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PubMed2003

Modelling and analysing exchangeable binary data with random cluster sizes.

Correlated binary data occur very frequently in cluster sample surveys, dependent repeated cancer screening, teratological experiments, ophthalmologic and otolaryngologic studies, and other clinical trials. The standard methods to analyse these data include the use of beta-binomial models and generalized estimating equations with third and fourth moments specified by 'working matrices'. However, in many applications it is reasonable to assume that the data from the same cluster are exchangeable. When all sampled clusters have equal sizes, Bowman and George introduced maximum likelihood estimates (MLEs) of the population parameters such as the marginal means, moments, and correlations of order two and higher. They also extended their approach to sampled clusters with unequal sizes. It seems that their extension has a gap. This paper points out the source of this gap and shows that estimates introduced by Bowman and George are not the MLEs of the parameters which are used to identify the joint distribution of correlated binary data. We show that the MLEs of the population parameters have no closed form in general and should be calculated by numerical methods. We apply our results and a generalized estimating equation procedure to a data set from a double-blind randomized clinical trial comparing two antibiotics, cefaclor and amoxicillin, used for the treatment of acute otitis media. To see the performance of the MLEs with small or moderate sample sizes, several simulation studies are also conducted.

Amoxicillin↗
PubMed2000

Quantitative endoscopy: initial accuracy measurements.

The geometric optics of an endoscope can be used to determine the absolute size of an object in an endoscopic field without knowing the actual distance from the object. This study explores the accuracy of a technique that estimates absolute object size from endoscopic images. Quantitative endoscopy involves calibrating a rigid endoscope to produce size estimates from 2 images taken with a known traveled distance between the images. The heights of 12 samples, ranging in size from 0.78 to 11.80 mm, were estimated with this calibrated endoscope. Backup distances of 5 mm and 10 mm were used for comparison. The mean percent error for all estimated measurements when compared with the actual object sizes was 1.12%. The mean errors for 5-mm and 10-mm backup distances were 0.76% and 1.65%, respectively. The mean errors for objects <2 mm and > or =2 mm were 0.94% and 1.18%, respectively. Quantitative endoscopy estimates endoscopic image size to within 5% of the actual object size. This method remains promising for quantitatively evaluating object size from endoscopic images. It does not require knowledge of the absolute distance of the endoscope from the object, rather, only the distance traveled by the endoscope between images.

Calibration↗
PubMedDate not supplied

On the number of measurements necessary to assess regional cerebral blood flow by local laser Doppler recordings: a simulation study with data from 45 rabbits.

Laser Doppler fluxmetry may improve the monitoring of cortical blood flow in neurosurgical patients. So far, however, the variability of laser Doppler readings found in the cerebral cortex has prevented a consequent usage of the technique in clinical practice. The current report analyzes the regional variability of laser Doppler readings from experimental animals. Typical frequency histograms of observed flow values display non-Gaussian distributions. A simulation technique is used to assess the number of measuring sites required for valid estimates of regional cortical flow. From a total of 990 local flow measurements from 45 rabbits random samples of sizes between 5 and 100 were repeatedly drawn to estimate the variability of median flow thus determined. The study underlines that small sample sizes below n = 20 are associated with a large variability (95th percentile: +38%) which decreases in a biphasic manner. Sample sizes above n = 25 are necessary to obtain more reliable information on regional cerebral blood flow: the 95th percentiles remain between 24 and 28% up to n = 45, and are still at 15% with n = 99.

Animals↗
PubMed2005

Multisystemic Therapy for social, emotional, and behavioral problems in youth aged 10-17.

BACKGROUND: Multisystemic Therapy (MST) is an intensive, home-based intervention for families of youth with social, emotional, and behavioral problems. Masters-level therapists engage family members in identifying and changing individual, family, and environmental factors thought to contribute to problem behavior. Intervention may include efforts to improve communication, parenting skills, peer relations, school performance, and social networks. Most MST trials were conducted by program developers in the USA; results of one independent trial are available and others are in progress. OBJECTIVES: To provide unbiased estimates of the impacts of MST on restrictive out-of-home living arrangements, crime and delinquency, and other behavioral and psychosocial outcomes for youth and families. SEARCH STRATEGY: Electronic searches were made of bibliographic databases (including the Cochrane Library, C2-SPECTR, PsycINFO, Science Direct and Sociological Abstracts) as well as government and professional websites, from 1985 to January 2003. Reference lists of articles were examined, and experts were contacted. SELECTION CRITERIA: Studies where youth (age 10-17) with social, emotional, and/or behavioral problems were randomised to licensed MST programs or other conditions (usual services or alternative treatments). DATA COLLECTION AND ANALYSIS: Two reviewers independently reviewed 266 titles and abstracts; 95 full-text reports were retrieved, and 35 unique studies were identified. Two reviewers independently read all study reports for inclusion. Eight studies were eligible for inclusion. Two reviewers independently assessed study quality and extracted data from these studies. Significant heterogeneity among studies was identified (assessed using Chi-square and I(2)), hence random effects models were used to pool data across studies. Odds ratios were used in analyses of dichotomous outcomes; standardised mean differences were used with continuous outcomes. Adjustments were made for small sample sizes (using Hedges g). Pooled estimates were weighted with inverse variance methods, and 95% confidence intervals were used. MAIN RESULTS: The most rigorous (intent-to-treat) analysis found no significant differences between MST and usual services in restrictive out-of-home placements and arrests or convictions. Pooled results that include studies with data of varying quality tend to favor MST, but these relative effects are not significantly different from zero. The study sample size is small and effects are not consistent across studies; hence, it is not clear whether MST has clinically significant advantages over other services. AUTHORS' CONCLUSIONS: There is inconclusive evidence of the effectiveness of MST compared with other interventions with youth. There is no evidence that MST has harmful effects.

Adolescent↗
PubMed1998

Estimation of the log-normal mean.

The most commonly used estimator for a log-normal mean is the sample mean. In this paper, we show that this estimator can have a large mean square error, even for large samples. Then, we study three main alternative estimators: (i) a uniformly minimum variance unbiased (UMVU) estimator; (ii) a maximum likelihood (ML) estimator; (iii) a conditionally minimal mean square error (MSE) estimator. We find that the conditionally minimal MSE estimator has the smallest mean square error among the four estimators considered here, regardless of the sample size and the skewness of the log-normal population. However, for large samples (n > or = 200), the UMVU estimator, the ML estimator, and the conditionally minimal MSE estimators have very similar mean square errors. Since the ML estimator is the easiest to compute among these three estimators, for large samples we recommend the use of the ML estimator. For small to moderate samples, we recommend the use of the conditionally minimal MSE estimator.

Bayes Theorem↗
PubMed2001

Optimal estimation of transposition rates of insertion sequences for molecular epidemiology.

Outbreaks of infectious disease can be confirmed by identifying clusters of DNA fingerprints among bacterial isolates from infected individuals. This procedure makes assumptions about the underlying properties of the genetic marker used for fingerprinting. In particular, it requires that each fingerprint changes sufficiently slowly within an individual that isolates from separate individuals infected by the same strain will exhibit similar or identical fingerprints. We propose a model for the probability that an individual's fingerprint will change over a given period of time. We use this model together with published data in order to estimate the fingerprint change rate for IS6110 in human tuberculosis, obtaining a value of 0.0139 changes per copy per year. Although we focus on insertion sequences (IS), our method applies to other fingerprinting techniques such as pulsed-field gel electrophoresis (PFGE). We suggest sampling intervals that produce the least error in estimates of the fingerprint change rate, as well as sample sizes that achieve specified levels of error in the estimate.

Bias↗
PubMed2004

Quantification of variability and uncertainty using mixture distributions: evaluation of sample size, mixing weights, and separation between components.

Variability is the heterogeneity of values within a population. Uncertainty refers to lack of knowledge regarding the true value of a quantity. Mixture distributions have the potential to improve the goodness of fit to data sets not adequately described by a single parametric distribution. Uncertainty due to random sampling error in statistics of interests can be estimated based upon bootstrap simulation. In order to evaluate the robustness of using mixture distribution as a basis for estimating both variability and uncertainty, 108 synthetic data sets generated from selected population mixture log-normal distributions were investigated, and properties of variability and uncertainty estimates were evaluated with respect to variation in sample size, mixing weight, and separation between components of mixtures. Furthermore, mixture distributions were compared with single-component distributions. Findings include: (1). mixing weight influences the stability of variability and uncertainty estimates; (2). bootstrap simulation results tend to be more stable for larger sample sizes; (3). when two components are well separated, the stability of bootstrap simulation is improved; however, a larger degree of uncertainty arises regarding the percentiles coinciding with the separated region; (4). when two components are not well separated, a single distribution may often be a better choice because it has fewer parameters and better numerical stability; and (5). dependencies exist in sampling distributions of parameters of mixtures and are influenced by the amount of separation between the components. An emission factor case study based upon NO(x) emissions from coal-fired tangential boilers is used to illustrate the application of the approach.

Journal Article↗
PubMed2002

Spectrum bias or spectrum effect? Subgroup variation in diagnostic test evaluation.

Diagnostic tests must be evaluated in a clinically relevant population. However, test performance often varies across population subgroups. Spectrum bias, a term commonly used to describe this heterogeneity, is typically thought to occur when diagnostic test performance varies across patient subgroups and a study of that test's performance does not adequately represent all subgroups. Yet subgroup variation is not a bias if appropriate analyses are conducted. Failure to recognize and address heterogeneity will lead to estimates of test performance that are not generalizable to the relevant clinical populations. Heterogeneity can be addressed with relatively simple stratification procedures, limited primarily by the sample size and the precision of the estimates. This paper proposes the use of the term spectrum effect, rather than spectrum bias, and outlines strategies for using stratified sensitivity and specificity estimates, likelihood ratios, and receiver-operating characteristic curves. Investigators of diagnostic tests should consider the potential for spectrum effect seriously and should address heterogeneity in their analyses. Furthermore, clinicians should consider study samples carefully to determine whether results are generalizable to their specific patient population.

Adult↗
PubMed1983

Estimating species richness using the jackknife procedure.

An exact expression is given for the jackknife estimate of the number of species in a community and for the variance of this number when quadrat sampling procedures are used. The jackknife estimate is a function of the number of species that occur in one and only one quadrat. The variance of the number of species can be constructed, as can approximate two-sided confidence intervals. The behavior of the jackknife estimate, as affected by quadrat size, sample size and sampling area, is investigated by simulation.

Animals↗
PubMed2005

A practical comparison of group-sequential and adaptive designs.

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Algorithms↗
PubMed2001

Challenges of subgroup analyses in multinational clinical trials: experiences from the MERIT-HF trial.

BACKGROUND: International placebo-controlled survival trials (Metoprolol Controlled-Release Randomised Intervention Trial in Heart Failure [MERIT-HF], Cardiac Insufficiency Bisoprolol Study [CIBIS-II], and Carvedilol Prospective Randomized Cumulative Survival trial [COPERNICUS]) evaluating the effects of b-blockade in patients with heart failure have all demonstrated highly significant positive effects on total mortality as well as total mortality plus all-cause hospitalization. Also, the analysis of the US Carvedilol Program indicated an effect on these end points. Although none of these trials are large enough to provide definitive results in any particular subgroup, it is natural for physicians to examine the consistency of results across various subgroups or risk groups. Our purpose was to examine both predefined and post hoc subgroups in the MERIT-HF trial to provide guidance as to whether any subgroup is at increased risk, despite an overall strongly positive effect, and to discuss the difficulties and limitations in conducting such subgroup analyses. METHODS: The study was conducted at 313 clinical sites in 16 randomization regions across 14 countries, with a total of 3991 patients. Total mortality (first primary end point) and total mortality plus all-cause hospitalization (second primary end point) were analyzed on a time to first event. The first secondary end point was total mortality plus hospitalization for heart failure. RESULTS: Overall, MERIT-HF demonstrated a hazard ratio of 0.66 for total mortality and 0.81 for mortality plus all-cause hospitalization. The hazard ratio of the first secondary end point of mortality plus hospitalization for heart failure was 0.69. The results were remarkably consistent for both primary outcomes and the first secondary outcome across all predefined subgroups as well as for nearly all post hoc subgroups. The results of the post hoc US subgroup showed a mortality hazard ratio of 1.05. However, the US results regarding both the second primary combined outcome of total mortality plus all-cause hospitalization and of the first secondary combined outcome of total mortality plus heart failure hospitalization were in concordance with the overall results of MERIT-HF. Tests of country by treatment interaction (14 countries) revealed a nonsignificant P value of.22 for total mortality. The mortality hazard ratio for US patients in New York Heart Association (NYHA) class III/IV was 0.80, and it was 2.24 for patients in NYHA class II, which is not consistent with causality by biologic gradient. We have not been able to identify any confounding factor in baseline characteristics, baseline treatment, or treatment during follow-up that could account for any treatment by country interaction. Thus we attribute the US subgroup mortality hazard ratio to be due to chance. CONCLUSIONS: Just as we must be extremely cautious in overinterpreting positive effects in subgroups, even those that are predefined, we must also be cautious in focusing on subgroups with an apparent neutral or negative trend. We should examine subgroups to obtain a general sense of consistency, which is clearly the case in MERIT-HF. We should expect some variation of the treatment effect around the overall estimate as we examine a large number of subgroups because of small sample size in subgroups and chance. Thus the best estimate of the treatment effect on total mortality for any subgroup is the estimate of the hazard ratio for the overall trial.

Adrenergic beta-Antagonists↗
PubMed1999

A comparison of two indirect methods for estimating average levels of gene flow using microsatellite data.

We compare the performance of Nm estimates based on FST and RST obtained from microsatellite data using simulations of the stepwise mutation model with range constraints in allele size classes. The results of the simulations suggest that the use of microsatellite loci can lead to serious overestimations of Nm, particularly when population sizes are large (N > 5000) and range constraints are high (K < 20). The simulations also indicate that, when population sizes are small (N </= 500) and migration rates are moderate (Nm approximately 2), violations to the assumption used to derive the Nm estimators lead to biased results. Under ideal conditions, i.e. large sample sizes (ns >/= 50) and many loci (nl >/= 20), RST performs better than FST for most of the parameter space. However, FST-based estimates are always better than RST when sample sizes are moderate or small (ns </= 10) and the number of loci scored is low (nl < 20). These are the conditions under which many real investigations are carried out and therefore we conclude that in many cases the most conservative approach is to use FST.

Alleles↗
PubMedDate not supplied

Development of probabilistic tools to assist in the establishment and management of cryopreserved plant germplasm collections.

A simple method, based on the binomial distribution, is proposed to calculate the probability of recovering at least one (or any other fixed number of) plant(s) from a cryobank sample using four given parameters: the percentage of plant recovery observed from a control sample, pobs, the number of propagules used for this control, n1, the number of propagules in the cryobank sample, n2, a chosen risk for the calculation of a confidence interval for the observed plant recovery, alpha. Using this method, it is possible to assess the number of propagules which should be rewarmed immediately after freezing in order to estimate the plant recovery percentage as a function of the total number of propagules available. It also allows the calculation of the minimum plant recovery percentage to ensure that the probability to recover at least one (or A, with A>1) plant(s) is higher than a fixed probability level, as a function of the control and the cryobank sample sizes. Reciprocally, once the plant recovery percentage has been estimated, it is possible to assess the minimum size of the cryobank sample to obtain a probability to recover at least one (or A, with A>1) plant(s) higher than some fixed level.

Binomial Distribution↗
PubMed2006

Assessing tiger population dynamics using photographic capture-recapture sampling.

Although wide-ranging, elusive, large carnivore species, such as the tiger, are of scientific and conservation interest, rigorous inferences about their population dynamics are scarce because of methodological problems of sampling populations at the required spatial and temporal scales. We report the application of a rigorous, noninvasive method for assessing tiger population dynamics to test model-based predictions about population viability. We obtained photographic capture histories for 74 individual tigers during a nine-year study involving 5725 trap-nights of effort. These data were modeled under a likelihood-based, "robust design" capture-recapture analytic framework. We explicitly modeled and estimated ecological parameters such as time-specific abundance, density, survival, recruitment, temporary emigration, and transience, using models that incorporated effects of factors such as individual heterogeneity, trap-response, and time on probabilities of photo-capturing tigers. The model estimated a random temporary emigration parameter of gamma" = gamma' = 0.10 +/- 0.069 (values are estimated mean +/- SE). When scaled to an annual basis, tiger survival rates were estimated at S = 0.77 +/- 0.051, and the estimated probability that a newly caught animal was a transient was tau = 0.18 +/- 0.11. During the period when the sampled area was of constant size, the estimated population size N(t) varied from 17 +/- 1.7 to 31 +/- 2.1 tigers, with a geometric mean rate of annual population change estimated as lambda = 1.03 +/- 0.020, representing a 3% annual increase. The estimated recruitment of new animals, B(t), varied from 0 +/- 3.0 to 14 +/- 2.9 tigers. Population density estimates, D, ranged from 7.33 +/- 0.8 tigers/100 km2 to 21.73 +/- 1.7 tigers/100 km2 during the study. Thus, despite substantial annual losses and temporal variation in recruitment, the tiger density remained at relatively high levels in Nagarahole. Our results are consistent with the hypothesis that protected wild tiger populations can remain healthy despite heavy mortalities because of their inherently high reproductive potential. The ability to model the entire photographic capture history data set and incorporate reduced-parameter models led to estimates of mean annual population change that were sufficiently precise to be useful. This efficient, noninvasive sampling approach can be used to rigorously investigate the population dynamics of tigers and other elusive, rare, wide-ranging animal species in which individuals can be identified from photographs or other means.

Animal Identification Systems↗
PubMed2001

Sample size considerations in genetic polymorphism studies.

OBJECTIVES: Molecular studies for genetic polymorphisms are being carried out for a number of different applications, such as genetic disorders in different populations, pharmacogenomics, genetic identification of ethnic groups for forensic and legal applications, genetic identification of breed/stock in animals and plants for commercial applications and conservation of germ plasm. In this paper, for a random sampling scheme, we address two questions: (A) What should be the minimum size of the sample so that, with a prespecified probability, all alleles at a given locus (or haplotypes at a given set of loci) are detected? (B) What should be the sample size so that the allele frequency distribution at a given locus (or haplotype frequency distribution at a given set of loci) is estimated reliably within permissible error limits? METHODS: We have used combinatorial probabilistic arguments and Monte Carlo simulations to answer these questions. RESULTS: We found that the minimum sample size required in case A depends mainly on the prespecified probability of detecting all alleles, while in case B, it varies greatly depending on the permissible error in estimation (which will vary with the application). We have obtained the minimum sample sizes for different degrees of polymorphism at a locus under high stringency, as well as a relaxed level of permissible error. We present a detailed sampling procedure for estimating allele frequencies at a given locus, which will be of use in practical applications. CONCLUSION: Since the sample size required for reliable estimation of allele frequency distribution increases with the number of alleles at the locus, there is a strong case for using biallelic markers (like single nucleotide polymorphisms) when the available sample size is about 800 or less.

Gene Frequency↗
PubMed1989

Consultation rates in English general practice.

Methods of estimating the annual consulting rate per patient are reviewed. Methodological problems include the definition of consultations as opposed to problems encountered, the definition of population at risk, the reliability of data about home visits and the limitations of extrapolating data collected over a short period. Estimates of consultation rate are usually obtained from surveys which have other primary objectives. The annual consultation rate in 1981, excluding telephone contacts, was estimated at 3.5 consultations per patient. In spite of its limited sample size, the general household survey provides a reliable estimate of the national consulting rate. There is, however, a need to validate it against a survey covering a longer period in which consultation rates are measured and not just estimated from memory. The total workload of the 'average' doctor changed little between 1970 and 1981 in spite of reducing list size. Home visits accounted for approximately 15% of all consultations in 1981 and this value has been consistent over the period 1980-83.

Adolescent↗
PubMed2003

A method to combine non-probability sample data with probability sample data in estimating spatial means of environmental variables.

In estimating spatial means of environmental variables of a region from data collected by convenience or purposive sampling, validity of the results can be ensured by collecting additional data through probability sampling. The precision of the pi estimator that uses the probability sample can be increased by interpolating the values at the nonprobability sample points to the probability sample points, and using these interpolated values as an auxiliary variable in the difference or regression estimator. These estimators are (approximately) unbiased, even when the nonprobability sample is severely biased such as in preferential samples. The gain in precision compared to the pi estimator in combination with Simple Random Sampling is controlled by the correlation between the target variable and interpolated variable. This correlation is determined by the size (density) and spatial coverage of the nonprobability sample, and the spatial continuity of the target variable. In a case study the average ratio of the variances of the simple regression estimator and pi estimator was 0.68 for preferential samples of size 150 with moderate spatial clustering, and 0.80 for preferential samples of similar size with strong spatial clustering. In the latter case the simple regression estimator was substantially more precise than the simple difference estimator.

Data Collection↗
PubMed2006

Spatial distribution of nymphs of Scaphoideus titanus (Homoptera: Cicadellidae) in grapes, and evaluation of sequential sampling plans.

The spatial distribution of the nymphs of Scaphoideus titanus Ball (Homoptera Cicadellidae), the vector of grapevine flavescence dorée (Candidatus Phytoplasma vitis, 16Sr-V), was studied by applying Taylor's power law. Studies were conducted from 2002 to 2005, in organic and conventional vineyards of Piedmont, northern Italy. Minimum sample size and fixed precision level stop lines were calculated to develop appropriate sampling plans. Model validation was performed, using independent field data, by means of Resampling Validation of Sample Plans (RVSP) resampling software. The nymphal distribution, analyzed via Taylor's power law, was aggregated, with b = 1.49. A sample of 32 plants was adequate at low pest densities with a precision level of D0 = 0.30; but for a more accurate estimate (D0 = 0.10), the required sample size needs to be 292 plants. Green's fixed precision level stop lines seem to be more suitable for field sampling: RVSP simulations of this sampling plan showed precision levels very close to the desired levels. However, at a prefixed precision level of 0.10, sampling would become too time-consuming, whereas a precision level of 0.25 is easily achievable. How these results could influence the correct application of the compulsory control of S. titanus and Flavescence dorée in Italy is discussed.

Animals↗