtype (fibrosarcoma, leiomyosarcoma, liposarcoma, malignant fibrous histiocytoma, malignant peripheral nerve tumor, synovial, or other), depth (superficial or deep), and site (upper extremity, lower extremity, visceral, thoracic or trunk, retrointraabdominal, or head or neck). Death from sarcoma or treatment complication was the predicted end point. Three prediction methods were compared, Kaplan-Meier analysis of all possible subsets, recursive partitioning, and Cox proportional hazards regression analysis. The concordance index was used as an accuracy measure with bootstrapping to correct for optimistic bias. RESULTS: Sarcoma-specific death at 12 years was 36% (95% confidence interval, 33% to 39%). The bootstrap-corrected concordance indices were as follows: Kaplan-Meier, 0.69; recursive partitioning, 0.74; and Cox regression, 0.77. A nomogram was drawn on the basis of the Cox regression model. This nomogram was internally validated using bootstrapping and shown to have excellent calibration. CONCLUSION: A nomogram has been developed to predict 12-year sarcoma-specific death. This tool may be useful for patient counseling, follow-up scheduling, and clinical trial eligibility determination.

Age Factors↗

Comparing the variances of two independent groups.

Comparing the variances of two independent groups is a classic problem. Methods for comparing alternative measures of dispersion have been derived that perform well in simulations, but all methods for comparing variances have been found to be unsatisfactory in terms of Type I error probabilities or power. Currently, it appears that the most successful method, in terms of controlling the probability of a Type I error, is based on the so-called mean half-square successive difference statistic where a bootstrap is used to estimate its standard error, and a calibrated bootstrap is used to control the probability of a Type I error. But the mean half-square successive difference statistic is not permutation-invariant, and it is fairly evident that power can be relatively poor. A slight modification of the percentile bootstrap method for computing a 1 - alpha confidence interval for the difference between the variances is considered that corrects these problems.

Humans↗

Determining the effective dimensionality of the genetic variance-covariance matrix.

Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by Amemiya (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the covariance structure at the sire level. In contrast, bootstrapping identified four dimensions with significant genetic variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.

Animals↗