True Proportions Research Articles

Borrowing information over time in binomial/logit normal models for small area estimation

Linear area level models for small area estimation, such as the Fay-Herriot model, face challenges when applied to discrete survey data. Such data commonly arise as direct survey estimates of the number of persons possessing some characteristic, such as the number of persons in poverty. For such applications, we examine a binomial/logit normal (BLN) model that assumes a binomial distribution for rescaled survey estimates and a normal distribution with a linear regression mean function for logits of the true proportions. Effective sample sizes are defined so variances given the true proportions equal corresponding sampling variances of the direct survey estimates. We extend the BLN model to bivariate and time series (first order autoregressive) versions to permit borrowing information from past survey estimates, then apply these models to data used by the U.S. Census Bureau’s Small Area Income and Poverty Estimates (SAIPE) program to predict county poverty for school-age children. We compare prediction results from the alternative models to see how much the bivariate and time series models reduce prediction error variances from those of the univariate BLN model. Standard conditional variance calculations for corresponding linear Gaussian models that suggest how much variance reduction will be achieved from borrowing information over time with linear models agree generally with the BLN empirical results.

National treatment patterns in patients presenting with Stage IVC head and neck cancer: analysis of the National Cancer Database.

Head and neck cancer patients presenting with distant metastases are generally considered incurable. Treatment patterns and survival by primary disease site and therapy have not been described. Retrospective cohort analysis of 2525 patients in the National Cancer Database (2003–2006). Kaplan–Meier and Cox proportional hazards analyses were performed. Combined locoregional and systemic therapy was the most common treatment regimen (39.2%), followed by no treatment (23.9%), locoregional (19.0%), and systemic treatment (17.8%). Multivariate analysis demonstrated decreased survival was associated with age 65–79 years hazard ratio [HR] 1.43, 95% confidence interval [CI] 1.14–1.80), Medicaid/uninsured status (HR 1.27, 95% CI 1.13–1.42), Medicare/other government insurance (HR 1.21, 95% 1.07–1.38), treatment at a nonacademic/research program (HR 1.17, 95% CI 1.07–1.27), and Charlson comorbidity score of 1 (HR 1.33, 95% 1.19–1.48). Compared to systemic therapy alone, receiving locoregional and systemic therapy was associated with decreased risk of death (HR 0.73, 95% CI 0.65–0.83). Only 14.6% and 0.6% of patients were recorded as receiving palliative therapy or being enrolled in a clinical trial, respectively. Significant treatment diversity exists in distantly metastatic head and neck cancer. Those who received combination locoregional and systemic therapy were more likely to have improved overall survival, but important factors in treatment selection are unknown. A small proportion of patients was found to receive either palliative therapy or was enrolled in a clinical trial, although these data likely underestimate the true proportions.

Variance in age-specific sex composition of Pacific halibut catches, and comparison of statistical and genetic methods for reconstructing sex ratios

Declines in size at age of Pacific halibut Hippoglossus stenolepis, in concert with sexually-dimorphic growth and a constant minimum commercial size limit, have led to the expectation that the sex composition of commercial catches should be increasingly female-biased. Sensitivity analyses suggest that variance in sex composition of landings may be the most influential source of uncertainty affecting current understanding of spawning stock biomass. However, there is no reliable way to determine sex at landing because all halibut are eviscerated at sea. In 2014, a statistical method based on survey data was developed to estimate the probability that fish of any given length at age (LAA) would be female, derived from the fundamental observation that large, young fish are likely female whereas small, old fish have a high probability of being male. Here, we examine variability in age-specific sex composition using at-sea commercial and closed-season survey catches, and compare the accuracy of the survey-based LAA technique to genetic markers for reconstructing the sex composition of catches. Sexing by LAA performed best for summer-collected samples, consistent with the hypothesis that the ability to characterize catches can be influenced by seasonal demographic shifts. Additionally, differences between survey and commercial selectivity that allow fishers to harvest larger fish within cohorts may generate important mismatch between survey and commercial datasets. Length-at-age-based estimates ranged from 4.7% underestimation of female proportion to 12.0% overestimation, with mean error of 5.8±1.5%. Ratios determined by genetics were closer to true sample proportions and displayed less variability; estimation to within <1% of true ratios was limited to genetics. Genetic estimation of female proportions ranged from 4.9% underestimation to 2.5% overestimation, with a mean absolute error of 1.2±1.2%. Males were generally more difficult to assign than females: 6.7% of males and 3.4% of females were incorrectly assigned. Although nuclear microsatellites proved more consistent at partitioning catches by sex, we recommend that SNP assays be developed to allow for rapid, cost-effective, and accurate sex identification.

Statistical analysis of a questionnaire: voluntary health insurance implementation among patients suffering from allergy and asthma

We consider statistical analysis of multiple answers in a questionnaire. We propose a new method of calculating simultaneous confidence regions. In a communication presented at the European Academy of Allergy and Clinical Immunology the authors (Borowicz et al. (2009)) reported the proportions of respondents which gave one of three possible exclusive answers in a questionnaire concerning the role of voluntary health insurance. There were three possible answers. Apart from percentages of answers confidence intervals of every single answer have been reported. Unfortunately inference about the population based on such intervals may lead to imprecise conclusions. The inference about the respective population suffering from allergy and asthma proportions requires the construction of two-dimensional confidence region. We propose the use of a simultaneous confidence intervals to inference about true population proportions. Most of our attention is given to the case of three possible answers but the results may be generalized to any questionnaire with more than two excluding answers.

Sample size requirements to estimate key design parameters from external pilot randomised controlled trials: a simulation study.

BackgroundExternal pilot or feasibility studies can be used to estimate key unknown parameters to inform the design of the definitive randomised controlled trial (RCT). However, there is little consensus on how large pilot studies need to be, and some suggest inflating estimates to adjust for the lack of precision when planning the definitive RCT.MethodsWe use a simulation approach to illustrate the sampling distribution of the standard deviation for continuous outcomes and the event rate for binary outcomes. We present the impact of increasing the pilot sample size on the precision and bias of these estimates, and predicted power under three realistic scenarios. We also illustrate the consequences of using a confidence interval argument to inflate estimates so the required power is achieved with a pre-specified level of confidence. We limit our attention to external pilot and feasibility studies prior to a two-parallel-balanced-group superiority RCT.ResultsFor normally distributed outcomes, the relative gain in precision of the pooled standard deviation (SDp) is less than 10% (for each five subjects added per group) once the total sample size is 70. For true proportions between 0.1 and 0.5, we find the gain in precision for each five subjects added to the pilot sample is less than 5% once the sample size is 60. Adjusting the required sample sizes for the imprecision in the pilot study estimates can result in excessively large definitive RCTs and also requires a pilot sample size of 60 to 90 for the true effect sizes considered here.ConclusionsWe recommend that an external pilot study has at least 70 measured subjects (35 per group) when estimating the SDp for a continuous outcome. If the event rate in an intervention group needs to be estimated by the pilot then a total of 60 to 100 subjects is required. Hence if the primary outcome is binary a total of at least 120 subjects (60 in each group) may be required in the pilot trial. It is very much more efficient to use a larger pilot study, than to guard against the lack of precision by using inflated estimates.

Multiple comparisons of [formula omitted] binomial proportions

Comparisons of k independent binomial proportions are studied. Piegorsch (1991) compared the Studentized-range implementation of the Wald interval and the Bonferroni-adjusted interval, both of which performed poorly for small values of the true proportions. Agresti et al. (2008) showed that adding one pseudo observation of each type in forming the Wald interval, along with the Studentized-range implementation, greatly improved the performance. A new two-stage method of multiple comparisons (global test followed by pairwise tests) is proposed. For the pairwise tests, three procedures are proposed, which are the LSD type, modified LSD, and inverse-sine based. Simulation studies show that the new procedures have relatively high power and that the modified LSD and inverse-sine based procedures maintain the familywise error rate near the nominal level.

Stochastic models for multiple pathways of temporal natural history on co-morbidity of chronic disease

Chronic diseases frequently co-occur in individuals. Susceptibility to co-morbidity, the temporal sequence and the transition rates governing the development of co-morbid diseases are often hidden or partially observable. To tackle these thorny issues we developed a series of co-morbidity stochastic models with latent variables to estimate the true proportions of susceptibility, temporal sequence, and transition rates. We begin with a bivariate co-morbidity model for two chronic diseases, then extend to a trivariate co-morbidity model for three chronic diseases, and to a generalized high-order co-morbidity model to accommodate more than three chronic diseases. To illustrate our approach we fitted the proposed model with data from a population-based health check-up for hypertension, diabetes mellitus (DM), and overweight in Matsu.Compared with 3.93% of co-morbidity directly estimated from empirical data, approximately 12% (10%–14%) of participants have the potential of developing both hypertension and DM from the underlying population. Hypertension prior to DM was 74% (54.10%–93.77%) of these subjects susceptible to co-morbidity. Those who developed DM first had a higher likelihood of having hypertension (65.85 per 100 person-years; 95% CI: 15.61–116.09) compared with those with hypertension first and DM later (36.37 cases per 100 person-years; 95% CI: 14.57–58.18). Gender, smoking, and alcohol drinking modeled by incorporating them as covariates with proportional hazards form had impacts on different parameters of interest. The deviance statistics, indicating a lack of statistical significance (p values were 0.26 for the bivariate model) for the model without covariates and for the model with covariates (all p values >0.05), suggest a satisfactory model fit. However, the trivariate co-morbidity model had poorer fit than the bivariate co-morbidity model.Our proposed co-morbidity stochastic latent variable models can tackle the problem of underestimating the proportion of susceptibility to co-morbidity, giving a clue to the temporal sequence of a constellation of co-morbid diseases, and quantifying the incidence rates of each disease and the corresponding transitions rates between co-morbid diseases. The generalized high-order co-morbidity model can be extended to model the complex pathway of high dimension of chronic diseases in the clinical field provided the dataset is sufficiently large.

Evaluation of Respondent-driven Sampling

Respondent-driven sampling is a novel variant of link-tracing sampling for estimating the characteristics of hard-to-reach groups, such as HIV prevalence in sex workers. Despite its use by leading health organizations, the performance of this method in realistic situations is still largely unknown. We evaluated respondent-driven sampling by comparing estimates from a respondent-driven sampling survey with total population data. Total population data on age, tribe, religion, socioeconomic status, sexual activity, and HIV status were available on a population of 2402 male household heads from an open cohort in rural Uganda. A respondent-driven sampling (RDS) survey was carried out in this population, using current methods of sampling (RDS sample) and statistical inference (RDS estimates). Analyses were carried out for the full RDS sample and then repeated for the first 250 recruits (small sample). We recruited 927 household heads. Full and small RDS samples were largely representative of the total population, but both samples underrepresented men who were younger, of higher socioeconomic status, and with unknown sexual activity and HIV status. Respondent-driven sampling statistical inference methods failed to reduce these biases. Only 31%-37% (depending on method and sample size) of RDS estimates were closer to the true population proportions than the RDS sample proportions. Only 50%-74% of respondent-driven sampling bootstrap 95% confidence intervals included the population proportion. Respondent-driven sampling produced a generally representative sample of this well-connected nonhidden population. However, current respondent-driven sampling inference methods failed to reduce bias when it occurred. Whether the data required to remove bias and measure precision can be collected in a respondent-driven sampling survey is unresolved. Respondent-driven sampling should be regarded as a (potentially superior) form of convenience sampling method, and caution is required when interpreting findings based on the sampling method.

S13.3 An empirical evaluation of respondent-driven sampling

ObjectiveRespondent-driven sampling (RDS) is an increasingly widely used variant of snowball sampling, that proponents claim can provide unbiased estimates. RDS has not been rigorously evaluated in the field. This study...

Ruminant brucellosis in Upper Egypt (2005–2008)

Brucellosis is endemic among humans and ruminant in Egypt and recent reports suggest that its incidence may be increasing. In this study we describe the frequency of brucellosis among different ruminant species in Upper Egypt and its spatial distribution using the data generated by a large-scale control campaign undertaken between 2005 and 2008. A total of 120,090 individual animals of different ruminant species were tested during the campaign. The true proportions of brucellosis were estimated as 0.79% (CI: 0.71%–0.87%), 0.13% (CI: 0.08%–0.18%), 1.16% (1.05%–1.27%) and 0.44% (0.34%–0.54%) among cattle, buffaloes, sheep and goats respectively. We estimated that 0.2% (CI: 0.16%–0.23%) of households in the study area keep at least one seropositive animal. Spatial autocorrelation of the proportions of seropositive households and seropositive animals was assessed using Global Univariate Moran's I and Local Univariate LISA. These analyses showed that the distribution of seropositive animals has considerable spatial heterogeneity with clustering in the northern governorates of the study area. Our results show that brucellosis is widespread and heterogeneously distributed in Upper Egypt. At the current level of available resources it is very unlikely that test and slaughter could be implemented with the intensity needed to be effective and other control measures that could replace or complement the test and slaughter policy in place should be considered. Also, this study illustrates some of the challenges faced by bilateral projects that have to accommodate an externally funded intervention with an ongoing national official disease control program.

Peters World Atlas: The Earth in its True Proportions (Revised and updated ed.)

Peters World Atlas: The Earth in its True Proportions (Revised and updated ed.)

A sensitive and reliable restriction enzyme assay to distinguish between the mosquitoes Culex torrentium and Culex pipiens

Culex pipiens pipiens Linnaeus and Culex torrentium Martini (Diptera: Culicidae) are closely related vector species that exist sympatrically in Europe. The two species are morphologically almost identical and can only be distinguished with certainty by characters of the male genitalia. Hence, correct species identification and conclusions on distribution and vector status are very difficult and often neglected. Therefore, we developed a reliable and simple mitochondrial cytochrome c oxidase subunit I (COI) gene restriction enzyme assay to discriminate between Cx. pipiens and Cx. torrentium, based on the analysis of morphologically identified male specimens. We sequenced approximately 830 bp in the 3' region of the mitochondrial COI gene of 18 morphologically identified males of Cx. pipiens and Cx. torrentium. Two restriction enzymes (FspBI and SspI) that could distinguish between the two species according to species-specific differences in these sequences were chosen. The restriction enzymes were tested on 227 samples from Sweden and verified by sequencing 44 of them. The enzyme FspBI correctly identified all investigated samples; the enzyme SspI identified all samples except one Cx. torrentium. We hope the method and the findings presented here will help to shed light on the true distribution and relative proportions of the two species in Europe.

Assessment of the species composition of forest floor horizons in mixed spruce-beech stands by Near Infrared Reflectance Spectroscopy (NIRS)

How the mixture of tree species modifies short-term decomposition has been well documented using litterbag studies. However, how litter of different tree species interact in the long-term is obscured by our inability to visually recognize the species identity of residual decomposition products in the two most decomposed layers of the forest floor (i.e. the Oe and Oa layers respectively). To overcome this problem, we used Near Infrared Reflectance Spectroscopy (NIRS) to determine indirectly the species composition of forest floor layers. For this purpose, controlled mixtures of increasing complexity comprising beech and spruce foliage materials at various stages of decomposition from sites differing in soil acid–base status were created. In addition to the controlled mixtures, natural mixtures of litterfall from mixed stands were used to develop prediction models. Following a calibration/validation procedure, the best regression models to predict the actual species proportion from spectral properties were selected for each tree species based on the highest coefficient of determination ( R 2) and the lowest root mean square error of prediction (RMSEP). For the validation, the R 2 (predictions versus true proportions) were 0.95 and 0.94 for both beech and spruce components in mixtures of materials at all stages of decomposition from the gradient of sites. The R 2 decreased only marginally by 0.04 when models were tested on independent samples of similar composition. The best models were used to predict the beech-spruce proportion in Oe and Oa layers of unknown composition. They provided in most cases plausible predictions when compared to the composition of the canopy above the sampling points. Thus, tedious and potentially erroneous hand sorting of forest floor layers may be replaced by the use of NIRS models to determine species composition, even at late stages of decomposition.

Detection and Interpretation of Opinion Expressions in Spoken Surveys

This paper describes a system for automatic opinion analysis from spoken messages collected in the context of a user satisfaction survey. Opinion analysis is performed from the perspective of opinion monitoring. A process is outlined for detecting segments expressing opinions in a speech signal. Methods are proposed for accepting or rejecting segments from messages that are not reliably analyzed due to the limitations of automatic speech recognition processes, for assigning opinion hypotheses to segments and for evaluating hypothesis opinion proportions. Specific language models are introduced for representing opinion concepts. These models are used for hypothesizing opinion carrying segments in a spoken message. Each segment is interpreted by a classifier based on the Adaboost algorithm which associates a pair of topic and polarity labels to each segment. The different processes are trained and evaluated on a telephone corpus collected in a deployed customer care service. The use of conditional random fields (CRFs) is also considered for detecting segments and results are compared for different types of data and approaches. By optimizing the choice of the strategy parameters, it is possible to estimate user opinion proportions with a Kullback-Leibler divergence of 0.047 bits with respect to the true proportions obtained with a manual annotation of the spoken messages. The proportions estimated with such a low divergence are accurate enough for monitoring user satisfaction over time.

A model predicting primary infections of Plasmopara viticola in different grapevine-growing areas of Italy

A dynamic model for Plasmopara viticola primary infections was evaluated by comparing model predictions with disease onset in: (i) 100 vineyards of northern, southern and insular Italy (1995 to 2007); (ii) 42 groups of potted grapevine plants exposed to inoculum (2006 to 2008). The model simulates the development of any oospore cohort during the primary inoculum season, including oospore germination, production and survival of sporangia, release, survival and dispersal of zoospores, and infection and incubation. The model showed high sensitivity, specificity, and accuracy both in vineyards and in potted plants. The true positive and negative proportions were TPP=0.99 and TNP=0.87, respectively. Because of a certain proportion of false positive predictions (FPP=0.13), confidence in prediction of non-infections was higher than in prediction of infections. These wrong predictions occurred early in the season or when oospore inoculum was low, or were triggered by isolated weak rain events. In only one case (a group of potted plants) there was infection when infection was not predicted (FNP=0.005). The model can be considered an accurate and robust predictor of P. viticola oospore infections and could be used to reduce or improve the timing of fungicide sprays.

Anterior dynamic ultrasound of the infant hip: evaluation of investigator dependence

Anterior dynamic ultrasound of the infant hip has been shown to be a valuable tool for detection of developmental dysplasia of the infant hip, but to what extent the results from this method depends on the investigator is unknown. To study to what extent the proportion of positive findings at anterior dynamic ultrasound investigation of infant hips varies with the observer. Information on all ultrasound investigations of infant hips at a county hospital between January 2004 and August 2007 was evaluated. Proportion of findings for different investigators were calculated and in a multivariable logistic regression analysis, risk of treatment by investigating orthopedic surgeon and radiologist were adjusted for each other as well as for calendar period and infant sex. There was a striking variation in proportion of positive findings depending on the investigator. The proportion of infants treated varied with orthopedic surgeon from 4.2 to 53.9% (95% CI: 2.27 to 7.13 and 43.0 to 64.6, respectively) and the corresponding variation for radiologists ranged from 7.4 (95% CI: 4.29 to 11.8) to 23.9% (95% CI: 17.2 to 31.8). In the adjusted analysis, variation between different investigators remained essentially unaltered. Although the true proportions of positive findings in our study are unknown, our findings are unlikely to be explained by selection bias or chance. Thus, our study suggests that anterior dynamic ultrasound of the infant hip is highly dependent on the investigator and further studies of the implications of our results are warranted.

Genotyping and inflated type I error rate in genome-wide association case/control studies.

BackgroundOne common goal of a case/control genome wide association study (GWAS) is to find SNPs associated with a disease. Traditionally, the first step in such studies is to assign a genotype to each SNP in each subject, based on a statistic summarizing fluorescence measurements. When the distributions of the summary statistics are not well separated by genotype, the act of genotype assignment can lead to more potential problems than acknowledged by the literature.ResultsSpecifically, we show that the proportions of each called genotype need not equal the true proportions in the population, even as the number of subjects grows infinitely large. The called genotypes for two subjects need not be independent, even when their true genotypes are independent. Consequently, p-values from tests of association can be anti-conservative, even when the distributions of the summary statistic for the cases and controls are identical. To address these problems, we propose two new tests designed to reduce the inflation in the type I error rate caused by these problems. The first algorithm, logiCALL, measures call quality by fully exploring the likelihood profile of intensity measurements, and the second algorithm avoids genotyping by using a likelihood ratio statistic.ConclusionGenotyping can introduce avoidable false positives in GWAS.

Auger Nanoprobe analysis of presolar ferromagnesian silicate grains from primitive CR chondrites QUE 99177 and MET 00426

We have investigated the presolar grain inventories of two CR chondrites, QUE 99177 and MET 00426, which are less altered than most members of this meteorite group. Both meteorites contain high abundances of O-anomalous presolar grains, with concentrations of 220 ± 40 and 160 ± 30 ppm for QUE 99177 and MET 00426, respectively. The presolar grain inventories are dominated by ferromagnesian silicates with group 1 oxygen isotopic compositions, indicative of origins in low mass red giant or asymptotic giant branch stars. Grains with pyroxene-like compositions are somewhat more common than those with olivine-like compositions, but most grains are non-stoichiometric with compositions intermediate between these two phases, consistent with recent work suggesting that amorphous interstellar silicates have stoichiometries between olivine and pyroxene type silicates. Although structural data are not available, one grain contains only Si and O, and has a stoichiometry consistent with SiO 2. Our presolar grains are much more Fe-rich than predicted by astronomical observations. Although secondary alteration may play a role in enhancing the Fe contents of presolar grains, it seems unlikely that the large and ubiquitous Fe enrichments observed in the grains from this study can be due only to secondary processing, particularly given the highly primitive nature of these two meteorites. Grain condensation in the stellar outflows where these grains formed likely proceeded under rapidly changing kinetic conditions that may have enhanced the incorporation of Fe into the grains over that expected based on equilibrium condensation theory. Both QUE 99177 and MET 00426 appear to contain unusually low abundances of oxide grains and have higher silicate/oxide ratios than other primitive meteorites analyzed to date. We explore various possibilities for this discrepancy, but note that most scenarios are not likely to result in the preferential destruction of oxides relative to silicates. Thus, the highest silicate/oxide ratios, such as those observed in the CR chondrites, should reflect the true initial proportions of presolar silicate and oxide grains in the parent molecular cloud from which the solar nebula evolved.

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Parentage Analysis with Few Contributing Breeders: Validation and Improvement

Validation of parental allocation using PAPA software (Duchesne P, Godbout MH, Bernatchez L. 2002. PAPA (package for the analysis of parental allocation): a computer program for simulated and real parental allocation. Mol Ecol Notes. 2:191-193.) was investigated under the assumption that only a small proportion of potential breeders contributed to the offspring sample. Inbreeding levels proved to have a large impact on allocation error rate. Consequently, simulations from artificial, unrelated parents may strongly underestimate allocation error, and so, whenever possible, simulations based on the actual parental genotypes should be run. An unexpected and interesting finding was that ambiguity (the highest likelihood is shared by several parental pairs) rates below 10% stood very close to exact allocation error rates (true proportions of wrong allocations). Hence, the ambiguity rate statistic may be viewed as a ready-made indicator of the resolution power of a specific parental allocation run and, if not exceeding 10%, used as an estimate of allocation error rate. It was found that the PAPA simulator, even with few contributing breeders, can be trusted to output reasonably accurate estimates of allocation error as long as those estimates do not exceed 15%. Indeed, most discrepancies between exact and estimated error then stood below 3%. Reproductive success variance had little impact on error estimate discrepancies within the same range. Finally, a (focal set) method was described to correct the estimated family sizes computed directly from parental allocations. Essentially, this method makes use of the detailed structure of the allocation probabilities associated with each parental pair with at least 1 allocated offspring. The allocation probabilities are expressed in matrix form, and the subsequent calculations are run based on standard matrix algebra. On average, this method provided better estimates of family sizes for each investigated combination of parameter values. As the size of offspring samples increased, the corrections improved until a plateau was finally reached. Typically, samples comprising 250, 500, and 1000 offspring would bring corrections in the order of 10-20%, 20-30%, and 30-40%, respectively.