Profile Likelihood Confidence Intervals Research Articles

Evaluating Testing, Profile Likelihood Confidence Interval Estimation, and Model Comparisons for Item Covariate Effects in Linear Logistic Test Models.

The linear logistic test model (LLTM) has been widely applied to investigate the effects of item covariates on item difficulty. The LLTM was extended with random item residuals to account for item differences not explained by the item covariates. This extended LLTM is called the LLTM-R. In this article, statistical inference methods are investigated for these two models. Type I error rates and power are compared via Monte Carlo studies. Based on the simulation results, the use of the likelihood ratio test (LRT) is recommended over the paired-sample t test based on sum scores, the Wald z test, and information criteria, and the LRT is recommended over the profile likelihood confidence interval because of the simplicity of the LRT. In addition, it is concluded that the LLTM-R is the better general model approach. Inferences based on the LLTM while the LLTM-R is the true model appear to be largely biased in the liberal way, while inferences based on the LLTM-R while the LLTM is the true model are only biased in a very minor and conservative way. Furthermore, in the absence of residual variance, Type I error rate and power were acceptable except for power when the number of items is small (10 items) and also the number of persons is small (200 persons). In the presence of residual variance, however, the number of items needs to be large (80 items) to avoid an inflated Type I error and to reach a power level of .90 for a moderate effect.

Two new methods to fit models for network meta-analysis with random inconsistency effects

BackgroundMeta-analysis is a valuable tool for combining evidence from multiple studies. Network meta-analysis is becoming more widely used as a means to compare multiple treatments in the same analysis. However, a network meta-analysis may exhibit inconsistency, whereby the treatment effect estimates do not agree across all trial designs, even after taking between-study heterogeneity into account. We propose two new estimation methods for network meta-analysis models with random inconsistency effects.MethodsThe model we consider is an extension of the conventional random-effects model for meta-analysis to the network meta-analysis setting and allows for potential inconsistency using random inconsistency effects. Our first new estimation method uses a Bayesian framework with empirically-based prior distributions for both the heterogeneity and the inconsistency variances. We fit the model using importance sampling and thereby avoid some of the difficulties that might be associated with using Markov Chain Monte Carlo (MCMC). However, we confirm the accuracy of our importance sampling method by comparing the results to those obtained using MCMC as the gold standard. The second new estimation method we describe uses a likelihood-based approach, implemented in the metafor package, which can be used to obtain (restricted) maximum-likelihood estimates of the model parameters and profile likelihood confidence intervals of the variance components.ResultsWe illustrate the application of the methods using two contrasting examples. The first uses all-cause mortality as an outcome, and shows little evidence of between-study heterogeneity or inconsistency. The second uses “ear discharge" as an outcome, and exhibits substantial between-study heterogeneity and inconsistency. Both new estimation methods give results similar to those obtained using MCMC.ConclusionsThe extent of heterogeneity and inconsistency should be assessed and reported in any network meta-analysis. Our two new methods can be used to fit models for network meta-analysis with random inconsistency effects. They are easily implemented using the accompanying R code in the Additional file 1. Using these estimation methods, the extent of inconsistency can be assessed and reported.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0184-5) contains supplementary material, which is available to authorized users.

Abstract PD1-07: Mammographic density and SNPs add to Tyrer-Cuzick and Gail model breast cancer risk in a UK screening cohort

Abstract Background: The predicting risk of cancer at screening study (PROCAS) in Manchester UK is a prospective study of breast cancer risk estimation. This article considers whether mammographic density and SNPs in PROCAS may help refine breast cancer risk estimation using the Gail (BCRAT) and Tyrer-Cuzick (TC, or IBIS) models, based on incident and prevalent breast cancers identified between two three-yearly screening rounds. Methods: Mammographic density was measured at entry as a percentage using the average visual assessment from two trained readers. Tyrer-Cuzick and Gail risks were based on a questionnaire completed at the same time. The contribution of density to risk models was assessed after adjustment for age and body mass index (BMI) using odds ratios (ORs) and profile likelihood confidence intervals (CIs). A secondary analysis compared cancer pathology characteristics using a two-sided Wilcoxon test. Eighteen breast cancer risk variants (SNP18) were assessed with a polygenic risk score (PRS) alongside TC and density in a subset of 8870 women with 341 prospective cancers. Results: Analysis included 50628 women of routine screening age (47-73 yrs), recruited between Aug 2009 and Jul 2014. 697 had a breast cancer diagnosed after enrolment. Median follow-up was 3.2 years. Visually assessed percentage breast density (inter-quartile range odds ratio (IQR OR) 1.48 (95%CI 1.34-1.63)) was a slightly stronger univariate risk factor than TC (IQR OR 1.36 (1.25-1.48)) or Gail (IQR OR 1.22 (1.12-1.33)). It continued to add information after allowing for TC (IQR OR 1.47 (1.33-1.62)) or Gail (IQR OR 1.45 (1.32-1.60)). 36472/50628 (72%) women had less than 3.5% 10-yr risk from the TC model and breast density combined. Women with dense breasts were more likely to have a higher stage breast cancer (P <.001). SNP18 showed a 2 fold relative breast cancer risk between the top and bottom quintile. Using a combined analysis of SNP18, TC and density there was a 5.6 fold risk between those identified at NICE defined high risk compared to low risk. Conclusion: Breast density and SNPs when combined with the TC or Gail risk model identify a larger number of high risk women at screening, and it is associated with higher stage of disease. Approximately 70% of women are identified with a combined TC and density risk assessment of less than 3.5% 10-yr risk (average or less than average risk), for whom three-yearly screening might be effective. SNP18 adds further precision and addition of further newly identified SNPs is likely to add greater discrimination. Citation Format: Evans DG, Astley SM, Brentnall A, Howell A, Cuzick J. Mammographic density and SNPs add to Tyrer-Cuzick and Gail model breast cancer risk in a UK screening cohort. [abstract]. In: Proceedings of the Thirty-Eighth Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2015 Dec 8-12; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2016;76(4 Suppl):Abstract nr PD1-07.

Mammographic density adds accuracy to both the Tyrer-Cuzick and Gail breast cancer risk models in a prospective UK screening cohort.

IntroductionThe Predicting Risk of Cancer at Screening study in Manchester, UK, is a prospective study of breast cancer risk estimation. It was designed to assess whether mammographic density may help in refinement of breast cancer risk estimation using either the Gail model (Breast Cancer Risk Assessment Tool) or the Tyrer-Cuzick model (International Breast Intervention Study model).MethodsMammographic density was measured at entry as a percentage visual assessment, adjusted for age and body mass index. Tyrer-Cuzick and Gail 10-year risks were based on a questionnaire completed contemporaneously. Breast cancers were identified at the entry screen or shortly thereafter. The contribution of density to risk models was assessed using odds ratios (ORs) with profile likelihood confidence intervals (CIs) and area under the receiver operating characteristic curve (AUC). The calibration of predicted ORs was estimated as a percentage [(observed vs expected (O/E)] from logistic regression.ResultsThe analysis included 50,628 women aged 47–73 years who were recruited between October 2009 and September 2013. Of these, 697 had breast cancer diagnosed after enrolment. Median follow-up was 3.2 years. Breast density [interquartile range odds ratio (IQR-OR) 1.48, 95 % CI 1.34–1.63, AUC 0.59] was a slightly stronger univariate risk factor than the Tyrer-Cuzick model [IQR-OR 1.36 (95 % CI 1.25–1.48), O/E 60 % (95 % CI 44–74), AUC 0.57] or the Gail model [IQR-OR 1.22 (95 % CI 1.12–1.33), O/E 46 % (95 % CI 26–65 %), AUC 0.55]. It continued to add information after allowing for Tyrer-Cuzick [IQR-OR 1.47 (95 % CI 1.33–1.62), combined AUC 0.61] or Gail [IQR-OR 1.45 (95 % CI 1.32–1.60), combined AUC 0.59].ConclusionsBreast density may be usefully combined with the Tyrer-Cuzick model or the Gail model.Electronic supplementary materialThe online version of this article (doi:10.1186/s13058-015-0653-5) contains supplementary material, which is available to authorized users.

Confidence intervals for the ratio of two Poisson rates under one-way differential misclassification using double sampling

Wald, profile likelihood, and marginal likelihood confidence intervals are derived for the ratio of two Poisson rates in the presence of one-way differentially misclassified data using double sampling. Monte Carlo simulations demonstrate the reliability and relative performance of the intervals, and an example from cancer epidemiology illustrates their application and interpretation in a real-world scenario. All of the methods described are implemented and freely available in the R package poisDoubleSamp on the Comprehensive R Archive Network (CRAN).

Simulation-based Bayesian inference for latent traits of item response models: Introduction to the ltbayes package for R.

This paper introduces the ltbayes package for R. This package includes a suite of functions for investigating the posterior distribution of latent traits of item response models. These include functions for simulating realizations from the posterior distribution, profiling the posterior density or likelihood function, calculation of posterior modes or means, Fisher information functions and observed information, and profile likelihood confidence intervals. Inferences can be based on individual response patterns or sets of response patterns such as sum scores. Functions are included for several common binary and polytomous item response models, but the package can also be used with user-specified models. This paper introduces some background and motivation for the package, and includes several detailed examples of its use.

Comparing confidence intervals for Goodman and Kruskal's gamma coefficient

This study was motivated by the question which type of confidence interval (CI) one should use to summarize sample variance of Goodman and Kruskal's coefficient gamma. In a Monte-Carlo study, we investigated the coverage and computation time of the Goodman–Kruskal CI, the Cliff-consistent CI, the profile likelihood CI, and the score CI for Goodman and Kruskal's gamma, under several conditions. The choice for Goodman and Kruskal's gamma was based on results of Woods [Consistent small-sample variances for six gamma-family measures of ordinal association. Multivar Behav Res. 2009;44:525–551], who found relatively poor coverage for gamma for very small samples compared to other ordinal association measures. The profile likelihood CI and the score CI had the best coverage, close to the nominal value, but those CIs could often not be computed for sparse tables. The coverage of the Goodman–Kruskal CI and the Cliff-consistent CI was often poor. Computation time was fast to reasonably fast for all types of CI.

Neospora caninum serostatus is affected by age and species variables in cohabiting water buffaloes and beef cattle

The aim of this study was to investigate how Neospora caninum serostatus may be affected by variables such as host species (water buffaloes or cattle) and age in animals cohabiting in the same ranch. A convenience cross-sectional study was performed on four ranches in the Northeast of Argentina, where water buffalo are cohabitating with beef cattle. Blood samples were collected from 1350 female water buffaloes (Bubalus bubalis) and 880 female beef cattle (Bos taurus and Bos indicus crossbreeds) from four ranches. Calving and weaning percentages at herd level for each ranch were also recorded. N. caninum antibody levels were measured by an indirect fluorescent antibody test (IFAT) (reciprocal antibody titers ≥100). Serological results were classified into 2 categories (0: negative; 1: positive). A logistic regression model was used to describe the relationship between N. caninum serostatus and specie (water buffalo or cattle), age or ranch and their interactions. Likelihood ratio tests were used to assess the significance of the model and their terms. Odds ratios were estimated and 95% profile likelihood (LR) and Wald confidence intervals (CI) obtained. Overall, specific antibody titers were found in 43.3% (584/1350) of water buffaloes and 28.6% (252/880) of cattle. Seropositive water buffaloes and cattle were observed on all ranches. Age was statistically significant (p=0.01) with an overall estimate of logit (log odds) of age of 0.03 for both species. This indicates that for every one year increase in age, the expected change in log odds of being seropositive increased by 0.03. On three of four ranches a water buffalo was 4.48, 1.54 and 2.25 times more likely to be seropositive than cattle for animals of the same age. The N. caninum serostatus was affected by age in the first place, but also by species on at least three of the four ranches. Calving and weaning percentages were higher in water buffaloes than in beef cattle (p<0.05). Even though the low pathogenicity that N. caninum seems to have in water buffaloes, this study reinforces the importance of this specie as maintenance of the disease.

Some New Random Effect Models for Correlated Binary Responses

AbstractExchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are constructed for several copula families. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed and their performance are assessed in a simulation experiment. The sensitivity of the inference to the specification of the copula family is also investigated through simulations. Numerical examples are presented.

A new profile likelihood confidence interval for the mean probability of detection in collaborative studies of binary test methods

A confidence interval for the probability of detection across laboratories (LPOD) for qualitative methods, described in the AOAC INTERNATIONAL guidelines for validation of microbiological methods for food and environmental surfaces, is considered. It is demonstrated that under certain conditions, the observed confidence of this confidence interval can be rather low, so that statistical minimum requirements are not fulfilled. A new profile likelihood confidence interval based on a latent random laboratory effect approach is proposed. Observed confidence levels for this confidence interval demonstrate its applicability already for a small number of laboratories.

Przedział ufności profile likelihood dla prawdopodobieństwa sukcesu w modelu regresji logistycznej Firtha

In the first part of the paper the results of the simulation study, comparing the coverage properties of Wald’s and the profile likelihood confidence intervals for the probability of a success in the Firth’s logistic regression, are described. The efficient algorithm for computing profile likelihood confidence intervals is proposed. In the second part of the paper the theoretical results are applied to the bankruptcy model.

Selection models with monotone weight functions in meta analysis

Publication bias, the fact that studies identified for inclusion in a meta analysis do not represent all studies on the topic of interest, is commonly recognized as a threat to the validity of a meta analysis. One way to explicitly model publication bias is via weighted probability distributions. We adopt the non-parametric approach initially introduced by Dear and Begg (1992) but impose that the weight function w is monotonely non-increasing as a function of the p-value. Since in meta analysis one typically only has few studies or "observations," regularization of the estimation problem seems sensible. In addition, virtually all parametric weight functions proposed so far in the literature are in fact decreasing. We discuss how to estimate a decreasing weight function in the above model and illustrate the new methodology on two well-known examples. Some basic properties of the log-likelihood function and computation of a p-value quantifying the evidence against the null hypothesis of a constant weight function are indicated. In addition, we provide an approximate selection bias adjusted profile likelihood confidence interval for the treatment effect. The corresponding software and the data sets used to illustrate it are provided as the R package selectMeta (Rufibach, 2011).

Frequentist analysis of hierarchical models for population dynamics and demographic data

Hierarchical models include random effects or latent state variables. This class of models includes state–space models for population dynamics, which incorporate process and sampling variation, and models with random individual or year effects in capture–mark–recapture models, for example. This paper reviews methods for frequentist analysis of hierarchical models and gives an example of a non-Gaussian, potentially nonlinear analysis of Lapwing data using the Monte Carlo kernel likelihood (MCKL) method for maximum-likelihood estimation and bridge sampling for calculation of likelihood values given estimated parameters. The Lapwing example uses the state–space model as part of an integrated population model, which combines survey data with ring-recovery demographic data. The methods reviewed include filtering methods, such as the Kalman filter and sequential Monte Carlo (or particle filtering) methods, Monte Carlo expectation maximization, data cloning, and MCKL. The latter methods estimate the maximum-likelihood parameters but omit a normalizing constant from the likelihood that is needed for model comparisons, such as the Akaike information criterion and likelihood ratio tests. The methods reviewed for normalizing constant calculation include filtering, importance sampling, likelihood ratios from importance sampling, and bridge sampling. For the Lapwing example, a novel combination of MCKL parameter estimation, bridge sampling likelihood calculation, and profile likelihood confidence intervals for an integrated population model is presented to illustrate the feasibility of these methods. A complementary view of Bayesian and frequentist analysis is taken.

Late Rectal Toxicity on RTOG 94-06: Analysis Using a Mixture Lyman Model

To estimate the parameters of the Lyman normal-tissue complication probability model using censored time-to-event data for Grade ≥2 late rectal toxicity among patients treated on Radiation Therapy Oncology Group 94-06, a dose-escalation trial designed to determine the maximum tolerated dose for three-dimensional conformal radiotherapy of prostate cancer. The Lyman normal-tissue complication probability model was fitted to data from 1,010 of the 1,084 patients accrued on Radiation Therapy Oncology Group 94-06 using an approach that accounts for censored observations. Separate fits were obtained using dose-volume histograms for whole rectum and dose-wall histograms for rectal wall. With a median follow-up of 7.2 years, the crude incidence of Grade ≥2 late rectal toxicity was 15% (n = 148). The parameters of the Lyman model fitted to dose-volume histograms data, with 95% profile-likelihood confidence intervals, were TD(50) = 79.1 Gy (75.3 Gy, 84.3 Gy), m = 0.146 (0.107, 0.225), and n = 0.077 (0.041, 0.156). The fit based on dose-wall histogram data was not significantly different. Patients with cardiovascular disease had a significantly higher incidence of late rectal toxicity (p = 0.015), corresponding to a dose-modifying factor of 5.3%. No significant association with late rectal toxicity was found for diabetes, hypertension, rectal volume, rectal length, neoadjuvant hormone therapy, or prescribed dose per fraction (1.8 Gy vs. 2 Gy). These results, based on a large cohort of patients from a multi-institutional trial, are expected to be widely representative of the ability of the Lyman model to describe the long-term risk of Grade ≥2 late rectal toxicity after three-dimensional conformal radiotherapy of prostate cancer.

The Impact of Footwear and Packweight on Injury and Illness Among Long-Distance Hikers

To determine the prevalence and predictors of injury and illness among long-distance hikers. This was a cross-sectional study of long-distance hikers (> 500 miles [805 km]) along the Appalachian Trail and Pacific Crest Trails between August and October of 2006. An 8-page survey instrument was made available to hikers at a designated station near the northern terminus of the respective trails. The survey questions were yes/no or multiple choice. Independent variables included packweight, footwear, and type and frequency of water purification. chi(2) tests to compare categorical data and the Cochran-Armitage test for trend were used (P < .05 significant). We used logistic regression to compare the variables concurrently, and significance was determined using likelihood ratio tests. Profile likelihood confidence intervals for the odds ratios are reported. Of the 128 hikers completing surveys that met inclusion criteria, the mean age was 33 years (range = 18-65 years), 94% walked >1500 miles (2400 km), and 70% were male. Using univariate analysis, trends were noted in the proportion of hikers reporting paresthesias and increasing packweight (35% with 10-20 pound [4.5-9 kg] packs, 50% with 21-30 pound [9.5-13.5 kg] packs, and 69% with >31 pound [14 kg] packs [P < .002]), as well as in the proportion of hikers reporting paresthesias and increasing footwear rigidity (29% sandals, 36% running shoes, 42% hiking shoes, and 68% hiking boots [P < .001]). In multivariate analysis compared to sandals, the odds ratio of suffering from paresthesias with running shoes was 1.57 (95% CI 0.3, 12.2), hiking shoes 1.73 (95% CI 0.3, 13.9), and hiking boots 3.9 (95% CI 0.7, 32.1) (P = .16). Compared to 10 to 20 pound (4.5-9 kg) packs, the odds ratios of suffering from paresthesias with 21 to 30 pound (9.5-13.5 kg) packs was 1.5 (95% CI 0.6, 3.9), and for > 31 pounds (14 kg) was 2.2 (CI 0.7, 7.1) (P = .03). Adjusting for footwear and pack weight, only pack weight was significantly associated with paresthesias. Packweight and footwear were not significantly associated with other musculoskeletal injuries, such as joint sprains or chronic pain, and muscle injuries. There is an association between packweight and the prevalence of paresthesias among long-distance hikers. The association between type of footwear and the prevalence of paresthesias is significant when analyzed independently, but loses its significance when the variables are examined together. This suggests that there is confounding between footwear and packweight.

A bivariate distribution with gamma and beta marginals with application to drought data

The first known bivariate distribution with gamma and beta marginals is introduced. Various representations are derived for its joint probability density function (pdf), joint cumulative distribution function (cdf), product moments, conditional pdfs, conditional cdfs, conditional moments, joint moment generating function, joint characteristic function and entropies. The method of maximum likelihood and the method of moments are used to derive the associated estimation procedures as well as the Fisher information matrix, variance–covariance matrix and the profile likelihood confidence intervals. An application to drought data from Nebraska is provided. Some other applications are also discussed. Finally, an extension of the bivariate distribution to the multivariate case is proposed.

Score and profile likelihood confidence intervals for contingency table parameters

A straightforward approach to computing score and profile likelihood confidence intervals for contingency table parameters is described. The computational approach herein avoids two main limitations of existing methods: (1) Compared with existing methods, this paper's approach is applicable to a much broader class of parameters. (2) Unlike existing methods, this paper's approach is not case-specific and, hence, lends itself to a general, yet very simple, computational algorithm. This paper describes the 'sliding quadratic' computational algorithm and illustrates its use on examples that have not been previously considered in the literature. A small-scale simulation study highlights the advantage of using score and profile likelihood intervals rather than Wald intervals.

Effects of Reservoir Operations on Hatchery Coastal Rainbow Trout in Lake Roosevelt, Washington

AbstractIt is suspected that reservoir operations limit the mitigation fishery for coastal rainbow trout Oncorhynchus mykiss irideus in Lake Roosevelt, Washington. Entrainment through Grand Coulee Dam has been suggested as the primary impact of reservoir operations. However, the causal mechanisms and effects of entrainment have been difficult to quantify. A logistic regression model was used to examine the effect of reservoir operations on the coastal rainbow trout tag return probability. Eight independent variables were studied: release location, presence–absence of a tag reward, minimum reservoir elevation (m above mean sea level (msl)) during a sample year, reservoir elevation on the fish release date, mean daily water retention time (d) 2 weeks postrelease, mean daily retention time 4 weeks postrelease, mean annual water retention time, and water year type (associated with shallow, average, or deep drawdown events). Models were selected on the basis of likelihood ratio tests, odds ratio confidence intervals (CIs), and predictive ability. Analyses indicated that the significant independent variables were release location, water year, release elevation, and mean water retention time at 4 weeks postrelease. Angler return of tagged fish was 1.86 times more likely after a shallow drawdown event than after a deep drawdown event (95% profile likelihood CI = 1.15–3.03). The effect of mean water retention time was dependent on reservoir elevation at the time of release. When release elevation was low (366–381 m above msl), increasing mean water retention time increased the probability of tag return. However, when release elevation was high (381–393 m above msl), increasing mean water retention time did not increase the probability of tag return. The logistic regression model can be used by fisheries managers to predict the impacts of hydropower operations on the coastal rainbow trout fishery in Lake Roosevelt, thereby allowing for annual adjustments to release strategies that would maximize harvest potential.

Estimation of abundance and dispersal distance of the sugarcane click beetle Melanotus sakishimensis Ohira (Coleoptera: Elateridae) on Kurima Island, Okinawa, by mark-recapture experiments

The absolute population density and natural mean dispersal distance of the sugarcane click beetle Melanotus sakishimensis Ohira (Coleoptera: Elateridae) were estimated by using mark-recapture experiments in an agricultural area (180 ha) on Kurima Island, Miyakojima, Okinawa in mid-February, from 2002 to 2006. Funnel-vane traps with synthetic sex pheromone were uniformly placed along field roads at 100 points to capture adult males. Estimates of population densities of males that were obtained by the Jolly-Seber and Yamamura methods from 2002 to 2006 were 33,761, 29,727, 14,960, 11,360 and 8,634, respectively. The Yamamura method was adopted in 2004 and 2005 when the survival rates estimated by Jolly-Seber method became larger than 1. The estimate of lifetime natural mean dispersal distance (±SE) that was calculated by eliminating the influence of artificial trap removal was 193.8±11.0 m. The estimate of the male removal rate (and the 95% profile likelihood confidence interval) was 0.131 (0.117–0.147), indicating that the amount of male removal was not sufficient for the population control in this experiment.

Confidence intervals for parameters of two diagnostic tests in the absence of a gold standard

We derive a profile-likelihood confidence interval and a score based confidence interval to estimate the population prevalences, test sensitivities, and test specificities of two conditionally independent diagnostic tests when no gold standard is available. We are motivated by a real-data example on the study of the properties for two fallible diagnostic tests for bovine immunodeficiency virus. We compare the coverage and average width of two new intervals with an interval based on the asymptotic normality of the maximum likelihood estimator and a Bayesian interval estimator via Monte Carlo simulation. We determine that for the parameter configurations considered here, the profile-likelihood, score, and Bayesian intervals all perform adequately in terms of coverage, but overall, the profile-likelihood interval performs best in terms of yielding at least nominal coverage with minimum expected width.