A pseudo-likelihood method for estimating misclassification probabilities in competing-risks settings when true-event data are partially observed

Outcome misclassification occurs frequently in binary-outcome studies and can result in biased estimation of quantities such as the incidence, prevalence, cause-specific hazards, cumulative incidence functions, and so forth. A number of remedies have been proposed to address the potential misclassification of the outcomes in such data. The majority of these remedies lie in the estimation of misclassification probabilities, which are in turn used to adjust analyses for outcome misclassification. A number of authors advocate using a gold-standard procedure on a sample internal to the study to learn about the extent of the misclassification. With this type of internal validation, the problem of quantifying the misclassification also becomes a missing data problem as, by design, the true outcomes are only ascertained on a subset of the entire study sample. Although, the process of estimating misclassification probabilities appears simple conceptually, the estimation methods proposed so far have several methodological and practical shortcomings. Most methods rely on missing outcome data to be missing completely at random (MCAR), a rather stringent assumption which is unlikely to hold in practice. Some of the existing methods also tend to be computationally-intensive. To address these issues, we propose a computationally-efficient, easy-to-implement, pseudo-likelihood estimator of the misclassification probabilities under a missing at random (MAR) assumption, in studies with an available internal-validation sample. We present the estimator through the lens of studies with competing-risks outcomes, though the estimator extends beyond this setting. We describe the consistency and asymptotic distributional properties of the resulting estimator, and derive a closed-form estimator of its variance. The finite-sample performance of this estimator is evaluated via simulations. Using data from a real-world study with competing-risks outcomes, we illustrate how the proposed method can be used to estimate misclassification probabilities. We also show how the estimated misclassification probabilities can be used in an external study to adjust for possible misclassification bias when modeling cumulative incidence functions.     

Quantitative assessment of adverse events in clinical trials: Comparison of methods at an interim and the final analysis

In clinical study reports (CSRs), adverse events (AEs) are commonly summarized using the incidence proportion (IP). IPs can be calculated for all types of AEs and are often interpreted as the probability that a treated patient experiences specific AEs. Exposure time can be taken into account with time-to-event methods. Using one minus Kaplan–Meier (1-KM) is known to overestimate the AE probability in the presence of competing events (CEs). The use of a nonparametric estimator of the cumulative incidence function (CIF) has therefore been advocated as more appropriate. In this paper, we compare different methods to estimate the probability of one selected AE. In particular, we investigate whether the proposed methods provide a reasonable estimate of the AE probability at an interim analysis (IA). The characteristics of the methods in the presence of a CE are illustrated using data from a breast cancer study and we quantify the potential bias in a simulation study. At the final analysis performed for the CSR, 1-KM systematically overestimates and in most cases IP slightly underestimates the given AE probability. CIF has the lowest bias in most simulation scenarios. All methods might lead to biased estimates at the IA except for AEs with early onset. The magnitude of the bias varies with the time-to-AE and/or CE occurrence, the selection of event-specific hazards and the amount of censoring. In general, reporting AE probabilities for prespecified fixed time points is recommended.     

Effects of exposure misclassification on regression analyses of epidemiologic follow-up study data

In epidemiologic studies, subjects are often misclassified as to their level of exposure. Ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests. For situations in which there is misclassification of exposure in a follow-up study with categorical data, we have developed a model that permits consideration of any number of exposure categories and any number of multiple-category covariates. When used with logistic and Poisson regression procedures, this model helps assess the potential for bias when misclassification is ignored. When reliable ancillary information is available, the model can be used to correct for misclassification bias in the estimates produced by these regression procedures.     

Analyzing self‐controlled case series data when case confirmation rates are estimated from an internal validation sample

Vaccine safety studies are often electronic health record (EHR)‐based observational studies. These studies often face significant methodological challenges, including confounding and misclassification of adverse event. Vaccine safety researchers use self‐controlled case series (SCCS) study design to handle confounding effect and employ medical chart review to ascertain cases that are identified using EHR data. However, for common adverse events, limited resources often make it impossible to adjudicate all adverse events observed in electronic data. In this paper, we considered four approaches for analyzing SCCS data with confirmation rates estimated from an internal validation sample: (1) observed cases, (2) confirmed cases only, (3) known confirmation rate, and (4) multiple imputation (MI). We conducted a simulation study to evaluate these four approaches using type I error rates, percent bias, and empirical power. Our simulation results suggest that when misclassification of adverse events is present, approaches such as observed cases, confirmed case only, and known confirmation rate may inflate the type I error, yield biased point estimates, and affect statistical power. The multiple imputation approach considers the uncertainty of estimated confirmation rates from an internal validation sample, yields a proper type I error rate, largely unbiased point estimate, proper variance estimate, and statistical power.     

The impact of under and over-recording of cancer on death certificates in a competing risks analysis: A simulation study

Background: With linked register and cause of death data becoming more accessible than ever, competing risks methodology is being increasingly used as a way of obtaining “real world” probabilities of death broken down by specific causes. It is important, in terms of the validity of these studies, to have accurate cause of death information. However, it is well documented that cause of death information taken from death certificates is often lacking in accuracy and completeness. Methods: We assess through use of a simulation study the effect of under and over-recording of cancer on death certificates in a competing risks analysis consisting of three competing causes of death: cancer, heart disease and other causes. Using realistic levels of misclassification, we consider 24 scenarios and examine the bias in the cause-specific hazard ratios and the cumulative incidence function. Results: The bias in the cumulative incidence function was highest in the oldest age group reaching values as high as 2.6 percentage units for the “good” cancer prognosis scenario and 9.7 percentage units for the “poor” prognosis scenario. Conclusion: The bias resulting from the chosen levels of misclassification in this study accentuate concerns that unreliable cause of death information may be providing misleading results. The results of this simulation study convey an important message to applied epidemiological researchers.     

Comparing the effects of continuous and discrete covariate mismeasurement,with emphasis on the dichotomization of mismeasured predictors

It is well known that imprecision in the measurement of predictor variables typically leads to bias in estimated regression coefficients. We compare the bias induced by measurement error in a continuous predictor with that induced by misclassification of a binary predictor in the contexts of linear and logistic regression. To make the comparison fair, we consider misclassification probabilities for a binary predictor that correspond to dichotomizing an imprecise continuous predictor in lieu of its precise counterpart. On this basis, nondifferential binary misclassification is seen to yield more bias than nondifferential continuous measurement error. However, it is known that differential misclassification results if a binary predictor is actually formed by dichotomizing a continuous predictor subject to nondifferential measurement error. When the postulated model linking the response and precise continuous predictor is correct, this differential misclassification is found to yield less bias than continuous measurement error, in contrast with nondifferential misclassification, i.e., dichotomization reduces the bias due to mismeasurement. This finding, however, is sensitive to the form of the underlying relationship between the response and the continuous predictor. In particular, we give a scenario where dichotomization involves a trade-off between model fit and misclassification bias. We also examine how the bias depends on the choice of threshold in the dichotomization process and on the correlation between the imprecise predictor and a second precise predictor.     

Quantifying the Potential Bias when Directly Comparing Standardised Mortality Ratios for In-Unit Neonatal Mortality

Introduction

The Standardised Mortality Ratio (SMR) is increasingly used to compare the performance of different healthcare providers. However, it has long been known that differences in the populations of the providers can cause biased results when directly comparing two SMRs. This is potentially a particular problem in neonatal medicine where units provide different levels of care.

Methods

Using data from The Neonatal Survey (TNS), babies born at 24 to 31 weeks gestational age from 2002 to 2011 and admitted to one of 11 UK neonatal units were identified. Risk-adjusted SMRs were calculated for each unit using a previously published model to estimate the expected number of deaths. The model parameters were then re-estimated based on data from each individual neonatal unit (“reference” unit) and these then applied to each of the other units to estimate the number of deaths each unit would have observed if they had the same underlying mortality rates as each of the “reference” hospitals. The ratios of the SMRs were then calculated under the assumption of identical risk-specific probabilities of death.

Results

7243 babies were included in all analyses. When comparing between Network Neonatal Units (Level 3) the ratio of SMRs ranged from 0.92 to 1.00 and for the comparisons within Local Neonatal Units (Level 2) ranged from 0.79 to 1.56. However when comparing between neonatal units providing different levels of care ratios up to 1.68 were observed.

Conclusions

If the populations of healthcare providers differ considerably then it is likely that bias will be an issue when directly comparing SMRs. In neonatal care, the comparison of Network Neonatal Units is likely to be useful but caution is required when comparing Local Neonatal Units or between units of different types. Tools to quantify the likely bias are required.     

Adjusting survival estimates for premature transmitter failure: a case study from the Sacramento-San Joaquin Delta

In telemetry studies, premature tag failure causes negative bias in fish survival estimates because tag failure is interpreted as fish mortality. We used mark-recapture modeling to adjust estimates of fish survival for a previous study where premature tag failure was documented. High rates of tag failure occurred during the Vernalis Adaptive Management Plan’s (VAMP) 2008 study to estimate survival of fall-run Chinook salmon (Oncorhynchus tshawytscha) during migration through the San Joaquin River and Sacramento-San Joaquin Delta, California. Due to a high rate of tag failure, the observed travel time distribution was likely negatively biased, resulting in an underestimate of tag survival probability in this study. Consequently, the bias-adjustment method resulted in only a small increase in estimated fish survival when the observed travel time distribution was used to estimate the probability of tag survival. Since the bias-adjustment failed to remove bias, we used historical travel time data and conducted a sensitivity analysis to examine how fish survival might have varied across a range of tag survival probabilities. Our analysis suggested that fish survival estimates were low (95% confidence bounds range from 0.052 to 0.227) over a wide range of plausible tag survival probabilities (0.48–1.00), and this finding is consistent with other studies in this system. When tags fail at a high rate, available methods to adjust for the bias may perform poorly. Our example highlights the importance of evaluating the tag life assumption during survival studies, and presents a simple framework for evaluating adjusted survival estimates when auxiliary travel time data are available.     

Case–Control Analysis with Partial Knowledge of Exposure Misclassification Probabilities

Consider case control analysis with a dichotomous exposure variable that is subject to misclassification. If the classification probabilities are known, then methods are available to adjust odds-ratio estimates in light of the misclassification. We study the realistic scenario where reasonable guesses, but not exact values, are available for the classification probabilities. If the analysis proceeds by simply treating the guesses as exact, then even small discrepancies between the guesses and the actual probabilities can seriously degrade odds-ratio estimates. We show that this problem is mitigated by a Bayes analysis that incorporates uncertainty about the classification probabilities as prior information.     

Estimating dengue transmission intensity from serological data: A comparative analysis using mixture and catalytic models

BackgroundDengue virus (DENV) infection is a global health concern of increasing magnitude. To target intervention strategies, accurate estimates of the force of infection (FOI) are necessary. Catalytic models have been widely used to estimate DENV FOI and rely on a binary classification of serostatus as seropositive or seronegative, according to pre-defined antibody thresholds. Previous work has demonstrated the use of thresholds can cause serostatus misclassification and biased estimates. In contrast, mixture models do not rely on thresholds and use the full distribution of antibody titres. To date, there has been limited application of mixture models to estimate DENV FOI.MethodsWe compare the application of mixture models and time-constant and time-varying catalytic models to simulated data and to serological data collected in Vietnam from 2004 to 2009 (N ≥ 2178) and Indonesia in 2014 (N = 3194).ResultsThe simulation study showed larger mean FOI estimate bias from the time-constant and time-varying catalytic models (-0.007 (95% Confidence Interval (CI): -0.069, 0.029) and -0.006 (95% CI -0.095, 0.043)) than from the mixture model (0.001 (95% CI -0.036, 0.065)). Coverage of the true FOI was > 95% for estimates from both the time-varying catalytic and mixture model, however the latter had reduced uncertainty. When applied to real data from Vietnam, the mixture model frequently produced higher FOI and seroprevalence estimates than the catalytic models.ConclusionsOur results suggest mixture models represent valid, potentially less biased, alternatives to catalytic models, which could be particularly useful when estimating FOI from data with largely overlapping antibody titre distributions.     

Regressive models for risk prediction of repeated multinomial outcomes: An illustration using Health and Retirement Study data

Life expectancy is increasing in many countries and this may lead to a higher frequency of adverse health outcomes. Therefore, there is a growing demand for predicting the risk of a sequence of events based on specified factors from repeated outcomes. We proposed regressive models and a framework to predict the joint probabilities of a sequence of events for multinomial outcomes from longitudinal studies. The Markov chain is used to link marginal and sequence of conditional probabilities to predict the joint probability. Marginal and sequence of conditional probabilities are estimated using marginal and regressive models. An application is shown using the Health and Retirement Study data. The bias of parameter estimates for all models from all bootstrap simulation is less than 1% in most of the cases. The estimated mean squared error is also very low. Results from the simulation study show negligible bias and the usefulness of the proposed model. The proposed model and framework would be useful to solve real-life problems from various fields and big data analysis.     

Estimating the cumulative incidence of SARS-CoV-2 with imperfect serological tests: Exploiting cutoff-free approaches

Large-scale serological testing in the population is essential to determine the true extent of the current SARS-CoV-2 pandemic. Serological tests measure antibody responses against pathogens and use predefined cutoff levels that dichotomize the quantitative test measures into sero-positives and negatives and use this as a proxy for past infection. With the imperfect assays that are currently available to test for past SARS-CoV-2 infection, the fraction of seropositive individuals in serosurveys is a biased estimator of the cumulative incidence and is usually corrected to account for the sensitivity and specificity. Here we use an inference method—referred to as mixture-model approach—for the estimation of the cumulative incidence that does not require to define cutoffs by integrating the quantitative test measures directly into the statistical inference procedure. We confirm that the mixture model outperforms the methods based on cutoffs, leading to less bias and error in estimates of the cumulative incidence. We illustrate how the mixture model can be used to optimize the design of serosurveys with imperfect serological tests. We also provide guidance on the number of control and case sera that are required to quantify the test’s ambiguity sufficiently to enable the reliable estimation of the cumulative incidence. Lastly, we show how this approach can be used to estimate the cumulative incidence of classes of infections with an unknown distribution of quantitative test measures. This is a very promising application of the mixture-model approach that could identify the elusive fraction of asymptomatic SARS-CoV-2 infections. An R-package implementing the inference methods used in this paper is provided. Our study advocates using serological tests without cutoffs, especially if they are used to determine parameters characterizing populations rather than individuals. This approach circumvents some of the shortcomings of cutoff-based methods at exactly the low cumulative incidence levels and test accuracies that we are currently facing in SARS-CoV-2 serosurveys.     

Cycling Empirical Antibiotic Therapy in Hospitals: Meta-Analysis and Models

The rise of resistance together with the shortage of new broad-spectrum antibiotics underlines the urgency of optimizing the use of available drugs to minimize disease burden. Theoretical studies suggest that coordinating empirical usage of antibiotics in a hospital ward can contain the spread of resistance. However, theoretical and clinical studies came to different conclusions regarding the usefulness of rotating first-line therapy (cycling). Here, we performed a quantitative pathogen-specific meta-analysis of clinical studies comparing cycling to standard practice. We searched PubMed and Google Scholar and identified 46 clinical studies addressing the effect of cycling on nosocomial infections, of which 11 met our selection criteria. We employed a method for multivariate meta-analysis using incidence rates as endpoints and find that cycling reduced the incidence rate/1000 patient days of both total infections by 4.95 [9.43–0.48] and resistant infections by 7.2 [14.00–0.44]. This positive effect was observed in most pathogens despite a large variance between individual species. Our findings remain robust in uni- and multivariate metaregressions. We used theoretical models that reflect various infections and hospital settings to compare cycling to random assignment to different drugs (mixing). We make the realistic assumption that therapy is changed when first line treatment is ineffective, which we call “adjustable cycling/mixing”. In concordance with earlier theoretical studies, we find that in strict regimens, cycling is detrimental. However, in adjustable regimens single resistance is suppressed and cycling is successful in most settings. Both a meta-regression and our theoretical model indicate that “adjustable cycling” is especially useful to suppress emergence of multiple resistance. While our model predicts that cycling periods of one month perform well, we expect that too long cycling periods are detrimental. Our results suggest that “adjustable cycling” suppresses multiple resistance and warrants further investigations that allow comparing various diseases and hospital settings.     

Estimating Effective Population Size from Linkage Disequilibrium between Unlinked Loci: Theory and Application to Fruit Fly Outbreak Populations

There is a substantial literature on the use of linkage disequilibrium (LD) to estimate effective population size using unlinked loci. The estimates are extremely sensitive to the sampling process, and there is currently no theory to cope with the possible biases. We derive formulae for the analysis of idealised populations mating at random with multi-allelic (microsatellite) loci. The ‘Burrows composite index’ is introduced in a novel way with a ‘composite haplotype table’. We show that in a sample of diploid size , the mean value of or from the composite haplotype table is biased by a factor of , rather than the usual factor for a conventional haplotype table. But analysis of population data using these formulae leads to estimates that are unrealistically low. We provide theory and simulation to show that this bias towards low estimates is due to null alleles, and introduce a randomised permutation correction to compensate for the bias. We also consider the effect of introducing a within-locus disequilibrium factor to , and find that this factor leads to a bias in the estimate. However this bias can be overcome using the same randomised permutation correction, to yield an altered with lower variance than the original , and one that is also insensitive to null alleles. The resulting formulae are used to provide estimates on 40 samples of the Queensland fruit fly, Bactrocera tryoni, from populations with widely divergent expectations. Linkage relationships are known for most of the microsatellite loci in this species. We find that there is little difference in the estimated values from using known unlinked loci as compared to using all loci, which is important for conservation studies where linkage relationships are unknown.     

Safety of Onartuzumab in Patients with Solid Tumors: Experience to Date from the Onartuzumab Clinical Trial Program

Background

Onartuzumab, a recombinant humanized monovalent monoclonal antibody directed against MET, the receptor for the hepatocyte growth factor, has been investigated for the treatment of solid tumors. This publication describes the safety profile of onartuzumab in patients with solid tumors using data from the global onartuzumab clinical development program.

Methods

Adverse event (AE) and laboratory data from onartuzumab phase II/III studies were analyzed and coded into standardized terms according to industry standards. The severity of AEs was assessed using the NCI Common Toxicity Criteria, Version 4. Medical Dictionary for Regulatory Activities (MedDRA) AEs were grouped using the standardized MedDRA queries (SMQs) “gastrointestinal (GI) perforation”, “embolic and thrombotic events, venous (VTE)”, and “embolic and thrombotic events, arterial (ATE)”, and the Adverse Event Group Term (AEGT) “edema.” The safety evaluable populations (patients who received at least one dose of study treatment) for each study were included in this analysis.

Results

A total of 773 onartuzumab-treated patients from seven studies (phase II, n = 6; phase III, n = 1) were included. Edema and VTEs were reported in onartuzumab-treated patients in all seven studies. Edema events in onartuzumab arms were generally grade 1–2 in severity, observed more frequently than in control arms and at incidences ranging from 25.4−65.7% for all grades and from 1.2−14.1% for grade 3. Hypoalbuminemia was also more frequent in onartuzumab arms and observed at frequencies between 77.8% and 98.3%. The highest frequencies of all grade and grade ≥3 VTE events were 30.3% and 17.2%, respectively in onartuzumab arms. The cumulative incidence of all grade ATE events ranged from 0−5.6% (grade ≥3, 0−5.1%) in onartuzumab arms. The frequency of GI perforation was below 10% in all studies; the highest estimates were observed in studies with onartuzumab plus bevacizumab for all grades (0−6.2%) and grade ≥3 (0−6.2%).

Conclusions

The frequencies of VTE, ATE, GI perforation, hypoalbuminemia, and edema in clinical studies were higher in patients receiving onartuzumab than in control arms; these are considered to be expected events in patients receiving onartuzumab.     

On confidence intervals for genotype relative risks and attributable risks from case parent trio designs for candidate-gene studies

Scherag et al. [Hum Hered 2002;54:210-217] recently proposed point estimates and asymptotic as well as exact confidence intervals for genotype relative risks (GRRs) and the attributable risk (AR) in case parent trio designs using single nucleotide polymorphism (SNP) data. The aim of this study was the investigation of coverage probabilities and bias in estimates if the marker locus is not identical to the disease locus. Using a variety of parameter constellations, including marker allele frequencies identical to and different from the SNP at the disease locus, we performed an analytical study to quantify the bias and a Monte-Carlo simulation study for quantifying both bias and coverage probabilities. No bias was observed if marker and trait locus coincided. Two parameters had a strong impact on coverage probabilities of confidence intervals and bias in point estimates if they did not coincide: the linkage disequilibrium (LD) parameter delta and the allele frequency at the marker SNP. If marker allele frequencies were different from the allele frequencies at the functional SNP, substantial biases occurred. Further, if delta between the marker and the disease locus was lower than the maximum possible delta, estimates were also biased. In general, biases were towards the null hypothesis for both GRRs and AR. If one GRR was not increased, as e.g. in a recessive genetic model, biases away from the null could be observed. If both GRRs were in identical directions and if both were substantially larger than 1, the bias always was towards the null. When applying point estimates and confidence intervals for GRRs and AR in candidate gene studies, great care is needed. Effect estimates are substantially biased towards the null if either the allele frequencies at the marker SNP and the true disease locus are different or if the LD between the marker SNP and the disease locus is not at its maximum. A bias away from the null occurs only in uncommon study situations; it is small and can therefore be ignored for applications.     

A finite mixture distribution model for data collected from twins.

Most analyses of data collected from a classical twin study of monozygotic (MZ) and dizygotic (DZ) twins assume that zygosity has been diagnosed without error. However, large scale surveys frequently resort to questionnaire-based methods of diagnosis which classify twins as MZ or DZ with less than perfect accuracy. This article describes a mixture distribution approach to the analysis of twin data when zygosity is not perfectly diagnosed. Estimates of diagnostic accuracy are used to weight the likelihood of the data according to the probability that any given pair is either MZ or DZ. The performance of this method is compared to fully accurate diagnosis, and to the analysis of samples that include some misclassified pairs. Conventional analysis of samples containing misclassified pairs yields biased estimates of variance components, such that additive genetic variance (A) is underestimated while common environment (C) and specific environment (E) components are overestimated. The bias is non-trivial; for 10% misclassification, true values of Additive genetic: Common environment: Specific Environment variance components of.6:.2:.2 are estimated as.48:.29:.23, respectively. The mixture distribution yields unbiased estimates, while showing relatively little loss of statistical precision for misclassification rates of 15% or less. The method is shown to perform quite well even when no information on zygosity is available, and may be applied when pair-specific estimates of zygosity probabilities are available.     

The Impact of Exposure Misclassification on Associations Between Prepregnancy BMI and Adverse Pregnancy Outcomes

Prepregnancy BMI is a widely used marker of maternal nutritional status that relies on maternal self‐report of prepregnancy weight and height. Pregravid BMI has been associated with adverse health outcomes for the mother and infant, but the impact of BMI misclassification on measures of effect has not been quantified. The authors applied published probabilistic bias analysis methods to quantify the impact of exposure misclassification bias on well‐established associations between self‐reported prepregnancy BMI category and five pregnancy outcomes (small for gestational age (SGA) and large for gestational age (LGA) birth, spontaneous preterm birth (sPTB), gestational diabetes mellitus (GDM), and preeclampsia) derived from a hospital‐based delivery database in Pittsburgh, PA (2003–2005; n = 18,362). The bias analysis method recreates the data that would have been observed had BMI been correctly classified, assuming given classification parameters. The point estimates derived from the bias analysis account for random error as well as systematic error caused by exposure misclassification bias and additional uncertainty contributed by classification errors. In conventional multivariable logistic regression models, underweight women were at increased risk of SGA and sPTB, and reduced risk of LGA, whereas overweight, obese, and severely obese women had elevated risks of LGA, GDM, and preeclampsia compared with normal‐weight women. After applying the probabilistic bias analysis method, adjusted point estimates were attenuated, indicating the conventional estimates were biased away from the null. However, the majority of relations remained readily apparent. This analysis suggests that in this population, associations between self‐reported prepregnancy BMI and pregnancy outcomes are slightly overestimated.     

The Independent Evolution Method Is Not a Viable Phylogenetic Comparative Method

Phylogenetic comparative methods (PCMs) use data on species traits and phylogenetic relationships to shed light on evolutionary questions. Recently, Smaers and Vinicius suggested a new PCM, Independent Evolution (IE), which purportedly employs a novel model of evolution based on Felsenstein’s Adaptive Peak Model. The authors found that IE improves upon previous PCMs by producing more accurate estimates of ancestral states, as well as separate estimates of evolutionary rates for each branch of a phylogenetic tree. Here, we document substantial theoretical and computational issues with IE. When data are simulated under a simple Brownian motion model of evolution, IE produces severely biased estimates of ancestral states and changes along individual branches. We show that these branch-specific changes are essentially ancestor-descendant or “directional” contrasts, and draw parallels between IE and previous PCMs such as “minimum evolution”. Additionally, while comparisons of branch-specific changes between variables have been interpreted as reflecting the relative strength of selection on those traits, we demonstrate through simulations that regressing IE estimated branch-specific changes against one another gives a biased estimate of the scaling relationship between these variables, and provides no advantages or insights beyond established PCMs such as phylogenetically independent contrasts. In light of our findings, we discuss the results of previous papers that employed IE. We conclude that Independent Evolution is not a viable PCM, and should not be used in comparative analyses.     

Standardizing the Protocol for Hemispherical Photographs: Accuracy Assessment of Binarization Algorithms

Hemispherical photography is a well-established method to optically assess ecological parameters related to plant canopies; e.g. ground-level light regimes and the distribution of foliage within the crown space. Interpreting hemispherical photographs involves classifying pixels as either sky or vegetation. A wide range of automatic thresholding or binarization algorithms exists to classify the photographs. The variety in methodology hampers ability to compare results across studies. To identify an optimal threshold selection method, this study assessed the accuracy of seven binarization methods implemented in software currently available for the processing of hemispherical photographs. Therefore, binarizations obtained by the algorithms were compared to reference data generated through a manual binarization of a stratified random selection of pixels. This approach was adopted from the accuracy assessment of map classifications known from remote sensing studies. Percentage correct () and kappa-statistics () were calculated. The accuracy of the algorithms was assessed for photographs taken with automatic exposure settings (auto-exposure) and photographs taken with settings which avoid overexposure (histogram-exposure). In addition, gap fraction values derived from hemispherical photographs were compared with estimates derived from the manually classified reference pixels. All tested algorithms were shown to be sensitive to overexposure. Three of the algorithms showed an accuracy which was high enough to be recommended for the processing of histogram-exposed hemispherical photographs: “Minimum” ( 98.8%; 0.952), “Edge Detection” ( 98.1%; 0.950), and “Minimum Histogram” ( 98.1%; 0.947). The Minimum algorithm overestimated gap fraction least of all (11%). The overestimation by the algorithms Edge Detection (63%) and Minimum Histogram (67%) were considerably larger. For the remaining four evaluated algorithms (IsoData, Maximum Entropy, MinError, and Otsu) an incompatibility with photographs containing overexposed pixels was detected. When applied to histogram-exposed photographs, these algorithms overestimated the gap fraction by at least 180%.