Epidemiology and SARIMA model of deaths in a tertiary comprehensive hospital in Hangzhou from 2015 to 2022.

BACKGROUND: By analysing the deaths of inpatients in a tertiary hospital in Hangzhou, this study aimed to understand the epidemiological distribution characteristics and the composition of the causes of death. Additionally, this study aimed to predict the changing trend in the number of deaths, providing valuable insights for hospitals to formulate relevant strategies and measures aimed at reducing mortality rates. METHODS: In this study, data on inpatient mortality at a tertiary hospital in Hangzhou from 2015 to 2022 were obtained via the population information registration system of the Chinese Center for Disease Control and Prevention. The death data of inpatients were described and analysed through a retrospective study. Excel 2016 was utilized for data sorting, and SPSS 22.0 software was employed for data analysis. The statistical inference of single factor differences was conducted via χ2 tests. The SARIMA model was established via the forecast, aTSA, and tseries software packages (version 4.3.0) to forecast future changes in the number of deaths. RESULTS: A total of 1938 inpatients died at the tertiary hospital in Hangzhou, with the greatest number of deaths occurring in 2022 (262, 13.52%). The sex ratio was 2.22:1, and there were significant differences between sexes in terms of age, marital status, educational level, and place of residence (P < 0.05). The percentage of males in the groups aged of 20 to 29 and 30 to 39 years was significantly greater than that of females (χ2 = 46.905, P < 0.001). More females than males died in the widowed group, and divorced and married males experienced a greater number of deaths than divorced and married females did (χ2 = 61.130, P < 0.001). The proportions of male students with a junior college and senior high school education were significantly greater than that of female students (χ2 = 12.310, P < 0.05). The primary causes of mortality within the hospital setting included circulatory system diseases, injury, poisoning, tumours, and respiratory system diseases. These leading factors accounted for 86.12% of all recorded deaths. Finally, the SARIMA (2, 1, 1) (1, 1, 1)12 model was determined to be the optimal model, with an AIC of 380.23, a BIC of 392.79, and an AICc of 381.81. The MAPE was 14.99%, indicating a satisfactory overall fit of this model. The relative error between the predicted and actual number of deaths in 2022 was 8.02%. Therefore, the SARIMA (2, 1, 1) (1, 1, 1)12 model demonstrates good predictive performance. CONCLUSIONS: Hospitals should enhance the management of sudden cardiac death, acute myocardial infarction, severe craniocerebral injury, lung cancer, and lung infection to reduce the mortality rate. The SARIMA model can be employed for predicting the number of deaths.

Early warning and predicting of COVID-19 using zero-inflated negative binomial regression model and negative binomial regression model.

BACKGROUND: It is difficult to detect the outbreak of emergency infectious disease based on the exiting surveillance system. Here we investigate the utility of the Baidu Search Index, an indicator of how large of a keyword is in Baidu's search volume, in the early warning and predicting the epidemic trend of COVID-19. METHODS: The daily number of cases and the Baidu Search Index of 8 keywords (weighted by population) from December 1, 2019 to March 15, 2020 were collected and analyzed with times series and Spearman correlation with different time lag. To predict the daily number of COVID-19 cases using the Baidu Search Index, Zero-inflated negative binomial regression was used in phase 1 and negative binomial regression model was used in phase 2 and phase 3 based on the characteristic of independent variable. RESULTS: The Baidu Search Index of all keywords in Wuhan was significantly higher than Hubei (excluded Wuhan) and China (excluded Hubei). Before the causative pathogen was identified, the search volume of "Influenza" and "Pneumonia" in Wuhan increased with the number of new onset cases, their correlation coefficient was 0.69 and 0.59, respectively. After the pathogen was public but before COVID-19 was classified as a notifiable disease, the search volume of "SARS", "Pneumonia", "Coronavirus" in all study areas increased with the number of new onset cases with the correlation coefficient was 0.69 ~ 0.89, while "Influenza" changed to negative correlated (rs: -0.56 ~ -0.64). After COVID-19 was closely monitored, the Baidu Search Index of "COVID-19", "Pneumonia", "Coronavirus", "SARS" and "Mask" could predict the epidemic trend with 15 days, 5 days and 6 days lead time, respectively in Wuhan, Hubei (excluded Wuhan) and China (excluded Hubei). The predicted number of cases would increase 1.84 and 4.81 folds, respectively than the actual number of cases in Wuhan and Hubei (excluded Wuhan) from 21 January to 9 February. CONCLUSION: The Baidu Search Index could be used in the early warning and predicting the epidemic trend of COVID-19, but the search keywords changed in different period. Considering the time lag from onset to diagnosis, especially in the areas with medical resources shortage, internet search data can be a highly effective supplement of the existing surveillance system.

Linking cognitive strategy, neural mechanism, and movement statistics in group foraging behaviors.

Foraging for food is a rich and ubiquitous animal behavior that involves complex cognitive decisions, and interactions between different individuals and species. There has been exciting recent progress in understanding multi-agent foraging behavior from cognitive, neuroscience, and statistical perspectives, but integrating these perspectives can be elusive. This paper seeks to unify these perspectives, allowing statistical analysis of observational animal movement data to shed light on the viability of cognitive models of foraging strategies. We start with cognitive agents with internal preferences expressed as value functions, and implement this in a biologically plausible neural network, and an equivalent statistical model, where statistical predictors of agents' movements correspond to the components of the value functions. We test this framework by simulating foraging agents and using Bayesian statistical modeling to correctly identify the factors that best predict the agents' behavior. As further validation, we use this framework to analyze an open-source locust foraging dataset. Finally, we collect new multi-agent real-world bird foraging data, and apply this method to analyze the preferences of different species. Together, this work provides an initial roadmap to integrate cognitive, neuroscience, and statistical approaches for reasoning about animal foraging in complex multi-agent environments.

A Bayesian latent-subgroup platform design for dose optimization.

The US Food and Drug Administration launched Project Optimus to reform the dose optimization and dose selection paradigm in oncology drug development, calling for the paradigm shift from finding the maximum tolerated dose to the identification of optimal biological dose (OBD). Motivated by a real-world drug development program, we propose a master-protocol-based platform trial design to simultaneously identify OBDs of a new drug, combined with standards of care or other novel agents, in multiple indications. We propose a Bayesian latent subgroup model to accommodate the treatment heterogeneity across indications, and employ Bayesian hierarchical models to borrow information within subgroups. At each interim analysis, we update the subgroup membership and dose-toxicity and -efficacy estimates, as well as the estimate of the utility for risk-benefit tradeoff, based on the observed data across treatment arms to inform the arm-specific decision of dose escalation and de-escalation and identify the OBD for each arm of a combination partner and an indication. The simulation study shows that the proposed design has desirable operating characteristics, providing a highly flexible and efficient way for dose optimization. The design has great potential to shorten the drug development timeline, save costs by reducing overlapping infrastructure, and speed up regulatory approval.

Binomial models uncover biological variation during feature selection of droplet-based single-cell RNA sequencing.

Effective analysis of single-cell RNA sequencing (scRNA-seq) data requires a rigorous distinction between technical noise and biological variation. In this work, we propose a simple feature selection model, termed "Differentially Distributed Genes" or DDGs, where a binomial sampling process for each mRNA species produces a null model of technical variation. Using scRNA-seq data where cell identities have been established a priori, we find that the DDG model of biological variation outperforms existing methods. We demonstrate that DDGs distinguish a validated set of real biologically varying genes, minimize neighborhood distortion, and enable accurate partitioning of cells into their established cell-type groups.

Development of a High-Resolution Indoor Radon Map Using a New Machine Learning-Based Probabilistic Model and German Radon Survey Data.

BACKGROUND: Radon is a carcinogenic, radioactive gas that can accumulate indoors and is undetected by human senses. Therefore, accurate knowledge of indoor radon concentration is crucial for assessing radon-related health effects or identifying radon-prone areas. OBJECTIVES: Indoor radon concentration at the national scale is usually estimated on the basis of extensive measurement campaigns. However, characteristics of the sampled households often differ from the characteristics of the target population owing to the large number of relevant factors that control the indoor radon concentration, such as the availability of geogenic radon or floor level. Furthermore, the sample size usually does not allow estimation with high spatial resolution. We propose a model-based approach that allows a more realistic estimation of indoor radon distribution with a higher spatial resolution than a purely data-based approach. METHODS: A multistage modeling approach was used by applying a quantile regression forest that uses environmental and building data as predictors to estimate the probability distribution function of indoor radon for each floor level of each residential building in Germany. Based on the estimated probability distribution function, a probabilistic Monte Carlo sampling technique was applied, enabling the combination and population weighting of floor-level predictions. In this way, the uncertainty of the individual predictions is effectively propagated into the estimate of variability at the aggregated level. RESULTS: The results show an approximate lognormal distribution of indoor radon in dwellings in Germany with an arithmetic mean of 63 Bq/m3, a geometric mean of 41 Bq/m3, and a 95th percentile of 180 Bq/m3. The exceedance probabilities for 100 and 300 Bq/m3 are 12.5% (10.5 million people affected) and 2.2% (1.9 million people affected), respectively. In large cities, individual indoor radon concentration is generally estimated to be lower than in rural areas, which is due to the different distribution of the population on floor levels. DISCUSSION: The advantages of our approach are that is yields a) an accurate estimation of indoor radon concentration even if the survey is not fully representative with respect to floor level and radon concentration in soil, and b) an estimate of the indoor radon distribution with a much higher spatial resolution than basic descriptive statistics. https://doi.org/10.1289/EHP14171.

Summary statistics knockoffs inference with family-wise error rate control.

Testing multiple hypotheses of conditional independence with provable error rate control is a fundamental problem with various applications. To infer conditional independence with family-wise error rate (FWER) control when only summary statistics of marginal dependence are accessible, we adopt GhostKnockoff to directly generate knockoff copies of summary statistics and propose a new filter to select features conditionally dependent on the response. In addition, we develop a computationally efficient algorithm to greatly reduce the computational cost of knockoff copies generation without sacrificing power and FWER control. Experiments on simulated data and a real dataset of Alzheimer's disease genetics demonstrate the advantage of the proposed method over existing alternatives in both statistical power and computational efficiency.

Unit information Dirichlet process prior.

Prior distributions, which represent one's belief in the distributions of unknown parameters before observing the data, impact Bayesian inference in a critical and fundamental way. With the ability to incorporate external information from expert opinions or historical datasets, the priors, if specified appropriately, can improve the statistical efficiency of Bayesian inference. In survival analysis, based on the concept of unit information (UI) under parametric models, we propose the unit information Dirichlet process (UIDP) as a new class of nonparametric priors for the underlying distribution of time-to-event data. By deriving the Fisher information in terms of the differential of the cumulative hazard function, the UIDP prior is formulated to match its prior UI with the weighted average of UI in historical datasets and thus can utilize both parametric and nonparametric information provided by historical datasets. With a Markov chain Monte Carlo algorithm, simulations and real data analysis demonstrate that the UIDP prior can adaptively borrow historical information and improve statistical efficiency in survival analysis.

Visibility graph-based covariance functions for scalable spatial analysis in non-convex partially Euclidean domains.

We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not guaranteed to be positive definite on such domains, while existing non-Euclidean approaches fail to respect the partially Euclidean nature of these domains where the geodesic distance agrees with the Euclidean distances for some pairs of points. Using a visibility graph on the domain, we propose a class of covariance functions that preserve Euclidean-based covariances between points that are connected in the domain while incorporating the non-convex geometry of the domain via conditional independence relationships. We show that the proposed method preserves the partially Euclidean nature of the intrinsic geometry on the domain while maintaining validity (positive definiteness) and marginal stationarity of the covariance function over the entire parameter space, properties which are not always fulfilled by existing approaches to construct covariance functions on non-convex domains. We provide useful approximations to improve computational efficiency, resulting in a scalable algorithm. We compare the performance of our method with those of competing state-of-the-art methods using simulation studies on synthetic non-convex domains. The method is applied to data regarding acidity levels in the Chesapeake Bay, showing its potential for ecological monitoring in real-world spatial applications on irregular domains.

Comprehensive Statistical Approach to Investigate the Risk Factors Affecting the Occurrences of Cellulitis Episodes among Patients with Lymphedema.

Background: Cellulitis is an infection of the skin and the tissues just under the skin. As any disease, cellulitis has various physiological and physical effects that deteriorate a patient's quality of life. Luckily, cellulitis can be treated when dealt with in a timely fashion. Nonetheless, some patients may experience more than one episode of cellulitis or a recurrence of cellulitis that was previously cured. In fact, the occurrences of cellulitis episodes are believed to follow a statistical distribution. The frequency distribution of cellulitis episodes is scrutinized herein. We aimed to investigate the risk factors that affect the number of cellulitis episodes and the pattern of association between cancer types and cellulitis episodes by using analytical and visual approaches.Methods: A statistical approach applying a two-part count regression model was used instead of the traditional one-part count model. Moreover, multiple correspondence analysis was used to support the finding of count regression models.Results: The results of analysis of the sample from the National Cheng Kung University hospital in Taiwan revealed the mean age of patients was 58.7 ± 14.31 years old. The two-part regression model is conceptually and numerically better than the one-part regression model when examining the risks factors that affect cellulitis episodes. Particularly, we found the significant factors based on the best model are cellulitis history ([Formula: see text]; P value < 0.001), clinical stage of cancer (3) ([Formula: see text]; P value < 0.001), no cancer ([Formula: see text]; P value < 0.05), cancer of female reproductive organs ([Formula: see text]; P value < 0.05), breast cancer ([Formula: see text]; P value < 0.05), and age ≥ 60 years ([Formula: see text]; P value < 0.05). Multiple correspondence analysis approach found cancer types (breast and female reproductive organ), age ≥ 60 years, and cellulitis history were more likely to link to excess zero cellulitis or one cellulitis episode.

Global forecasting of chronic kidney disease mortality rates and numbers with the generalized additive model.

BACKGROUND: Chronic kidney disease (CKD) is an important public health problem worldwide; therefore, forecasting CKD mortality rates and death numbers globally is vital for planning CKD prevention programs. This study aimed to characterize the temporal trends in CKD mortality at the international level from 1990 to 2019 and predict CKD mortality rates and numbers until 2030. METHODS: Data were obtained from the Global Burden of Disease 2019 Study. A joinpoint regression model was used to estimate the average annual percentage change in CKD mortality rates and numbers. Finally, we used a generalized additive model to predict CKD mortality through 2030. RESULTS: The number of CKD-related deaths worldwide increased from 591.80 thousand in 1990 to 1425.67 thousand in 2019. The CKD age-adjusted mortality rate increased from 15.95 per 100,000 people to 18.35 per 100,000 people during the same period. Between 2020 and 2030, the number of CKD deaths is forecasted to increase further to 1812.85 thousand by 2030. The CKD age-adjusted mortality rate is expected to decrease slightly to 17.76 per 100,000 people (95% credible interval (CrI): 13.84 to 21.68). Globally, it is predicted that in the next decade, the CKD mortality rate will decrease in men, women, all subgroups of disease etiology except glomerulonephritis, people younger than 40 years old, and all groupings of countries based on the sociodemographic index (SDI) except high-middle-SDI countries. CONCLUSIONS: The CKD mortality rate is predicted to decrease in the next decade. However, more attention should be given to people with glomerulonephritis, people over 40 years old, and people in high- to middle-income countries because the mortality rate due to CKD in these subgroups is expected to increase until 2030.

Prediction on the spatial distribution of the seropositive rate of schistosomiasis in Hunan Province, China: a machine learning model integrated with the Kriging method.

Schistosomiasis remains a formidable challenge to global public health. This study aims to predict the spatial distribution of schistosomiasis seropositive rates in Hunan Province, pinpointing high-risk transmission areas and advocating for tailored control measures in low-endemic regions. Six machine learning models and their corresponding hybrid machine learning-Kriging models were employed to predict the seropositive rate. The optimal model was selected through internal and external validations to simulate the spatial distribution of seropositive rates. Our results showed that the hybrid machine learning-Kriging model demonstrated superior predictive performance compared to basic machine learning model and the Cubist-Kriging model emerged as the most optimal model for this study. The predictive map revealed elevated seropositive rates around Dongting Lake and its waterways with significant clustering, notably in the central and northern regions of Yiyang City and the northeastern areas of Changde City. The model identified gross domestic product, annual average wind speed and the nearest distance from the river as the top three predictors of seropositive rates, with annual average daytime surface temperature contributing the least. In conclusion, our research has revealed that integrating the Kriging method significantly enhances the predictive performance of machine learning models. We developed a Cubist-Kriging model with high predictive performance to forecast the spatial distribution of schistosomiasis seropositive rates. These findings provide valuable guidance for the precise prevention and control of schistosomiasis.

Designing cancer screening trials for reduction in late-stage cancer incidence.

Before implementing a biomarker test for early cancer detection into routine clinical care, the test must demonstrate clinical utility, that is, the test results should lead to clinical actions that positively affect patient-relevant outcomes. Unlike therapeutical trials for patients diagnosed with cancer, designing a randomized controlled trial (RCT) to demonstrate the clinical utility of an early detection biomarker with mortality and related endpoints poses unique challenges. The hurdles stem from the prolonged natural progression of the disease and the lack of information regarding the time-varying screening effect on the target asymptomatic population. To facilitate the study design of screening trials, we propose using a generic multistate disease history model and derive model-based effect sizes. The model links key performance metrics of the test, such as sensitivity, to primary endpoints like the incidence of late-stage cancer. It also incorporates the practical implementation of the biomarker-testing program in real-world scenarios. Based on the chronological time scale aligned with RCT, our method allows the assessment of study powers based on key features of the new program, including the test sensitivity, the length of follow-up, and the number and frequency of repeated tests. The calculation tool from the proposed method will enable practitioners to perform realistic and quick evaluations when strategizing screening trials for specific diseases. We use numerical examples based on the National Lung Screening Trial to demonstrate the method.

Nonparametric worst-case bounds for publication bias on the summary receiver operating characteristic curve.

The summary receiver operating characteristic (SROC) curve has been recommended as one important meta-analytical summary to represent the accuracy of a diagnostic test in the presence of heterogeneous cutoff values. However, selective publication of diagnostic studies for meta-analysis can induce publication bias (PB) on the estimate of the SROC curve. Several sensitivity analysis methods have been developed to quantify PB on the SROC curve, and all these methods utilize parametric selection functions to model the selective publication mechanism. The main contribution of this article is to propose a new sensitivity analysis approach that derives the worst-case bounds for the SROC curve by adopting nonparametric selection functions under minimal assumptions. The estimation procedures of the worst-case bounds use the Monte Carlo method to approximate the bias on the SROC curves along with the corresponding area under the curves, and then the maximum and minimum values of PB under a range of marginal selection probabilities are optimized by nonlinear programming. We apply the proposed method to real-world meta-analyses to show that the worst-case bounds of the SROC curves can provide useful insights for discussing the robustness of meta-analytical findings on diagnostic test accuracy.

Exploring mixture estimators in stratified random sampling.

Advancements in sensor technology have brought a revolution in data generation. Therefore, the study variable and several linearly related auxiliary variables are recorded due to cost-effectiveness and ease of recording. These auxiliary variables are commonly observed as quantitative and qualitative (attributes) variables and are jointly used to estimate the study variable's population mean using a mixture estimator. For this purpose, this work proposes a family of generalized mixture estimators under stratified sampling to increase efficiency under symmetrical and asymmetrical distributions and study the estimator's behavior for different sample sizes for its convergence to the Normal distribution. It is found that the proposed estimator estimates the population mean of the study variable with more precision than the competitor estimators under Normal, Uniform, Weibull, and Gamma distributions. It is also revealed that the proposed estimator follows the Cauchy distribution when the sample size is less than 35; otherwise, it converges to normality. Furthermore, the implementation of two real-life datasets related to the health and finance sectors is also presented to support the proposed estimator's significance.

Periodically correlated time series and the Variable Bandpass Periodic Block Bootstrap.

This research introduces a novel approach to resampling periodically correlated time series using bandpass filters for frequency separation called the Variable Bandpass Periodic Block Bootstrap and then examines the significant advantages of this new method. While bootstrapping allows estimation of a statistic's sampling distribution by resampling the original data with replacement, and block bootstrapping is a model-free resampling strategy for correlated time series data, both fail to preserve correlations in periodically correlated time series. Existing extensions of the block bootstrap help preserve the correlation structures of periodically correlated processes but suffer from flaws and inefficiencies. Analyses of time series data containing cyclic, seasonal, or periodically correlated principal components often seen in annual, daily, or other cyclostationary processes benefit from separating these components. The Variable Bandpass Periodic Block Bootstrap uses bandpass filters to separate a periodically correlated component from interference such as noise at other uncorrelated frequencies. A simulation study is presented, demonstrating near universal improvements obtained from the Variable Bandpass Periodic Block Bootstrap when compared with prior block bootstrapping methods for periodically correlated time series.

Prevalence estimates for COVID-19-related health behaviors based on the cheating detection triangular model.

BACKGROUND: Survey studies in medical and health sciences predominantly apply a conventional direct questioning (DQ) format to gather private and highly personal information. If the topic under investigation is sensitive or even stigmatizing, such as COVID-19-related health behaviors and adherence to non-pharmaceutical interventions in general, DQ surveys can lead to nonresponse and untruthful answers due to the influence of social desirability bias (SDB). These effects seriously threaten the validity of the results obtained, potentially leading to distorted prevalence estimates for behaviors for which the prevalence in the population is unknown. While this issue cannot be completely avoided, indirect questioning techniques (IQTs) offer a means to mitigate the harmful influence of SDB by guaranteeing the confidentiality of individual responses. The present study aims at assessing the validity of a recently proposed IQT, the Cheating Detection Triangular Model (CDTRM), in estimating the prevalence of COVID-19-related health behaviors while accounting for cheaters who disregard the instructions. METHODS: In an online survey of 1,714 participants in Taiwan, we obtained CDTRM prevalence estimates via an Expectation-Maximization algorithm for three COVID-19-related health behaviors with different levels of sensitivity. The CDTRM estimates were compared to DQ estimates and to available official statistics provided by the Taiwan Centers for Disease Control. Additionally, the CDTRM allowed us to estimate the share of cheaters who disregarded the instructions and adjust the prevalence estimates for the COVID-19-related health behaviors accordingly. RESULTS: For a behavior with low sensitivity, CDTRM and DQ estimates were expectedly comparable and in line with official statistics. However, for behaviors with medium and high sensitivity, CDTRM estimates were higher and thus presumably more valid than DQ estimates. Analogously, the estimated cheating rate increased with higher sensitivity of the behavior under study. CONCLUSIONS: Our findings strongly support the assumption that the CDTRM successfully controlled for the validity-threatening influence of SDB in a survey on three COVID-19-related health behaviors. Consequently, the CDTRM appears to be a promising technique to increase estimation validity compared to conventional DQ for health-related behaviors, and sensitive attributes in general, for which a strong influence of SDB is to be expected.

Investigating the Heterogeneity of "Study Twins".

Meta-analyses are commonly performed based on random-effects models, while in certain cases one might also argue in favor of a common-effect model. One such case may be given by the example of two "study twins" that are performed according to a common (or at least very similar) protocol. Here we investigate the particular case of meta-analysis of a pair of studies, for example, summarizing the results of two confirmatory clinical trials in phase III of a clinical development program. Thereby, we focus on the question of to what extent homogeneity or heterogeneity may be discernible and include an empirical investigation of published ("twin") pairs of studies. A pair of estimates from two studies only provide very little evidence of homogeneity or heterogeneity of effects, and ad hoc decision criteria may often be misleading.

Modelling wound area in studies of wound healing interventions.

BACKGROUND: Experimental studies of wound healing often use survival analysis and time to event outcomes or differences in wound area at a specific time point. However, these methods do not use a potentially large number of observations made over the course of a trial and may be inefficient. A model-based approach can leverage all trial data, but there is little guidance on appropriate models and functional forms to describe wound healing. METHODS: We derive a general statistical model and review a wide range of plausible mathematical models to describe wound healing. We identify a range of possible derived estimands and their derivation from the models. Using data from a trial of an intervention to promote ulcer healing in patients affected by leprosy that included three measurement methods repeated across the course of the study, we compare the goodness-of-fit of the models using a range of methods and estimate treatment effects and healing rate functions with the best-fitting models. RESULTS: Overall, we included 5,581 ulcer measurements of 1,578 unique images from 130 patients. We examined the performance of a range of models. The square root, log square root, and log quadratic models were the best fitting models across all outcome measurement methods. The estimated treatment effects magnitude and sign varied by time post-randomisation, model type, and outcome type, but across all models there was little evidence of effectiveness. The estimated effects were significantly more precise than non-parametric alternatives. For example, estimated differences from the three outcome measurements at 42-days post-randomisation were - 0.01 cm2 (-0.77, 0.74), -0.44 cm2 (-1.64, 0.76), and 0.11 cm2 (-0.87, 1.08) using a non-parametric method versus - 0.03 cm2 (-0.14, 0.06), 0.06 cm2 (-0.05, 0.17), and 0.03 cm2 (-0.07, 0.17) using a square-root model. CONCLUSIONS: Model-based analyses can dramatically improve the precision of estimates but care must be taken to carefully compare and select the best fitting models. The (log) square-root model is strongly recommended reflecting advice from a century ago.