Trends and projection in the proportion of (heavy) cannabis use in Germany from 1995 to 2021

AIMS

To measure the current trends of cannabis use in Germany, measure trends in the proportion of heavy cannabis users and estimate future cannabis use rates.

DESIGN

Repeated waves of the Epidemiological Survey on Substance Abuse, a cross-sectional survey conducted between 1995 and 2021 with a two-stage participant selection strategy where respondents completed a survey on substance use delivered through the post, over the telephone or on-line.

SETTING

Germany.

PARTICIPANTS/CASES

German-speaking participants aged between 18 and 59 years living in Germany who self-reported on their cannabis use in the past 12 months (n = 78 678). With the application of a weighting scheme, the data are nationally representative.

MEASUREMENTS

Questions on the frequency of cannabis use in the past 12 months and self-reported changes in frequency of use due to the COVID-19 pandemic.

FINDINGS

The prevalence of past 12-month cannabis users increased from 4.4% [95% confidence interval (CI) = 3.7, 5.1] in 1995 to 10.0% (95% CI = 8.9, 11.3) in 2021. Modeling these trends revealed a significant increase that accelerated over the past decade. The proportion of heavy cannabis users [cannabis use (almost) daily or at least 200 times per year] among past-year users has remained steady from 1995 (11.4%, 95% CI = 7.7, 16.5) to 2018 (9.5%, 95% CI = 7.6, 11.9), but significantly increased to 15.7% (95% CI = 13.1, 18.8) in 2021 during the COVID-19 pandemic. Extrapolating from these models, the prevalence of 12-month cannabis users in 2024 is expected to range between 10.4 and 15.0%, while the proportion of heavy cannabis users is unclear.

CONCLUSIONS

Trends from 1995 to 2021 suggest that the prevalence of past 12-month cannabis users in Germany will continue to increase, with expected rates between 10.4 and 15.0% for the German-speaking adult population, and that at least one in 10 cannabis users will continue to use cannabis heavily (almost daily or 200 + times in the past year).

Robust algorithm for the detection and classification of QRS complexes with different morphologies using the continuous spline wavelet transform with automatic scale detection

This work presents an algorithm for the detection and classification of QRS complexes based on the continuous wavelet transform (CWT) with splines. This approach can evaluate the CWT at any integer scale and the analysis is not restricted to powers of two. The QRS detector comprises four stages: implementation of CWT with splines, detection of QRS complexes, searching for undetected QRS complexes, and correction of the R wave peak location in detected QRS complexes. After, the onsets and ends of the QRS complexes are detected. The algorithm was evaluated with synthetic ECG and with the manually annotated databases: MIT-BIH Arrhythmia, European ST-T, QT and PTB Diagnostic ECG. Evaluation results of the QRS detector were: MIT-BIH arrhythmia database (109,447 beats analyzed), sensitivity Se = 99.72% and positive predictivity P+ = 99.87%; European ST-T database (790522 beats analyzed), Se = 99.92% and P+ = 99.55% and QT database (86498 beats analyzed), Se = 99.97% and P+ = 99.99%. To evaluate the delineation algorithm of the QRS onset (Qi) and QRS end (J) with the QT and PTB Diagnostic ECG databases, the mean and standard deviations of the differences between the automatic and manual annotated location of these points were calculated. The standard deviations were close to the accepted tolerances for deviations determined by the CSE experts. The proposed algorithm is robust to noise, artifacts and baseline drifts, classifies QRS complexes, automatically selects the CWT scale according to the sampling frequency of the ECG record used, and adapts to changes in the heart rate, amplitude and morphology of QRS complexes.

A Time-Varying Dynamic Partial Credit Model to Analyze Polytomous and Multivariate Time Series Data

The accessibility to electronic devices and the novel statistical methodologies available have allowed researchers to comprehend psychological processes at the individual level. However, there are still great challenges to overcome as, in many cases, collected data are more complex than the available models are able to handle. For example, most methods assume that the variables in the time series are measured on an interval scale, which is not the case when Likert-scale items were used. Ignoring the scale of the variables can be problematic and bias the results. Additionally, most methods also assume that the time series are stationary, which is rarely the case. To tackle these disadvantages, we propose a model that combines the partial credit model (PCM) of the item response theory framework and the time-varying autoregressive model (TV-AR), which is a popular model used to study psychological dynamics. The proposed model is referred to as the time-varying dynamic partial credit model (TV-DPCM), which allows to appropriately analyze multivariate polytomous data and nonstationary time series. We test the performance and accuracy of the TV-DPCM in a simulation study. Lastly, by means of an example, we show how to fit the model to empirical data and interpret the results.

Development of next-generation reference interval models to establish reference intervals based on medical data: current status, algorithms and future consideration

Evidence derived from laboratory medicine plays a pivotal role in the diagnosis, treatment monitoring, and prognosis of various diseases. Reference intervals (RIs) are indispensable tools for assessing test results. The accuracy of clinical decision-making relies directly on the appropriateness of RIs. With the increase in real-world studies and advances in computational power, there has been increased interest in establishing RIs using big data. This approach has demonstrated cost-effectiveness and applicability across diverse scenarios, thereby enhancing the overall suitability of the RI to a certain extent. However, challenges persist when tests results are influenced by age and sex. Reliance on a single RI or a grouping of RIs based on age and sex can lead to erroneous interpretation of results with significant implications for clinical decision-making. To address this issue, the development of next generation of reference interval models has arisen at an historic moment. Such models establish a curve relationship to derive continuously changing reference intervals for test results across different age and sex categories. By automatically selecting appropriate RIs based on the age and sex of patients during result interpretation, this approach facilitates clinical decision-making and enhances disease diagnosis/treatment as well as health management practices. Development of next-generation reference interval models use direct or indirect sampling techniques to select reference individuals and then employed curve fitting methods such as splines, polynomial regression and others to establish continuous models. In light of these studies, several observations can be made: Firstly, to date, limited interest has been shown in developing next-generation reference interval models, with only a few models currently available. Secondly, there are a wide range of methods and algorithms for constructing such models, and their diversity may lead to confusion. Thirdly, the process of constructing next-generation reference interval models can be complex, particularly when employing indirect sampling techniques. At present, normative documents pertaining to the development of next-generation reference interval models are lacking. In summary, this review aims to provide an overview of the current state of development of next-generation reference interval models by defining them, highlighting inherent advantages, and addressing existing challenges. It also describes the process, advanced algorithms for model building, the tools required and the diagnosis and validation of models. Additionally, a discussion on the prospects of utilizing big data for developing next-generation reference interval models is presented. The ultimate objective is to equip clinical laboratories with the theoretical framework and practical tools necessary for developing and optimizing next-generation reference interval models to establish next-generation reference intervals while enhancing the use of medical data resources to facilitate precision medicine.

Semiparametric distributed lag quantile regression for modeling time-dependent exposure mixtures

Studying time-dependent exposure mixtures has gained increasing attentions in environmental health research. When a scalar outcome is of interest, distributed lag (DL) models have been employed to characterize the exposures effects distributed over time on the mean of final outcome. However, there is a methodological gap on investigating time-dependent exposure mixtures with different quantiles of outcome. In this paper, we introduce semiparametric partial-linear single-index (PLSI) DL quantile regression, which can describe the DL effects of time-dependent exposure mixtures on different quantiles of outcome and identify susceptible periods of exposures. We consider two time-dependent exposure settings: discrete and functional, when exposures are measured in a small number of time points and at dense time grids, respectively. Spline techniques are used to approximate the nonparametric DL function and single-index link function, and a profile estimation algorithm is proposed. Through extensive simulations, we demonstrate the performance and value of our proposed models and inference procedures. We further apply the proposed methods to study the effects of maternal exposures to ambient air pollutants of fine particulate and nitrogen dioxide on birth weight in New York University Children's Health and Environment Study (NYU CHES).

SpatDistCalib: a GUI Python software for spatial-distortion correction of 2D detectors using splines

CCD-based X-ray detector systems often suffer from spatial distortions. Reproducible distortions can be quantitatively measured with a calibration grid and described as a displacement matrix or as spline functions. The measured distortion can be used afterwards to undistort raw images or to refine the actual position of each pixel, e.g. for azimuthal integration. This article describes a method using a regular grid, not necessarily orthogonal, to measure the distortions. The graphical user interface (GUI) Python software that is used to implement this method is available under a GPLv3 license on ESRF GitLab, and produces a spline file that is usable with data-reduction software such as FIT2D or pyFAI.

Inference in response-adaptive clinical trials when the enrolled population varies over time

A common assumption of data analysis in clinical trials is that the patient population, as well as treatment effects, do not vary during the course of the study. However, when trials enroll patients over several years, this hypothesis may be violated. Ignoring variations of the outcome distributions over time, under the control and experimental treatments, can lead to biased treatment effect estimates and poor control of false positive results. We propose and compare two procedures that account for possible variations of the outcome distributions over time, to correct treatment effect estimates, and to control type-I error rates. The first procedure models trends of patient outcomes with splines. The second leverages conditional inference principles, which have been introduced to analyze randomized trials when patient prognostic profiles are unbalanced across arms. These two procedures are applicable in response-adaptive clinical trials. We illustrate the consequences of trends in the outcome distributions in response-adaptive designs and in platform trials, and investigate the proposed methods in the analysis of a glioblastoma study.

Penalized estimation of a class of single-index varying-coefficient models for integrative genomic analysis

Recent technological advances have made it possible to collect high-dimensional genomic data along with clinical data on a large number of subjects. In the studies of chronic diseases such as cancer, it is of great interest to integrate clinical and genomic data to build a comprehensive understanding of the disease mechanisms. Despite extensive studies on integrative analysis, it remains an ongoing challenge to model the interaction effects between clinical and genomic variables, due to high dimensionality of the data and heterogeneity across data types. In this paper, we propose an integrative approach that models interaction effects using a single-index varying-coefficient model, where the effects of genomic features can be modified by clinical variables. We propose a penalized approach for separate selection of main and interaction effects. Notably, the proposed methods can be applied to right-censored survival outcomes based on a Cox proportional hazards model. We demonstrate the advantages of the proposed methods through extensive simulation studies and provide applications to a motivating cancer genomic study.

Effect of Various Edge Configurations on the Accuracy of the Modelling Shape of Shell Structures Using Spline Functions

Spline functions are a useful tool for modelling the shape of shell structures. They have curvature continuity that allows good approximation accuracy for various objects, including hyperboloid cooling towers, spherical domes, paraboloid bowls of radio telescopes, or many other types of smooth free surfaces. Spline models can be used to determine the displacement of structures based on point clouds from laser scanning or photogrammetry. The curvature continuity of splines may, however, cause local distortions in models that have edges. Edges may appear in point clouds where surface patches are joined, on surfaces equipped with additional technical infrastructure or with cracks and shifts in the structure. Taking the properties of spline functions into account, several characteristic types of edge configurations can be distinguished, which may, to a different extent, affect the values of modelling errors. The research conducted below was aimed at identifying such configurations based on theoretical considerations and then assessing their effect on the accuracy of modelling shell structures measured by laser scanning. It turned out to be possible to distinguish between edge configurations, based on the deviation values.

Novel and existing flexible survival methods for network meta-analyses

Aim: Technical Support Document 21 discusses trial-based, flexible relative survival models. The authors generalized flexible relative survival models to the network meta-analysis (NMA) setting while accounting for different treatment-effect specifications. Methods: The authors compared the standard parametric model with mixture, mixture cure and nonmixture cure, piecewise, splines and fractional polynomial models. The optimal treatment-effect parametrization was defined in two steps. First, all models were run with treatment effects on all parameters and subsequently the optimal model was defined by removing uncertain treatment effects, for which the parameter was smaller than its standard deviation. The authors used a network in previously treated advanced non-small-cell lung cancer. Results: Flexible model-based NMAs impact fit and incremental mean survival and they increase corresponding uncertainty. Treatment-effect specification impacts incremental survival, reduces uncertainty and improves the fit statistic. Conclusion: Extrapolation techniques already available for individual trials can now be used for NMAs to ensure that the most plausible extrapolations are being used for health technology assessment submissions.

Running speed and REM sleep control two distinct modes of rapid interhemispheric communication

Rhythmic gamma-band communication within and across cortical hemispheres is critical for optimal perception, navigation, and memory. Here, using multisite recordings in both rats and mice, we show that even faster ~140 Hz rhythms are robustly anti-phase across cortical hemispheres, visually resembling splines, the interlocking teeth on mechanical gears. Splines are strongest in superficial granular retrosplenial cortex, a region important for spatial navigation and memory. Spline-frequency interhemispheric communication becomes more coherent and more precisely anti-phase at faster running speeds. Anti-phase splines also demarcate high-activity frames during REM sleep. While splines and associated neuronal spiking are anti-phase across retrosplenial hemispheres during navigation and REM sleep, gamma-rhythmic interhemispheric communication is precisely in-phase. Gamma and splines occur at distinct points of a theta cycle and thus highlight the ability of interhemispheric cortical communication to rapidly switch between in-phase (gamma) and anti-phase (spline) modes within individual theta cycles during both navigation and REM sleep.

Gamma-rhythmic communication within and across cortical hemispheres is critical for optimal perception, navigation, and memory. Here, Ghosh et al. identify even faster ~140 Hz rhythms, named splines, that reflect anti-phase neuronal synchrony across hemispheres. The balance of anti-phase spline and in-phase gamma communication is dynamically controlled by behavior and sleep.

A dose-effect network meta-analysis model with application in antidepressants using restricted cubic splines

Network meta-analysis has been used to answer a range of clinical questions about the preferred intervention for a given condition. Although the effectiveness and safety of pharmacological agents depend on the dose administered, network meta-analysis applications typically ignore the role that drugs dosage plays in the results. This leads to more heterogeneity in the network. In this paper, we present a suite of network meta-analysis models that incorporate the dose-effect relationship using restricted cubic splines. We extend existing models into a dose-effect network meta-regression to account for study-level covariates and for groups of agents in a class-effect dose-effect network meta-analysis model. We apply our models to a network of aggregate data about the efficacy of 21 antidepressants and placebo for depression. We find that all antidepressants are more efficacious than placebo after a certain dose. Also, we identify the dose level at which each antidepressant's effect exceeds that of placebo and estimate the dose beyond which the effect of antidepressants no longer increases. When covariates were introduced to the model, we find that studies with small sample size tend to exaggerate antidepressants efficacy for several of the drugs. Our dose-effect network meta-analysis model with restricted cubic splines provides a flexible approach to modelling the dose-effect relationship in multiple interventions. Decision-makers can use our model to inform treatment choice.

Machine Learning to Identify Interaction of Single-Nucleotide Polymorphisms as a Risk Factor for Chronic Drug-Induced Liver Injury

Drug-induced liver injury (DILI) is a major cause of drug development failure and drug withdrawal from the market after approval. The identification of human risk factors associated with susceptibility to DILI is of paramount importance. Increasing evidence suggests that genetic variants may lead to inter-individual differences in drug response; however, individual single-nucleotide polymorphisms (SNPs) usually have limited power to predict human phenotypes such as DILI. In this study, we aim to identify appropriate statistical methods to investigate gene-gene and/or gene-environment interactions that impact DILI susceptibility. Three machine learning approaches, including Multivariate Adaptive Regression Splines (MARS), Multifactor Dimensionality Reduction (MDR), and logistic regression, were used. The simulation study suggested that all three methods were robust and could identify the known SNP-SNP interaction when up to 4% of genotypes were randomly permutated. When applied to a real-life DILI chronicity dataset, both MARS and MDR, but not logistic regression, identified combined genetic variants having better associations with DILI chronicity in comparison to the use of individual SNPs. Furthermore, a simple decision tree model using the SNPs identified by MARS and MDR was developed to predict DILI chronicity, with fair performance. Our study suggests that machine learning approaches may help identify gene-gene interactions as potential risk factors for better assessing complicated diseases such as DILI chronicity.

Comparison of Cox proportional hazards regression and generalized Cox regression models applied in dementia risk prediction

INTRODUCTION

The frequently used Cox regression applies two critical assumptions, which might not hold for all predictors. In this study, the results from a Cox regression model (CM) and a generalized Cox regression model (GCM) are compared.

METHODS

Data are from the Survey of Health, Ageing and Retirement in Europe (SHARE), which includes approximately 140,000 individuals aged 50 or older followed over seven waves. CMs and GCMs are used to estimate dementia risk. The results are internally and externally validated.

RESULTS

None of the predictors included in the analyses fulfilled the assumptions of Cox regression. Both models predict dementia moderately well (10-year risk: 0.737; 95% confidence interval [CI]: 0.699, 0.773; CM and 0.746; 95% CI: 0.710, 0.785; GCM).

DISCUSSION

The GCM performs significantly better than the CM when comparing pseudo-R2 and the log-likelihood. GCMs enable researcher to test the assumptions used by Cox regression independently and relax these assumptions if necessary.

Nonlinear and time-dependent effects of sparsely measured continuous time-varying covariates in time-to-event analysis

Many flexible extensions of the Cox proportional hazards model incorporate time-dependent (TD) and/or nonlinear (NL) effects of time-invariant covariates. In contrast, little attention has been given to the assessment of such effects for continuous time-varying covariates (TVCs). We propose a flexible regression B-spline-based model for TD and NL effects of a TVC. To account for sparse TVC measurements, we added to this model the effect of time elapsed since last observation (TEL), which acts as an effect modifier. TD, NL, and TEL effects are estimated with the iterative alternative conditional estimation algorithm. Furthermore, a simulation extrapolation (SIMEX)-like procedure was adapted to correct the estimated effects for random measurement errors in the observed TVC values. In simulations, TD and NL estimates were unbiased if the TVC was measured with a high frequency. With sparse measurements, the strength of the effects was underestimated but the TEL estimate helped reduce the bias, whereas SIMEX helped further to correct for bias toward the null due to "white noise" measurement errors. We reassessed the effects of systolic blood pressure (SBP) and total cholesterol, measured at two-year intervals, on cardiovascular risks in women participating in the Framingham Heart Study. Accounting for TD effects of SBP, cholesterol and age, the NL effect of cholesterol, and the TEL effect of SBP improved substantially the model's fit to data. Flexible estimates yielded clinically important insights regarding the role of these risk factors. These results illustrate the advantages of flexible modeling of TVC effects.

Generalized parametric cure models for relative survival

Cure models are used in time-to-event analysis when not all individuals are expected to experience the event of interest, or when the survival of the considered individuals reaches the same level as the general population. These scenarios correspond to a plateau in the survival and relative survival function, respectively. The main parameters of interest in cure models are the proportion of individuals who are cured, termed the cure proportion, and the survival function of the uncured individuals. Although numerous cure models have been proposed in the statistical literature, there is no consensus on how to formulate these. We introduce a general parametric formulation of mixture cure models and a new class of cure models, termed latent cure models, together with a general estimation framework and software, which enable fitting of a wide range of different models. Through simulations, we assess the statistical properties of the models with respect to the cure proportion and the survival of the uncured individuals. Finally, we illustrate the models using survival data on colon cancer, which typically display a plateau in the relative survival. As demonstrated in the simulations, mixture cure models which are not guaranteed to be constant after a finite time point, tend to produce accurate estimates of the cure proportion and the survival of the uncured. However, these models are very unstable in certain cases due to identifiability issues, whereas LC models generally provide stable results at the price of more biased estimates.

A Generic Multivariate Framework for the Integration of Microbiome Longitudinal Studies With Other Data Types

Simultaneous profiling of biospecimens using different technological platforms enables the study of many data types, encompassing microbial communities, omics, and meta-omics as well as clinical or chemistry variables. Reduction in costs now enables longitudinal or time course studies on the same biological material or system. The overall aim of such studies is to investigate relationships between these longitudinal measures in a holistic manner to further decipher the link between molecular mechanisms and microbial community structures, or host-microbiota interactions. However, analytical frameworks enabling an integrated analysis between microbial communities and other types of biological, clinical, or phenotypic data are still in their infancy. The challenges include few time points that may be unevenly spaced and unmatched between different data types, a small number of unique individual biospecimens, and high individual variability. Those challenges are further exacerbated by the inherent characteristics of microbial communities-derived data (e.g., sparse, compositional). We propose a generic data-driven framework to integrate different types of longitudinal data measured on the same biological specimens with microbial community data and select key temporal features with strong associations within the same sample group. The framework ranges from filtering and modeling to integration using smoothing splines and multivariate dimension reduction methods to address some of the analytical challenges of microbiome-derived data. We illustrate our framework on different types of multi-omics case studies in bioreactor experiments as well as human studies.

Clustering preference data in the presence of response-style bias

Preference data, such as Likert scale data, are often obtained in questionnaire-based surveys. Clustering respondents based on survey items is useful for discovering latent structures. However, cluster analysis of preference data may be affected by response styles, that is, a respondent's systematic response tendencies irrespective of the item content. For example, some respondents may tend to select ratings at the ends of the scale, which is called an 'extreme response style'. A cluster of respondents with an extreme response style can be mistakenly identified as a content-based cluster. To address this problem, we propose a novel method of clustering respondents based on their indicated preferences for a set of items while correcting for response-style bias. We first introduce a new framework to detect, and correct for, response styles by generalizing the definition of response styles used in constrained dual scaling. We then simultaneously correct for response styles and perform a cluster analysis based on the corrected preference data. A simulation study shows that the proposed method yields better clustering accuracy than the existing methods do. We apply the method to empirical data from four different countries concerning social values.

Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function

Background. Parametric modeling of survival data is important, and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalized linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This article describes the theoretical properties of these more flexible models and compares their performance to standard survival models in a reproducible case study. Methods. We describe how survival data may be analyzed with GLMs and their extensions: fractional polynomials, spline models, generalized additive models, generalized linear mixed (frailty) models, and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case study, we compare within-sample fit, the plausibility of extrapolations, and extrapolation performance based on data splitting. Results. Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case study, GLMs provided better within-sample fit and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and their extensions. Conclusions. The use of GLMs for parametric survival analysis can outperform standard parametric survival models, although the improvements were modest in our case study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case study will help to increase uptake of these models.

Flexible Modeling of the Association Between Cumulative Exposure to Low-Dose Ionizing Radiation From Cardiac Procedures and Risk of Cancer in Adults With Congenital Heart Disease

Adults with congenital heart disease are increasingly being exposed to low-dose ionizing radiation (LDIR) from cardiac procedures. In a recent study, Cohen et al. (Circulation. 2018;137(13):1334-1345) reported an association between increased LDIR exposure and cancer incidence but did not explore temporal relationships. Yet, the impact of past exposures probably accumulates over years, and its strength may depend on the amount of time elapsed since exposure. Furthermore, LDIR procedures performed shortly before a cancer diagnosis may have been ordered because of early symptoms of cancer, raising concerns about reversal causality bias. To address these challenges, we combined flexible modeling of cumulative exposures with competing-risks methodology to estimate separate associations of time-varying LDIR exposure with cancer incidence and all-cause mortality. Among 24,833 patients from the Quebec Congenital Heart Disease Database, 602 had incident cancer and 500 died during a follow-up period of up to 15 years (1995-2010). Initial results suggested a strong association of cancer incidence with very recent LDIR exposures, likely reflecting reverse causality bias. When exposure was lagged by 2 years, an increased cumulative LDIR dose from the previous 2-6 years was associated with increased cancer incidence, with a stronger association for women. These results illustrate the importance of accurate modeling of temporal relationships between time-varying exposures and health outcomes.

Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators

Correct specification of the exposure model is essential for unbiased estimation in marginal structural models with inverse-probability-of-treatment weights. However, although flexible modeling is commonplace when estimating effects of continuous covariates in outcome models, its use is less frequent in estimation of inverse probability weights. Using simulations, we assess the accuracy of the treatment effect estimates and covariate balance obtained with different exposure model specifications when the true relationship between a continuous, possibly time-varying covariate Lt and the logit of the probability of exposure is nonlinear. Specifically, we compare 4 approaches to modeling the effect of Lt when estimating inverse probability weights: a linear function, the covariate-balancing propensity score, and 2 easy-to-implement flexible methods that relax the assumption of linearity: cubic regression splines and fractional polynomials. Using data from 2 empirical studies, we compare linear exposure models with flexible exposure models to estimate the effect of sustained virological response to hepatitis C virus treatment on the progression of liver fibrosis. Our simulation results demonstrate that ignoring important nonlinear relationships when fitting the exposure model may provide poorer covariate balance and induce substantial bias in the estimated exposure-outcome associations. Analysts should routinely consider flexible modeling of continuous covariates when estimating inverse-probability-of-treatment weights.

Flexible identification procedure for thermodynamic constitutive models for magnetostrictive materials

We present a novel approach for identifying a multiaxial thermodynamic magneto-mechanical constitutive law by direct bi- or trivariate spline interpolation from available magnetization and magnetostriction data. Reference data are first produced with a multiscale model in the case of a magnetic field and uniaxial and shear stresses. The thermodynamic model fits well to the results of the multiscale model, after which the models are compared under complex multiaxial loadings. A surprisingly good agreement between the two models is found, but some differences in the magnetostrictive behaviour are also pointed out. Finally, the model is fitted to measurement results from an electrical steel sheet. The spline-based constitutive law overcomes several drawbacks of analytical approaches used earlier. The presented models and measurement results are openly available.

Understanding the relationship between duration of untreated psychosis and outcomes: A statistical perspective

AIM

Although the relationships between duration of untreated psychosis (DUP) and outcomes are often assumed to be linear, few studies have explored the functional form of these relationships. The aim of this study is to demonstrate the potential of recent advances in curve fitting approaches (splines) to explore the form of the relationship between DUP and global assessment of functioning (GAF).

METHODS

Curve fitting approaches were used in models to predict change in GAF at long-term follow-up using DUP for a sample of 83 individuals with schizophrenia.

RESULTS

The form of the relationship between DUP and GAF was non-linear. Accounting for non-linearity increased the percentage of variance in GAF explained by the model, resulting in better prediction and understanding of the relationship.

CONCLUSION

The relationship between DUP and outcomes may be complex and model fit may be improved by accounting for the form of the relationship. This should be routinely assessed and new statistical approaches for non-linear relationships exploited, if appropriate.

Saturating Splines and Feature Selection

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data via a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method. Unlike many existing approaches, our algorithm solves the original infinite-dimensional (for splines of degree at least two) optimization problem without pre-specified knot locations. We then adapt our algorithm to fit generalized additive models with saturating splines as coordinate functions and show that the saturation requirement allows our model to simultaneously perform feature selection and nonlinear function fitting. Finally, we briefly sketch how the method can be extended to higher order splines and to different requirements on the extension outside the data range.

ROBUST MIXED EFFECTS MODEL FOR CLUSTERED FAILURE TIME DATA: APPLICATION TO HUNTINGTON'S DISEASE EVENT MEASURES

An important goal in clinical and statistical research is properly modeling the distribution for clustered failure times which have a natural intraclass dependency and are subject to censoring. We handle these challenges with a novel approach that does not impose restrictive modeling or distributional assumptions. Using a logit transformation, we relate the distribution for clustered failure times to covariates and a random, subject-specific effect. The covariates are modeled with unknown functional forms, and the random effect may depend on the covariates and have an unknown and unspecified distribution. We introduce pseudovalues to handle censoring and splines for functional covariate effects, and frame the problem into fitting an additive logistic mixed effects model. Unlike existing approaches for fitting such models, we develop semiparametric techniques that estimate the functional model parameters without specifying or estimating the random effect distribution. We show both theoretically and empirically that the resulting estimators are consistent for any choice of random effect distribution and any dependency structure between the random effect and covariates. Last, we illustrate the method's utility in an application to a Huntington's disease study where our method provides new insights into differences between motor and cognitive impairment event times in at-risk subjects.

Contemporary group estimates adjusted for climatic effects provide a finer definition of the unknown environmental challenges experienced by growing pigs

Environmental descriptors derived from mean performances of contemporary groups (CGs) are assumed to capture any known and unknown environmental challenges. The objective of this paper was to obtain a finer definition of the unknown challenges, by adjusting CG estimates for the known climatic effects of monthly maximum air temperature (MaxT), minimum air temperature (MinT) and monthly rainfall (Rain). As the unknown component could include infection challenges, these refined descriptors may help to better model varying responses of sire progeny to environmental infection challenges for the definition of disease resilience. Data were recorded from 1999 to 2013 at a piggery in south-east Queensland, Australia (n = 31,230). Firstly, CG estimates of average daily gain (ADG) and backfat (BF) were adjusted for MaxT, MinT and Rain, which were fitted as splines. In the models used to derive CG estimates for ADG, MaxT and MinT were significant variables. The models that contained these significant climatic variables had CG estimates with a lower variance compared to models without significant climatic variables. Variance component estimates were similar across all models, suggesting that these significant climatic variables accounted for some known environmental variation captured in CG estimates. No climatic variables were significant in the models used to derive the CG estimates for BF. These CG estimates were used to categorize environments. There was no observable sire by environment interaction (Sire×E) for ADG when using the environmental descriptors based on CG estimates on BF. For the environmental descriptors based on CG estimates of ADG, there was significant Sire×E only when MinT was included in the model (p = .01). Therefore, this new definition of the environment, preadjusted by MinT, increased the ability to detect Sire×E. While the unknown challenges captured in refined CG estimates need verification for infection challenges, this may provide a practical approach for the genetic improvement of disease resilience.

Functional Generalized Structured Component Analysis

An extension of Generalized Structured Component Analysis (GSCA), called Functional GSCA, is proposed to analyze functional data that are considered to arise from an underlying smooth curve varying over time or other continua. GSCA has been geared for the analysis of multivariate data. Accordingly, it cannot deal with functional data that often involve different measurement occasions across participants and a large number of measurement occasions that exceed the number of participants. Functional GSCA addresses these issues by integrating GSCA with spline basis function expansions that represent infinite-dimensional curves onto a finite-dimensional space. For parameter estimation, functional GSCA minimizes a penalized least squares criterion by using an alternating penalized least squares estimation algorithm. The usefulness of functional GSCA is illustrated with gait data.

Modelling retinal pulsatile blood flow from video data

Modern day datasets continue to increase in both size and diversity. One example of such 'big data' is video data. Within the medical arena, more disciplines are using video as a diagnostic tool. Given the large amount of data stored within a video image, it is one of most time consuming types of data to process and analyse. Therefore, it is desirable to have automated techniques to extract, process and analyse data from video images. While many methods have been developed for extracting and processing video data, statistical modelling to analyse the outputted data has rarely been employed. We develop a method to take a video sequence of periodic nature, extract the RGB data and model the changes occurring across the contiguous images. We employ harmonic regression to model periodicity with autoregressive terms accounting for the error process associated with the time series nature of the data. A linear spline is included to account for movement between frames. We apply this model to video sequences of retinal vessel pulsation, which is the pulsatile component of blood flow. Slope and amplitude are calculated for the curves generated from the application of the harmonic model, providing clinical insight into the location of obstruction within the retinal vessels. The method can be applied to individual vessels, or to smaller segments such as 2 × 2 pixels which can then be interpreted easily as a heat map.

Nonparametric Regularized Regression for Phenotype-Associated Taxa Selection and Network Construction with Metagenomic Count Data

We use a metagenomic approach and network analysis to investigate the relationships between phenotypes across taxa under different environmental conditions. The network structure of taxa can be affected by the disease-associated environmental conditions. In addition, taxa abundance is differentiated under conditions. Therefore, knowing how the correlation or relative abundance changes with these factors would be of great interest to researchers. We develop a nonparametric regularized regression method to construct taxa association networks under different clinical conditions. We let the coefficients be unknown functions of the environmental variable. The varying coefficients are estimated by using regression splines. The proposed method is regularized with concave penalties, and an efficient group descent algorithm is developed for computation. We also apply the varying coefficient model to estimate taxa abundance to see how it changes across different environmental conditions. Moreover, for conducting inference, we propose a bootstrap method to construct the simultaneous confidence bands for the corresponding coefficients. We use different simulated designs and a real data set to demonstrate that our method can identify the network structures successfully under different environmental conditions. As such, the proposed method has potential applications for researchers to construct differential networks and identify taxa.

Constrained Dual Scaling for Detecting Response Styles in Categorical Data

Dual scaling (DS) is a multivariate exploratory method equivalent to correspondence analysis when analysing contingency tables. However, for the analysis of rating data, different proposals appear in the DS and correspondence analysis literature. It is shown here that a peculiarity of the DS method can be exploited to detect differences in response styles. Response styles occur when respondents use rating scales differently for reasons not related to the questions, often biasing results. A spline-based constrained version of DS is devised which can detect the presence of four prominent types of response styles, and is extended to allow for multiple response styles. An alternating nonnegative least squares algorithm is devised for estimating the parameters. The new method is appraised both by simulation studies and an empirical application.

Efficient and automatic methods for flexible regression on spatiotemporal data, with applications to groundwater monitoring

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of P-splines, we propose a Bayesian framework for choosing the smoothing parameter, which allows the construction of fully automatic data-driven methods for fitting flexible models to spatiotemporal data. An implementation, which is highly computationally efficient and exploits the sparsity of the design and penalty matrices, is proposed. The findings are illustrated using a simulation study and two examples, all concerned with the modelling of contaminants in groundwater. This suggests that the proposed strategy is more stable that competing methods based on the use of criteria such as generalised cross-validation and Akaike's Information Criterion. © 2015 The Authors. Environmetrics Published by John Wiley Sons Ltd.

New results on the single molecule localization problem in two and three dimensions

Fluorescence microscopy is an optical microscopy technique which has been extensively used to study specifically- labeled subcellular objects, such as proteins, and their functions. The best possible accuracy with which an object of interest can be localized when imaged using a fluorescence microscope is typically calculated using the Cramer- Rao lower bound (CRLB). The calculation of the CRLB, however, so far relied on an analytical expression for the image of the object. This can pose challenges in practice since it is often difficult to find appropriate analytical models for the images of general objects. Even if an appropriate analytical model is available, the lack of knowledge about the precise values of imaging parameters might also impose difficulties in the calculation oxf the CRLB. To address these challenges, we have developed an approach that directly uses an experimentally collected image set to calculate the best possible localization accuracy for a general subcellular object in two and three dimensions. In this approach, we fit smoothly connected piecewise polynomials, known as splines, to the experimentally collected image set to provide a continuous model of the object. This continuous model can then be used for the calculation of the best possible localization accuracy.

A sexually transmitted infection screening algorithm based on semiparametric regression models

Sexually transmitted infections (STIs) with Chlamydia trachomatis, Neisseria gonorrhoeae, and Trichomonas vaginalis are among the most common infectious diseases in the United States, disproportionately affecting young women. Because a significant portion of the infections present no symptoms, infection control relies primarily on disease screening. However, universal STI screening in a large population can be expensive. In this paper, we propose a semiparametric model-based screening algorithm. The model quantifies organism-specific infection risks in individual subjects and accounts for the within-subject interdependence of the infection outcomes of different organisms and the serial correlations among the repeated assessments of the same organism. Bivariate thin-plate regression spline surfaces are incorporated to depict the concurrent influences of age and sexual partners on infection acquisition. Model parameters are estimated by using a penalized likelihood method. For inference, we develop a likelihood-based resampling procedure to compare the bivariate effect surfaces across outcomes. Simulation studies are conducted to evaluate the model fitting performance. A screening algorithm is developed using data collected from an epidemiological study of young women at increased risk of STIs. We present evidence that the three organisms have distinct age and partner effect patterns; for C. trachomatis, the partner effect is more pronounced in younger adolescents. Predictive performance of the proposed screening algorithm is assessed through a receiver operating characteristic analysis. We show that the model-based screening algorithm has excellent accuracy in identifying individuals at increased risk, and thus can be used to assist STI screening in clinical practice.

A general framework for parametric survival analysis

Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User-friendly Stata software is provided, which significantly extends parametric survival models available in standard software.

Modeling exposure-lag-response associations with distributed lag non-linear models

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure-lag-response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others.

Inexact trajectory planning and inverse problems in the Hamilton-Pontryagin framework

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler-Lagrange equations is obtained from a higher-order Hamilton-Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre-Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton-Pontryagin principle and preserves the geometric properties of the continuous-time solution.

Trajectory analyses in alcohol treatment research

BACKGROUND

Various statistical methods have been used for data analysis in alcohol treatment studies. Trajectory analyses can better capture differences in treatment effects and may provide insight on the optimal duration of future clinical trials and grace periods. This improves on the limitation of commonly used parametric (e.g., linear) methods that cannot capture nonlinear temporal trends in the data.

METHODS

We propose an exploratory approach, using more flexible smoothing mixed effects models, more accurately to characterize the temporal patterns of the drinking data. We estimated the trajectories of the treatment arms for data sets from 2 sources: a multisite topiramate study, and the Combined Pharmacotherapies (acamprosate and naltrexone) and Behavioral Interventions study.

RESULTS

Our methods illustrate that drinking outcomes of both the topiramate and placebo arms declined over the entire course of the trial but with a greater rate of decline for the topiramate arm. By the point-wise confidence intervals, the heavy drinking probabilities for the topiramate arm might differ from those of the placebo arm as early as week 2. Furthermore, the heavy drinking probabilities of both arms seemed to stabilize at the end of the study. Overall, naltrexone was better than placebo in reducing drinking over time yet was not different from placebo for subjects receiving the combination of a brief medical management and an intensive combined behavioral intervention.

CONCLUSIONS

The estimated trajectory plots clearly showed nonlinear temporal trends of the treatment with different medications on drinking outcomes and offered more detailed interpretation of the results. This trajectory analysis approach is proposed as a valid exploratory method for evaluating efficacy in pharmacotherapy trials in alcoholism.

Population Encoding With Hodgkin-Huxley Neurons

The recovery of (weak) stimuli encoded with a population of Hodgkin-Huxley neurons is investigated. In the absence of a stimulus, the Hodgkin-Huxley neurons are assumed to be tonically spiking. The methodology employed calls for 1) finding an input-output (I/O) equivalent description of the Hodgkin-Huxley neuron and 2) devising a recovery algorithm for stimuli encoded with the I/O equivalent neuron(s). A Hodgkin-Huxley neuron with multiplicative coupling is I/O equivalent with an Integrate-and-Fire neuron with a variable threshold sequence. For bandlimited stimuli a perfect recovery of the stimulus can be achieved provided that a Nyquist-type rate condition is satisfied. A Hodgkin-Huxley neuron with additive coupling and deterministic conductances is first-order I/O equivalent with a Project-Integrate-and-Fire neuron that integrates a projection of the stimulus on the phase response curve. The stimulus recovery is formulated as a spline interpolation problem in the space of finite length bounded energy signals. A Hodgkin-Huxley neuron with additive coupling and stochastic conductances is shown to be first-order I/O equivalent with a Project-Integrate-and-Fire neuron with random thresholds. For stimuli modeled as elements of Sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion. Finally, all previous recovery results of stimuli encoded with Hodgkin-Huxley neurons with multiplicative and additive coupling, and deterministic and stochastic conductances are extended to stimuli encoded with a population of Hodgkin-Huxley neurons.

A Bayesian approach to functional-based multilevel modeling of longitudinal data: applications to environmental epidemiology

Flexible multilevel models are proposed to allow for cluster-specific smooth estimation of growth curves in a mixed-effects modeling format that includes subject-specific random effects on the growth parameters. Attention is then focused on models that examine between-cluster comparisons of the effects of an ecologic covariate of interest (e.g. air pollution) on nonlinear functionals of growth curves (e.g. maximum rate of growth). A Gibbs sampling approach is used to get posterior mean estimates of nonlinear functionals along with their uncertainty estimates. A second-stage ecologic random-effects model is used to examine the association between a covariate of interest (e.g. air pollution) and the nonlinear functionals. A unified estimation procedure is presented along with its computational and theoretical details. The models are motivated by, and illustrated with, lung function and air pollution data from the Southern California Children's Health Study.

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

Estimating the exposure-response relationships between particulate matter and mortality within the APHEA multicity project

Several studies have reported significant health effects of air pollution even at low levels of air pollutants, but in most of theses studies linear nonthreshold relations were assumed. We investigated the exposure-response association between ambient particles and mortality in the 22 European cities participating in the APHEA (Air Pollution and Health--A European Approach) project, which is the largest available European database. We estimated the exposure-response curves using regression spline models with two knots and then combined the individual city estimates of the spline to get an overall exposure-response relationship. To further explore the heterogeneity in the observed city-specific exposure-response associations, we investigated several city descriptive variables as potential effect modifiers that could alter the shape of the curve. We conclude that the association between ambient particles and mortality in the cities included in the present analysis, and in the range of the pollutant common in all analyzed cities, could be adequately estimated using the linear model. Our results confirm those previously reported in Europe and the United States. The heterogeneity found in the different city-specific relations reflects real effect modification, which can be explained partly by factors characterizing the air pollution mix, climate, and the health of the population.

Comparing the continuous representation of time-series expression profiles to identify differentially expressed genes

We present a general algorithm to detect genes differentially expressed between two nonhomogeneous time-series data sets. As increasing amounts of high-throughput biological data become available, a major challenge in genomic and computational biology is to develop methods for comparing data from different experimental sources. Time-series whole-genome expression data are a particularly valuable source of information because they can describe an unfolding biological process such as the cell cycle or immune response. However, comparisons of time-series expression data sets are hindered by biological and experimental inconsistencies such as differences in sampling rate, variations in the timing of biological processes, and the lack of repeats. Our algorithm overcomes these difficulties by using a continuous representation for time-series data and combining a noise model for individual samples with a global difference measure. We introduce a corresponding statistical method for computing the significance of this differential expression measure. We used our algorithm to compare cell-cycle-dependent gene expression in wild-type and knockout yeast strains. Our algorithm identified a set of 56 differentially expressed genes, and these results were validated by using independent protein-DNA-binding data. Unlike previous methods, our algorithm was also able to identify 22 non-cell-cycle-regulated genes as differentially expressed. This set of genes is significantly correlated in a set of independent expression experiments, suggesting additional roles for the transcription factors Fkh1 and Fkh2 in controlling cellular activity in yeast.

Curve Fitting With Clothoidal Splines

Clothoids, i.e. curves Z(s) in R ² whose curvatures x(s) are linear fitting functions of arclength s, have been used for some time for curve fitting purposes in engineering applications. The first part of the paper deals with some basic interpolation problems for clothoids and studies the existence and uniqueness of their solutions. The second part discusses curve fitting problems for clothoidal splines, i.e. C²-curves, which are composed of finitely many clothoids. An iterative method is described for finding a clothoidal spline Z(s) passing through given points Z _i ϵ R ² . i = 0,1,..., n+1, which minimizes the integral ∫ Z x ( s ) 2 d s . This algorithm is superlinearly convergent and needs only 0(n) operations per iteration. A similar algorithm is given for a related problem of smoothing by clothoidal splines.

An Approach to Peak Area Estimation

We consider the problem, arising in nuclear spectroscopy, of estimating peak areas in the presence of a baseline of unknown shape. We analyze a procedure that chooses the baseline to be as smooth as is consistent with the data and note that the estimates have a certain minimax optimality. Expressions are developed for the systematic and random errors of the estimate, and some large sample approximations are derived. Procedures for choosing a smoothing parameter are developed and illustrated by simulations.