Bayesian imputation of time-varying covariates in linear mixed models

Assessing treatment effect heterogeneity in the presence of missing effect modifier data in cluster-randomized trials

Understanding whether and how treatment effects vary across subgroups is crucial to inform clinical practice and recommendations. Accordingly, the assessment of heterogeneous treatment effects based on pre-specified potential effect modifiers has become a common goal in modern randomized trials. However, when one or more potential effect modifiers are missing, complete-case analysis may lead to bias and under-coverage. While statistical methods for handling missing data have been proposed and compared for individually randomized trials with missing effect modifier data, few guidelines exist for the cluster-randomized setting, where intracluster correlations in the effect modifiers, outcomes, or even missingness mechanisms may introduce further threats to accurate assessment of heterogeneous treatment effect. In this article, the performance of several missing data methods are compared through a simulation study of cluster-randomized trials with continuous outcome and missing binary effect modifier data, and further illustrated using real data from the Work, Family, and Health Study. Our results suggest that multilevel multiple imputation and Bayesian multilevel multiple imputation have better performance than other available methods, and that Bayesian multilevel multiple imputation has lower bias and closer to nominal coverage than standard multilevel multiple imputation when there are model specification or compatibility issues.

Comparing DIC and WAIC for multilevel models with missing data

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). We use a multilevel mediation model as an illustrative example to compare different types of DIC and WAIC. More specifically, we aim to compare the performance of conditional and marginal DICs and WAICs, and investigate their performance with missing data. We focus on two versions of DIC ( D I C 1 and D I C 2 ) and one version of WAIC. In addition, we explore whether it is necessary to include the nuisance models of incomplete exogenous variables in likelihood. Based on the simulation results, whether D I C 2 is better than D I C 1 and WAIC and whether we should include the nuisance models of exogenous variables in likelihood functions depend on whether we use marginal or conditional likelihoods. Overall, we find that the marginal likelihood based- D I C 2 that excludes the likelihood of covariate models generally had the highest true model selection rates.

Effects of transcranial direct current stimulation combined with Pilates-based exercises in the treatment of chronic low back pain in outpatient rehabilitation service in Brazil: double-blind randomised controlled trial protocol

INTRODUCTION

Chronic low back pain may be associated with pathoanatomical, neurophysiological, physical, psychological and social factors; thus, treatments to reduce symptoms are important to improve the quality of life of this population. We aimed to evaluate the effects of transcranial direct current stimulation (tDCS) combined with Pilates-based exercises compared with sham stimulation on pain, quality of life and disability in patients with chronic non-specific low back pain.

METHODS AND ANALYSIS

This is a protocol for a double-blind randomised controlled trial with participants, outcome assessor and statistician blinded. We will include 36 individuals with a history of non-specific chronic low back pain for more than 12 weeks and minimum pain intensity of 3 points on the Numerical Pain Rating Scale. Individuals will be randomised into two groups: (1) active tDCS combined with Pilates-based exercises and (2) sham tDCS combined with Pilates-based exercises. Three weekly sessions of the protocol will be provided for 4 weeks, and individuals will be submitted to three assessments: the first (T0) will be performed before the intervention protocol, the second (T1) immediately after the intervention protocol and the third (T2) will be a follow-up 1 month after the end of the intervention. We will assess pain, disability, central sensitisation, quality of life, pressure pain threshold, global impression of change, adverse events and medication use. The Numerical Pain Rating Scale and the Roland-Morris Disability Questionnaire will be used at T1 to assess pain and disability, respectively, as primary outcome measures.

ETHICS AND DISSEMINATION

This trial was prospectively registered in ClinicalTrials.gov website and ethically approved by the Ethics and Research Committee of the Faculty of Health Sciences of Trairi (report number: 5.411.244) before data collection. We will publish the results in a peer-reviewed medical journal and on institution websites.

TRIAL REGISTRATION NUMBER

ClinicalTrials.gov (NCT05467566).

Impact of timing of primary ileocecal resection on prognosis in patients with Crohn's disease

BACKGROUND

The advantage of early ileocecal resection after Crohn's disease diagnosis is a matter of debate. This study aims to assess the timing of ileocecal resection on prognosis, after correction for possible confounders.

METHODS

Patients with Crohn's disease with primary ileocecal resection between 2000 and 2019 were included in a retrospective multicentre cohort. The primary endpoint was endoscopic recurrence (Rutgeerts score ≥i2b) within 18 months. Secondary endpoints were escalation of inflammatory bowel disease medication within 18 months and re-resection during follow-up. The association between timing of ileocecal resection and these endpoints was investigated using multivariable proportional hazard models, corrected for covariates including Montreal classification, postoperative prophylaxis, smoking, indication for surgery, medication before ileocecal resection, perianal fistulas, surgical approach, histology, length of resected segment and calendar year.

RESULTS

In 822 patients ileocecal resection was performed after a median of 3.1 years (i.q.r. 0.7-8.0) after Crohn's disease diagnosis. The lowest incidence of endoscopic recurrence, escalation of inflammatory bowel disease medication and re-resection was observed for patients undergoing ileocecal resection shortly after diagnosis (0-1 months). After correction for covariates, patients with ileocecal resection at 0, 4 and 12 months after diagnosis had a cumulative incidence of 35 per cent, 48 per cent and 39 per cent for endoscopic recurrence, 20 per cent, 29 per cent and 28 per cent for escalation of inflammatory bowel disease medication and 20 per cent, 30 per cent and 34 per cent for re-resection, respectively. In the multivariable model ileocolonic disease (HR 1.39 (95 per cent c.i. 1.05 to 1.86)), microscopic inflammation of proximal and distal resection margins (HR 2.20 (95 per cent c.i. 1.21 to 3.87)) and postoperative prophylactic biological and immunomodulator (HR 0.16 (95 per cent c.i. 0.05 to 0.43)) were associated with endoscopic recurrence.

CONCLUSION

The timing of ileocecal resection was not associated with a change of disease course; in the multivariable model, the postoperative recurrence was not affected by timing of ileocecal resection.

An Investigation of Factored Regression Missing Data Methods for Multilevel Models with Cross-Level Interactions

A growing body of literature has focused on missing data methods that factorize the joint distribution into a part representing the analysis model of interest and a part representing the distributions of the incomplete predictors. Relatively little is known about the utility of this method for multilevel models with interactive effects. This study presents a series of Monte Carlo computer simulations that investigates Bayesian and multiple imputation strategies based on factored regressions. When the model's distributional assumptions are satisfied, these methods generally produce nearly unbiased estimates and good coverage, with few exceptions. Severe misspecifications that arise from substantially non-normal distributions can introduce biased estimates and poor coverage. Follow-up simulations suggest that a Yeo-Johnson transformation can mitigate these biases. A real data example illustrates the methodology, and the paper suggests several avenues for future research.

A wide range of missing imputation approaches in longitudinal data: a simulation study and real data analysis

BACKGROUND

Missing data is a pervasive problem in longitudinal data analysis. Several single-imputation (SI) and multiple-imputation (MI) approaches have been proposed to address this issue. In this study, for the first time, the function of the longitudinal regression tree algorithm as a non-parametric method after imputing missing data using SI and MI was investigated using simulated and real data.

METHOD

Using different simulation scenarios derived from a real data set, we compared the performance of cross, trajectory mean, interpolation, copy-mean, and MI methods (27 approaches) to impute missing longitudinal data using parametric and non-parametric longitudinal models and the performance of the methods was assessed in real data. The real data included 3,645 participants older than 18 years within six waves obtained from the longitudinal Tehran cardiometabolic genetic study (TCGS). The data modeling was conducted using systolic and diastolic blood pressure (SBP/DBP) as the outcome variables and included predictor variables such as age, gender, and BMI. The efficiency of imputation approaches was compared using mean squared error (MSE), root-mean-squared error (RMSE), median absolute deviation (MAD), deviance, and Akaike information criteria (AIC).

RESULTS

The longitudinal regression tree algorithm outperformed based on the criteria such as MSE, RMSE, and MAD than the linear mixed-effects model (LMM) for analyzing the TCGS and simulated data using the missing at random (MAR) mechanism. Overall, based on fitting the non-parametric model, the performance of the 27 imputation approaches was nearly similar. However, the SI traj-mean method improved performance compared with other imputation approaches.

CONCLUSION

Both SI and MI approaches performed better using the longitudinal regression tree algorithm compared with the parametric longitudinal models. Based on the results from both the real and simulated data, we recommend that researchers use the traj-mean method for imputing missing values of longitudinal data. Choosing the imputation method with the best performance is widely dependent on the models of interest and the data structure.

Methods for comparative effectiveness based on time to confirmed disability progression with irregular observations in multiple sclerosis

Real-world data sources offer opportunities to compare the effectiveness of treatments in practical clinical settings. However, relevant outcomes are often recorded selectively and collected at irregular measurement times. It is therefore common to convert the available visits to a standardized schedule with equally spaced visits. Although more advanced imputation methods exist, they are not designed to recover longitudinal outcome trajectories and typically assume that missingness is non-informative. We, therefore, propose an extension of multilevel multiple imputation methods to facilitate the analysis of real-world outcome data that is collected at irregular observation times. We illustrate multilevel multiple imputation in a case study evaluating two disease-modifying therapies for multiple sclerosis in terms of time to confirmed disability progression. This survival outcome is derived from repeated measurements of the Expanded Disability Status Scale, which is collected when patients come to the healthcare center for a clinical visit and for which longitudinal trajectories can be estimated. Subsequently, we perform a simulation study to compare the performance of multilevel multiple imputation to commonly used single imputation methods. Results indicate that multilevel multiple imputation leads to less biased treatment effect estimates and improves the coverage of confidence intervals, even when outcomes are missing not at random.

Noninterventional studies in the COVID-19 era: methodological considerations for study design and analysis

The global COVID-19 pandemic has generated enormous morbidity and mortality, as well as large health system disruptions including changes in use of prescription medications, outpatient encounters, emergency department admissions, and hospitalizations. These pandemic-related disruptions are reflected in real-world data derived from electronic medical records, administrative claims, disease or medication registries, and mobile devices. We discuss how pandemic-related disruptions in healthcare utilization may impact the conduct of noninterventional studies designed to characterize the utilization and estimate the effects of medical interventions on health-related outcomes. Using hypothetical studies, we highlight consequences that the pandemic may have on study design elements including participant selection and ascertainment of exposures, outcomes, and covariates. We discuss the implications of these pandemic-related disruptions on possible threats to external validity (participant selection) and internal validity (for example, confounding, selection bias, missing data bias). These concerns may be amplified in populations disproportionately impacted by COVID-19, such as racial/ethnic minorities, rural residents, or people experiencing poverty. We propose a general framework for researchers to carefully consider during the design and analysis of noninterventional studies that use real-world data from the COVID-19 era.

Compatibility in imputation specification

Missing data such as data missing at random (MAR) are unavoidable in real data and have the potential to undermine the validity of research results. Multiple imputation is one of the most widely used MAR-based methods in education and behavioral science applications. Arbitrarily specifying imputation models can lead to incompatibility and cause biased estimation. Building on the recent developments of model-based imputation and Arnold's compatibility work, this paper systematically summarizes when the traditional fully conditional specification (FCS) is applicable and how to specify a model-based imputation model if needed. We summarize two Compatibility Requirements to help researchers check compatibility more easily and a decision tree to check whether the traditional FCS is applicable in a given scenario. Additionally, we present a clear overview of two types of model-based imputation: the sequential and separate specifications. We illustrate how to specify model-based imputation with examples. Additionally, we provide example code of a free software program, Blimp, for implementing model-based imputation.

Evaluation of approaches for accommodating interactions and non-linear terms in multiple imputation of incomplete three-level data

Three-level data structures arising from repeated measures on individuals clustered within larger units are common in health research studies. Missing data are prominent in such studies and are often handled via multiple imputation (MI). Although several MI approaches can be used to account for the three-level structure, including adaptations to single- and two-level approaches, when the substantive analysis model includes interactions or quadratic effects, these too need to be accommodated in the imputation model. In such analyses, substantive model compatible (SMC) MI has shown great promise in the context of single-level data. Although there have been recent developments in multilevel SMC MI, to date only one approach that explicitly handles incomplete three-level data is available. Alternatively, researchers can use pragmatic adaptations to single- and two-level MI approaches, or two-level SMC-MI approaches. We describe the available approaches and evaluate them via simulations in the context of three three-level random effects analysis models involving an interaction between the incomplete time-varying exposure and time, an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. Results showed that all approaches considered performed well in terms of bias and precision when the target analysis involved an interaction with time, but the three-level SMC MI approach performed best when the target analysis involved an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. We illustrate the methods using data from the Childhood to Adolescence Transition Study.

Cross-cultural differences in men on active surveillance' anxiety: a longitudinal comparison between Italian and Dutch patients from the Prostate cancer Research International Active Surveillance study

Background

Men diagnosed with localized prostate cancer (PCa) on active surveillance (AS) have shown to cope with anxiety caused by living with an ‘untreated cancer’ and different factors can influence the tolerance level for anxiety in these patients. The present study analyzes Italian (Milan) and Dutch (Rotterdam) men prospectively included in the Prostate cancer International Active Surveillance (PRIAS) trial, aiming to explore whether socio-demographic factors (i.e. age, relationship status, education, nationality) may be relevant factors in conditioning the level of anxiety at AS entry and over time.

Methods

Italian and Dutch men participating in the IRB-approved PRIAS study, after signing an informed consent, filled in the Memorial Anxiety Scale for PCa (MAX-PC) at multiple time points after diagnosis. A linear mixed model was used to assess the relationship between the level of patient’s anxiety and time spent on AS, country of origin, the interaction between country and time on AS, patients’ relationship status and education, on PCa anxiety during AS.

Results

823 MAX-PC questionnaires were available for Italian and 307 for Dutch men, respectively. Median age at diagnosis was 64 years (IQR 60–70 years) and did not differ between countries. On average, Dutch men had a higher total MAX-PC score than Italian men. However, the level of their anxiety decreased over time. Dutch men on average had a higher score on the PCa anxiety sub-domain, which did not decrease over time. Minimal differences were observed in the sub-domains PSA anxiety and fear of recurrence.

Conclusion

Significant differences in PCa anxiety between the Italian and Dutch cohorts were observed, the latter group of men showing higher overall levels of anxiety. These differences were not related to the socio-demographic factors we studied. Although both PRIAS-centers are dedicated AS-centers, differences in PCa-care organization (e.g. having a multidisciplinary team) may have contributed to the observed different level of anxiety at the start and during AS.

Trial registration This study is registered in the Dutch Trial Registry (www.trialregister.nl) under NL1622 (registration date 11-03-2009), ‘PRIAS: Prostate cancer Research International: Active Surveillance—guideline and study for the expectant management of localized prostate cancer with curative intent’.

Response Surface Analysis with Missing Data

Response Surface Analysis (RSA) is gaining popularity in psychological research as a tool for investigating congruence hypotheses (e.g., consequences of self-other agreement, person-job fit, dyadic similarity). RSA involves the estimation of a nonlinear polynomial regression model and the interpretation of the resulting response surface. However, little is known about how best to conduct RSA when the underlying data are incomplete. In this article, we compare different methods for handling missing data in RSA. This includes different strategies for multiple imputation (MI) and maximum-likelihood (ML) estimation. Specifically, we consider the "just another variable" (JAV) approach to MI and ML, an approach that is in regular use in applications of RSA, and the more novel "substantive-model-compatible" (SMC) approach. In a simulation study, we evaluate the impact of these methods on focal outcomes of RSA, including the accuracy of parameter estimates, the shape of the response surface, and the testing of congruence hypotheses. Our findings suggest that the JAV approach can sometimes distort parameter estimates and conclusions about the shape of the response surface, whereas the SMC approach performs well overall. We illustrate applications of the methods in a worked example with real data and provide recommendations for their application in practice.

A Bayesian Latent Variable Selection Model for Nonignorable Missingness

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as leaving the data incomplete and failing to accommodate incomplete covariates with interactions, non-linear terms, and random slopes. We propose a Bayesian latent variable imputation approach to impute missing data due to MNAR (and other missingness mechanisms) and estimate the model of substantive interest simultaneously. In addition, even when the incomplete covariates involves interactions, non-linear terms, and random slopes, the proposed method can handle missingness appropriately. Computer simulation results suggested that the proposed Bayesian latent variable selection model (BLVSM) was quite effective when the outcome and/or covariates were MNAR. Except when the sample size was small, estimates from the proposed BLVSM tracked closely with those from the complete data analysis. With a small sample size, when the outcome was less predictable from the covariates, the missingness proportions of the covariates and the outcome were larger, and the missingness selection processes of the covariates and the outcome were more MNAR and MAR, the performance of BLVSM was less satisfactory. When the sample size was large, BLVSM always performed well. In contrast, the method with an MAR assumption provided biased estimates and undercoverage confidence intervals when the missingness was MNAR. The robustness and the implementation of BLVSM in real data were also illustrated. The proposed method is available in the Blimp software application, and the paper includes a data analysis example illustrating its use.

Unveiling mechanisms of change in digital interventions for depression: Study protocol for a systematic review and individual participant data meta-analysis

INTRODUCTION

The efficacy and effectiveness of digital interventions for depression are both well-established. However, precise effect size estimates for mediators transmitting the effects of digital interventions are not available; and integrative insights on the specific mechanisms of change in internet- and mobile-based interventions (IMIs)-as related to key features like delivery type, accompanying support and theoretical foundation-are largely pending.

OBJECTIVE

We will conduct a systematic review and individual participant data meta-analysis (IPD-MA) evaluating the mediators associated with therapeutic change in various IMIs for depression in adults.

METHODS

We will use three electronic databases (i.e., Embase, Medline/PubMed, PsycINFO) as well as an already established database of IPD to identify relevant published and unpublished studies. We will include (1) randomized controlled trials that examine (2) mediators of (3) guided and unguided (4) IMIs with (5) various theoretical orientations for (6) adults with (7) clinically relevant symptoms of depression (8) compared to an active or passive control condition (9) with depression symptom severity as primary outcome. Study selection, data extraction, as well as quality and risk of bias (RoB) assessment will be done independently by two reviewers. Corresponding authors of eligible primary studies will be invited to share their IPD for this meta-analytic study. In a 1-stage IPD-MA, mediation analyses (e.g., on potential mediators like self-efficacy, emotion regulation or problem solving) will be performed using a multilevel structural equation modeling approach within a random-effects framework. Indirect effects will be estimated, with multiple imputation for missing data; the overall model fit will be evaluated and statistical heterogeneity will be assessed. Furthermore, we will investigate if indirect effects are moderated by different variables on participant- (e.g., age, sex/gender, symptom severity), study- (e.g., quality, studies evaluating the temporal ordering of changes in mediators and outcomes), and intervention-level (e.g., theoretical foundation, delivery type, guidance).

DISCUSSION

This systematic review and IPD-MA will generate comprehensive information on the differential strength of mediators and associated therapeutic processes in digital interventions for depression. The findings might contribute to the empirically-informed advancement of psychotherapeutic interventions, leading to more effective interventions and improved treatment outcomes in digital mental health. Besides, with our novel approach to mediation analyses with IPD-MA, we might also add to a methodological progression of evidence-synthesis in psychotherapy process research.

STUDY REGISTRATION WITH OPEN SCIENCE FRAMEWORK OSF

https://osf.io/md7pq/.

An Introduction to Factored Regression Models with Blimp

In this paper, we provide an introduction to the factored regression framework. This modeling framework applies the rules of probability to break up or “factor” a complex joint distribution into a product of conditional regression models. Using this framework, we can easily specify the complex multivariate models that missing data modeling requires. The article provides a brief conceptual overview of factored regression and describes the functional notation used to conceptualize the models. Furthermore, we present a conceptual overview of how the models are estimated and imputations are obtained. Finally, we discuss how users can use the free software package, Blimp, to estimate the models in the context of a mediation example.

wEight chanGes, caRdio-mEtabolic risks and morTality in patients with hyperthyroidism (EGRET): a protocol for a CPRD-HES linked cohort study

INTRODUCTION

Hyperthyroidism is a common condition affecting up to 3% of the UK population. Treatment improves symptoms and reduces the risk of atrial fibrillation and stroke that contribute to increased mortality. The most common symptom is weight loss, which is reversed during treatment. However, the weight regain may be excessive, contributing to increased risk of obesity. Current treatment options include antithyroid drugs, radioiodine and thyroidectomy. Whether there are differences in either weight change or the long-term cardiometabolic risk between the three treatments is unclear.

METHODS AND ANALYSIS

The study will establish the natural history of weight change in hyperthyroidism, investigate the risk of obesity and risks of cardiometabolic conditions and death relative to the treatment. The data on patients diagnosed with hyperthyroidism between 1 January 1996 and 31 December 2015 will come from Clinical Practice Research Datalink linked to Hospital Episode Statistics and Office of National Statistics Death Registry. The weight changes will be modelled using a flexible joint modelling, accounting for mortality. Obesity prevalence in the general population will be sourced from Health Survey for England and compared with the post-treatment prevalence of obesity in patients with hyperthyroidism. The incidence and time-to-event of major adverse cardiovascular events, other cardiometabolic outcomes and mortality will be compared between the treatments using the inverse propensity weighting model. Incidence rate ratios of outcomes will be modelled with Poisson regression. Time to event will be analysed using Cox proportional hazards model. A competing risks approach will be adopted to estimate comparative incidences to allow for the impact of mortality.

ETHICS AND DISSEMINATION

The study will bring new knowledge on the risk of developing obesity, cardiometabolic morbidity and mortality following treatment for hyperthyroidism to inform clinical practice and public health policies. The results will be disseminated via open-access peer-reviewed publications and directly to the patients and public groups (Independent Scientific Advisory Committee protocol approval #20_000185).

Recurrence of primary sclerosing cholangitis after liver transplantation - analysing the European Liver Transplant Registry and beyond

Liver transplantation for primary sclerosing cholangitis (PSC) can be complicated by recurrence of PSC (rPSC). This may compromise graft survival but the effect on patient survival is less clear. We investigated the effect of post‐transplant rPSC on graft and patient survival in a large European cohort. Registry data from the European Liver Transplant Registry regarding all first transplants for PSC between 1980 and 2015 were supplemented with detailed data on rPSC from 48 out of 138 contributing transplant centres, involving 1,549 patients. Bayesian proportional hazards models were used to investigate the impact of rPSC and other covariates on patient and graft survival. Recurrence of PSC was diagnosed in 259 patients (16.7%) after a median follow‐up of 5.0 years (quantile 2.5%‐97.5%: 0.4–18.5), with a significant negative impact on both graft (HR 6.7; 95% CI 4.9–9.1) and patient survival (HR 2.3; 95% CI 1.5–3.3). Patients with rPSC underwent significantly more re‐transplants than those without rPSC (OR 3.6, 95% CI 2.7–4.8). PSC recurrence has a negative impact on both graft and patient survival, independent of transplant‐related covariates. Recurrence of PSC leads to higher number of re‐transplantations and a 33% decrease in 10‐year graft survival.

Using the Movember Foundation's GAP3 cohort to measure the effect of active surveillance on patient-reported urinary and sexual function-a retrospective study in low-risk prostate cancer patients

BACKGROUND

Active surveillance (AS) for low-risk prostate cancer (PCa) is intended to overcome potential side-effects of definitive treatment. Frequent prostate biopsies during AS may, however, impact erectile (EF) and urinary function (UF). The objective of this study was to test the influence of prostate biopsies on patient-reported EF and UF using multicenter data from the largest to-date AS-database.

METHODS

In this retrospective study, data analyses were performed using the Movember GAP3 database (v3.2), containing data from 21,169 AS participants from 27 AS-cohorts worldwide. Participants were included in the study if they had at least one follow-up prostate biopsy and completed at least one patient reported outcome measure (PROM) related to EF [Sexual Health Inventory for Men (SHIM)/five item International Index of Erectile Function (IIEF-5)] or UF [International Prostate Symptom Score (IPSS)] during follow-up. The longitudinal effect of the number of biopsies on either SHIM/IIEF-5 or IPSS were analyzed using linear mixed models to adjust for clustering at patient-level. Analyses were stratified by center; covariates included age and Gleason Grade group at diagnosis, and time on AS.

RESULTS

A total of 696 participants completed the SHIM/IIEF-5 3,175 times, with a median follow-up of 36 months [interquartile range (IQR) 20-55 months]. A total of 845 participants completed the IPSS 4,061 times, with a median follow-up of 35 months (IQR 19-56 months). The intraclass correlation (ICC) was 0.74 for the SHIM/IIEF-5 and 0.68 for the IPSS, indicating substantial differences between participants' PROMs. Limited heterogeneity between cohorts in the estimated effect of the number of biopsies on either PROM were observed. A significant association was observed between the number of biopsies and the SHIM/IIEF-5 score, but not for the IPSS score. Every biopsy was associated with a decrease in the SHIM/IIEF-5 score of an average 0.67 (95% CI, 0.47-0.88) points.

CONCLUSIONS

Repeated prostate biopsy as part of an AS protocol for men with low-risk PCa does not have a significant association with self-reported UF but does impact self-reported sexual function. Further research is, however, needed to understand whether the effect on sexual function implies a negative clinical impact on their quality of life and is meaningful from a patient's perspective. In the meantime, clinicians and patients should anticipate a potential decline in erectile function and hence consider incorporating the risk of this harm into their discussion about opting for AS and also when deciding on the stringency of follow-up biopsy schedules with long-term AS.

Multiple imputation of missing data in multilevel models with the R package mdmb: a flexible sequential modeling approach

Multilevel models often include nonlinear effects, such as random slopes or interaction effects. The estimation of these models can be difficult when the underlying variables contain missing data. Although several methods for handling missing data such as multiple imputation (MI) can be used with multilevel data, conventional methods for multilevel MI often do not properly take the nonlinear associations between the variables into account. In the present paper, we propose a sequential modeling approach based on Bayesian estimation techniques that can be used to handle missing data in a variety of multilevel models that involve nonlinear effects. The main idea of this approach is to decompose the joint distribution of the data into several parts that correspond to the outcome and explanatory variables in the intended analysis, thus generating imputations in a manner that is compatible with the substantive analysis model. In three simulation studies, we evaluate the sequential modeling approach and compare it with conventional as well as other substantive-model-compatible approaches to multilevel MI. We implemented the sequential modeling approach in the R package mdmb and provide a worked example to illustrate its application.

Tracking Study on the Relapse and Aftercare Effect of Drug Patients Released From a Compulsory Isolated Detoxification Center

BACKGROUND AND AIMS

There are no accurate statistical data on the relapse rate of drug abstainers after compulsory detoxification in China. This study aimed to collect relapse data for drug abstainers through follow-up visits, verify the effectiveness of professional social worker services and explore significant factors affecting relapse.

DESIGN AND SETTING

The drug abstainers released from Guangzhou T Compulsory Isolated Detoxification Center were randomly divided into two groups. The difference between the experimental group and the control group is that assistance services were provided by social workers to the former.

PARTICIPANTS

The study included 510 drug abstainers released from T Center, including 153 in the experimental group and 357 in the control group.

MEASUREMENTS

Demographic information, history of drug abuse, and motivation for drug rehabilitation (SOCRATES) were collected 1 month prior to drug abstainer release from compulsory detoxification. Then, the relapse situation after their release was tracked according to fixed time points.

FINDINGS

The overall relapse rate of 510 drug abstainers after their release from compulsory detoxification was 47.6%. The average survival time to relapse based on survival analysis was 220 days (N = 486), as calculated with Bayesian estimation by the MCMC method. The average survival times to relapse of the experimental group and control group were 393 and 175 days, respectively. By taking the specific survival time as the dependent variable and the group as the control variable (OR = 25.362), logistic regression analysis showed that marital status (OR = 2.666), previous compulsory detoxification experience (OR = 2.329) and location of household registration (OR = 1.557) had a significant impact on the survival time to relapse.

CONCLUSIONS

The occurrence of relapse among drug patients released from compulsory detoxification can be delayed effectively through the intervention of professional social worker services. Regardless of whether patients receive aftercare after compulsory detoxification, drug-using patients who are single, have multiple detoxification experiences and whose households are registered in other provinces deserve special attention. Relevant suggestions to avoid relapse are provided.

Evaluation of approaches for multiple imputation of three-level data

Background

Three-level data arising from repeated measures on individuals who are clustered within larger units are common in health research studies. Missing data are prominent in such longitudinal studies and multiple imputation (MI) is a popular approach for handling missing data. Extensions of joint modelling and fully conditional specification MI approaches based on multilevel models have been developed for imputing three-level data. Alternatively, it is possible to extend single- and two-level MI methods to impute three-level data using dummy indicators and/or by analysing repeated measures in wide format. However, most implementations, evaluations and applications of these approaches focus on the context of incomplete two-level data. It is currently unclear which approach is preferable for imputing three-level data.

Methods

In this study, we investigated the performance of various MI methods for imputing three-level incomplete data when the target analysis model is a three-level random effects model with a random intercept for each level. The MI methods were evaluated via simulations and illustrated using empirical data, based on a case study from the Childhood to Adolescence Transition Study, a longitudinal cohort collecting repeated measures on students who were clustered within schools. In our simulations we considered a number of different scenarios covering a range of different missing data mechanisms, missing data proportions and strengths of level-2 and level-3 intra-cluster correlations.

Results

We found that all of the approaches considered produced valid inferences about both the regression coefficient corresponding to the exposure of interest and the variance components under the various scenarios within the simulation study. In the case study, all approaches led to similar results.

Conclusion

Researchers may use extensions to the single- and two-level approaches, or the three-level approaches, to adequately handle incomplete three-level data. The two-level MI approaches with dummy indicator extension or the MI approaches based on three-level models will be required in certain circumstances such as when there are longitudinal data measured at irregular time intervals. However, the single- and two-level approaches with the DI extension should be used with caution as the DI approach has been shown to produce biased parameter estimates in certain scenarios.

Adherence to a plant-based, high-fibre dietary pattern is related to regression of non-alcoholic fatty liver disease in an elderly population

Dietary lifestyle intervention is key in treating non-alcoholic fatty liver disease (NAFLD). We aimed to examine the longitudinal relation between well-established dietary patterns as well as population-specific dietary patterns and NAFLD. Participants from two subsequent visits of the Rotterdam Study were included. All underwent serial abdominal ultrasonography (median follow-up: 4.4 years) and filled in a food frequency questionnaire. Secondary causes of steatosis were excluded. Dietary data from 389 items were collapsed into 28 food groups and a posteriori dietary patterns were identified using factor analysis. Additionally, we scored three a priori dietary patterns (Mediterranean Diet Score, Dutch Dietary Guidelines and WHO-score). Logistic mixed regression models were used to examine the relation between dietary patterns and NAFLD. Analyses were adjusted for demographic, lifestyle and metabolic factors. We included 963 participants of whom 343 had NAFLD. Follow-up data was available in 737 participants. Incident NAFLD was 5% and regressed NAFLD was 30%. We identified five a posteriori dietary patterns (cumulative explained variation [R²] = 20%). The patterns were characterised as: vegetable and fish, red meat and alcohol, traditional, salty snacks and sauces, high fat dairy & refined grains pattern. Adherence to the traditional pattern (i.e. high intake of vegetable oils/stanols, margarines/butters, potatoes, whole grains and sweets/desserts) was associated with regression of NAFLD per SD increase in Z-score (0.40, 95% CI 0.15–1.00). Adherence to the three a priori patterns all showed regression of NAFLD, but only the WHO-score showed a distinct association (0.73, 95% CI 0.53–1.00). Hence, in this large elderly population, adherence to a plant-based, high-fibre and low-fat diet was related to regression of NAFLD.

Construction and assessment of prediction rules for binary outcome in the presence of missing predictor data using multiple imputation and cross-validation: Methodological approach and data-based evaluation

We investigate calibration and assessment of predictive rules when missing values are present in the predictors. Our paper has two key objectives. The first is to investigate how the calibration of the prediction rule can be combined with use of multiple imputation to account for missing predictor observations. The second objective is to propose such methods that can be implemented with current multiple imputation software, while allowing for unbiased predictive assessment through validation on new observations for which outcome is not yet available. We commence with a review of the methodological foundations of multiple imputation as a model estimation approach as opposed to a purely algorithmic description. We specifically contrast application of multiple imputation for parameter (effect) estimation with predictive calibration. Based on this review, two approaches are formulated, of which the second utilizes application of the classical Rubin's rules for parameter estimation, while the first approach averages probabilities from models fitted on single imputations to directly approximate the predictive density for future observations. We present implementations using current software that allow for validation and estimation of performance measures by cross-validation, as well as imputation of missing data in predictors on the future data where outcome is missing by definition. To simplify, we restrict discussion to binary outcome and logistic regression throughout. Method performance is verified through application on two real data sets. Accuracy (Brier score) and variance of predicted probabilities are investigated. Results show substantial reductions in variation of calibrated probabilities when using the first approach.