Longitudinal studies in rheumatology: Some guidance for analysis

In a follow-up study, patients are monitored over time. Longitudinal and time-to-event studies are the two most important types of a follow-up study. In this paper, the focus is on longitudinal studies with a continuous response where patients are examined at several time points. While longitudinal studies provide a powerful tool for the evaluation of a treatment effect over time, a major problem is missing data caused, for example, by patients who drop out from the study. Many longitudinal studies in rheumatology use inappropriate statistical methodology because either they do not address correctly the correlated nature of the repeated measurements, or they treat the problem of missing data incorrectly. We will illustrate that there are interpretational and computational issues with the 'classical' approaches. Further, we expand here on more appropriate statistical techniques to analyze longitudinal studies. To this end, we focus on randomized controlled trials (RCTs) and illustrate the approaches on data from a fictive randomized controlled trial in rheumatology

Bayesian imputation of time-varying covariates in linear mixed models

Studies involving large observational datasets commonly face the challenge of dealing with multiple missing values. The most popular approach to overcome this challenge, multiple imputation using chained equations, however, has been shown to be sub-optimal in complex settings, specifically in settings with longitudinal outcomes, which cannot be easily and adequately included in the imputation models. Bayesian methods avoid this difficulty by specification of a joint distribution and thus offer an alternative. A popular choice for that joint distribution is the multivariate normal distribution. In more complicated settings, as in our two motivating examples that involve time-varying covariates, additional issues require consideration: the endo- or exogeneity of the covariate and its functional relation with the outcome. In such situations, the implied assumptions of standard methods may be violated, resulting in bias. In this work, we extend and study a more flexible, Bayesian alternative to the multivariate normal approach, to better handle complex incomplete longitudinal data. We discuss and compare assumptions of the two Bayesian approaches about the endo- or exogeneity of the covariates and the functional form of the association with the outcome, and illustrate and evaluate consequences of violations of those assumptions using simulation studies and two real data examples

Including historical data in the analysis of clinical trials

Data of previous trials with a similar setting are often available in the analysis of clinical trials. Several Bayesian methods have been proposed for including historical data as prior information in the analysis of the current trial, such as the (modified) power prior, the (robust) meta-analytic-predictive prior, the commensurate prior and methods proposed by Pocock and Murray et al. We compared these methods and illustrated their use in a practical setting, including an assessment of the comparability of the current and the historical data. The motivating data set consists of randomised controlled trials for acute myeloid leukaemia. A simulation study was used to compare the methods in terms of bias, precision, power and type I error rate. Methods that estimate parameters for the between-trial heterogeneity generally offer the best trade-off of power, precision and type I error, with the meta-analytic-predictive prior being the most promising method. The results show that it can be feasible to include historical data in the analysis of clinical trials, if an appropriate method is used to estimate the heterogeneity between trials, and the historical data satisfy criteria for comparability

Factors that influence data quality in caries experience detection: A multilevel modeling approach

Caries experience detection is prone to misclassification. For this reason, calibration exercises which aim at assessing and improving the scoring behavior of dental raters are organized. During a calibration exercise, a sample of children is examined by the benchmark scorer and the dental examiners. This produces a 2 × 2 contingency table with the true and possibly misclassified responses. The entries in this misclassification table allow to estimate the sensitivity and the specificity of the raters. However, in many dental studies, the uncertainty with which sensitivity and specificity are estimated is not expressed. Further, caries experience data have a hierarchical structure since the data are recorded for the surfaces nested in the teeth within the mouth. Therefore, it is important to report the uncertainty using confidence intervals and to take the clustering into account. Here we apply a Bayesian logistic multilevel model for estimating the sensitivity and specificity. The main goal of this research is to find the factors that influence the true scoring of caries experience accounting for the hierarchical structure in the data. In our analysis, we show that the dentition type and tooth or surface type affect the quality of caries experience detection. Copyrigh

GWAS on your notebook: Fast semi-parallel linear and logistic regression for genome-wide association studies

Background: Genome-wide association studies have become very popular in identifying genetic contributions to phenotypes. Millions of SNPs are being tested for their association with diseases and traits using linear or logistic regression models. This conceptually simple strategy encounters the following computational issues: a large number of tests and very large genotype files (many Gigabytes) which cannot be directly loaded into the software memory. One of the solutions applied on a grand scale is cluster computing involving large-scale resources. We show how to speed up the computations using matrix operations in pure R code.Results: We improve speed: computation time from 6 hours is reduced to 10-15 minutes. Our approach can handle essentially an unlimited amount of covariates efficiently, using projections. Data files in GWAS are vast and reading them into computer memory becomes an important issue. However, much improvement can be made if the data is structured beforehand in a way allowing for easy access to blocks of SNPs. We propose several solutions based on the R packages ff and ncdf.We adapted the semi-parallel computations for logistic regression. We show that in a typical GWAS setting, where SNP effects are very small, we do not lose any precision and our computations are few hundreds times faster than standard procedures.Conclusions: We provide very fast algorithms for GWAS written in pure R code. We also show how to rearrange SNP data for fast access

Dynamic prediction of outcome for patients with severe aortic stenosis: Application of joint models for longitudinal and time-to-event data

Background: Physicians utilize different types of information to predict patient prognosis. For example: confronted with a new patient suffering from severe aortic stenosis (AS), the cardiologist considers not only the severity of the AS but also patient characteristics, medical history, and markers such as BNP. Intuitively, doctors adjust their prediction of prognosis over time, with the change in clinical status, aortic valve area and BNP at each outpatient clinic visit. With the help of novel statistical approaches to model outcomes, it is now possible t

Genome-wide Analysis of Large-scale Longitudinal Outcomes using Penalization - GALLOP algorithm

Genome-wide association studies (GWAS) with longitudinal phenotypes provide opportunities to identify genetic variations associated with changes in human traits over time. Mixed models are used to correct for the correlated nature of longitudinal data. GWA studies are notorious for their computational challenges, which are considerable when mixed models for thousands of individuals are fitted to millions of SNPs. We present a new algorithm that speeds up a genome-wide analysis of longitudinal data by several orders of magnitude. It solves the equivalent penalized least squares problem efficiently, computing variances in an initial step. Factorizations and transformations are used to avoid inversion of large matrices. Because the system of equations is bordered, we can re-use components, which can be precomputed for the mixed model without a SNP. Two SNP effects (main and its interaction with time) are obtained. Our method completes the analysis a thousand times faster than the R package lme4, providing an almost identical solution for the coefficients and p-values. We provide an R implementation of our algorithm

Bayesian hierarchical modeling of longitudinal glaucomatous visual fields using a two-stage approach

The Bayesian approach has become increasingly popular because it allows to fit quite complex models to data via Markov chain Monte Carlo sampling. However, it is also recognized nowadays that Markov chain Monte Carlo sampling can become computationally prohibitive when applied to a large data set. We encountered serious computational difficulties when fitting an hierarchical model to longitudinal glaucoma data of patients who participate in an ongoing Dutch study. To overcome this problem, we applied and extended a recently proposed two-stage approach to model these data. Glaucoma is one of the leading causes of blindness in the world. In order to detect deterioration at an early stage, a model for predicting visual fields (VFs) in time is needed. Hence, the true underlying VF progression can be determined, and treatment strategies can then be optimized to prevent further VF loss. Because we were unable to fit these data with the classical one-stage approach upon which the current popular Bayesian software is based, we made use of the two-stage Bayesian approach. The considered hierarchical longitudinal model involves estimating a large number of random effects and deals with censoring and high measurement variability. In addition, we extended the approach with tools for model evaluation. Copyrigh

Incident somatic comorbidity after psychosis: Results from a retrospective cohort study based on Flemish general practice data

Background: Psychotic conditions and especially schizophrenia, have been associated with increased morbidity and mortality. Many studies are performed in specialized settings with a strong focus on schizophrenia. Somatic comorbidity after psychosis is studied, using a general practice comorbidity registration network. Methods. Hazard ratios are presented resulting from frailty models to assess the risk of subsequent somatic disease after a diagnosis of psychosis compared to people without psychosis matched on practice, age and gender. Diseases studied are cancer, physical trauma, diabetes mellitus, gastrointestinal disorders, joint disorders, irritable bowel syndrome, general infections, metabolic disorders other than diabetes, hearing and vision problems, anemia, cardiovascular disease, alcohol abuse, lung disorders, mouth and teeth problems, sexually transmitted diseases. Results: Significant higher risks after a diagnosis of psychosis were found for the emergence of diabetes, physical trauma, gastrointestinal disorders, alcohol abuse, chronic lung disease and teeth and mouth problems. With regard to diabetes, by including the type of antipsychotic medication it is clear that the significant overall effect was largely due to the use of atypical antipsychotic medication. No significant higher risk was seen for cancer, joint conditions, irritable bowel syndrome, general infections, other metabolic conditions, hearing/vision problems, anaemia, cardiovascular disease or diabetes, in case no atypical antipsychotic medication was used. Conclusion: Significantly higher morbidity rates for some somatic conditions in patients with psychosis are apparent. People with a diagnosis of psychosis benefit from regular assessments for the emergence of somatic disorders and risk factors, including diabetes in case of atypical antipsychotic medication

Predicting hemoglobin levels in whole blood donors using transition models and mixed effects models

Background: To optimize the planning of blood donations but also to continue motivating the volunteers it is important to streamline the practical organization of the timing of donations. While donors are asked to return for donation after a suitable period, still a relevant proportion of blood donors is deferred from donation each year due to a too low hemoglobin level. Rejection of donation may demotivate the candidate donor and implies an inefficient planning of the donation process. Hence, it is important to predict the future hemoglobin level to improve the planning of donors' visits to the blood bank. Methods. The development of the hemoglobin prediction rule is based on longitudinal (panel) data from blood donations collected by Sanquin (the only blood product collecting and supplying organization in the Netherlands). We explored and contrasted two popular statistical models, i.e. the transition (autoregressive) model and the mixed effects model as plausible models to account for the dependence among subsequent hemoglobin levels within a donor. Results: The predictors of the future hemoglobin level are age, season, hemoglobin levels at the previous visits, and a binary variable indicating whether a donation was made at the previous visit. Based on cross-validation, the areas under the receiver operating characteristic curve (AUCs) for male donors are 0.83 and 0.81 for the transition model and the mixed effects model, respectively; for female donors we obtained AUC values of 0.73 and 0.72 for the transition model and the mixed effects model, respectively. Conclusion: We showed that the transition models and the mixed effects models provide a much better prediction compared to a multiple linear regression model. In general, the transition model provides a somewhat better prediction than the mixed effects model, especially at high visit numbers. In addition, the transition model offers a better trade-off between sensitivity and specificity when varying the cut-off values for eligibility in predicted values. Hence transition models make the prediction of hemoglobin level more precise and may lead to less deferral from donation in the future