Longitudinal data analysis for generalized linear models with follow-up dependent on outcome-related variables

Genetics of longitudinal kidney function in children and adults with systemic lupus erythematosus

OBJECTIVES

Genome-wide association studies (GWAS) have identified loci associated with estimated glomerular filtration rate (eGFR). Few LN risk loci have been identified to date. We tested the association of SLE and eGFR polygenic risk scores (PRS) with repeated eGFR measures from children and adults with SLE.

METHODS

Patients from two tertiary care lupus clinics that met ≥4 ACR and/or SLICC criteria for SLE were genotyped on the Illumina MEGA or Omni1-Quad arrays. PRSs were calculated for SLE and eGFR, using published weighted GWA-significant alleles. eGFR was calculated using the CKD-EPI and Schwartz equations. We tested the effect of eGFR- and SLE-PRSs on eGFR mean and variance, adjusting for age at diagnosis, sex, ancestry, follow-up time, and clinical event flags.

RESULTS

We included 1158 SLE patients (37% biopsy-confirmed LN) with 36 733 eGFR measures over a median of 7.6 years (IQR: 3.9-15.3). LN was associated with lower within-person mean eGFR [LN: 93.8 (s.d. 26.4) vs non-LN: 101.6 (s.d. 17.7) mL/min per 1.73 m2; P < 0.0001] and higher variance [LN median: 157.0 (IQR: 89.5, 268.9) vs non-LN median: 84.9 (IQR: 46.9, 138.2) (mL/min per 1.73 m2)2; P < 0.0001]. Increasing SLE-PRSs were associated with lower mean eGFR and greater variance, while increasing eGFR-PRS was associated with increased eGFR mean and variance.

CONCLUSION

We observed significant associations between SLE and eGFR PRSs and repeated eGFR measurements, in a large cohort of children and adults with SLE. Longitudinal eGFR may serve as a powerful alternative outcome to LN categories for discovery of LN risk loci.

Causal inference with longitudinal data subject to irregular assessment times

Data collected in the context of usual care present a rich source of longitudinal data for research, but often require analyses that simultaneously enable causal inferences from observational data while handling irregular and informative assessment times. An inverse-weighting approach to this was recently proposed, and handles the case where the assessment times are at random (ie, conditionally independent of the outcome process given the observed history). In this paper, we extend the inverse-weighting approach to handle a special case of assessment not at random, where assessment and outcome processes are conditionally independent given past observed covariates and random effects. We use multiple outputation to accomplish the same purpose as inverse-weighting, and apply it to the Liang semi-parametric joint model. Moreover, we develop an alternative joint model that does not require covariates for the outcome model to be known at times where there is no assessment of the outcome. We examine the performance of these methods through simulation and illustrate them through a study of the causal effect of wheezing on time spent playing outdoors among children aged 2-9 years and enrolled in the TargetKids! study.

On the Nature of Informative Presence Bias in Analyses of Electronic Health Records

Electronic health records (EHRs) offer unprecedented opportunities to answer epidemiologic questions. However, unlike in ordinary cohort studies or randomized trials, EHR data are collected somewhat idiosyncratically. In particular, patients who have more contact with the medical system have more opportunities to receive diagnoses, which are then recorded in their EHRs. The goal of this article is to shed light on the nature and scope of this phenomenon, known as informative presence, which can bias estimates of associations. We show how this can be characterized as an instance of misclassification bias. As a consequence, we show that informative presence bias can occur in a broader range of settings than previously thought, and that simple adjustment for the number of visits as a confounder may not fully correct for bias. Additionally, where previous work has considered only underdiagnosis, investigators are often concerned about overdiagnosis; we show how this changes the settings in which bias manifests. We report on a comprehensive series of simulations to shed light on when to expect informative presence bias, how it can be mitigated in some cases, and cases in which new methods need to be developed.

OUP accepted manuscript

OBJECTIVE

Electronic health record (EHR)-derived data are extensively used in health research. However, the pattern of patient interaction with the healthcare system can result in informative presence bias if those who have poorer health have more data recorded than healthier patients. We aimed to determine how informative presence affects bias across multiple scenarios informed by real-world healthcare utilization patterns.

MATERIALS AND METHODS

We conducted an analysis of EHR data from a pediatric healthcare system as well as simulation studies to characterize conditions under which informative presence bias is likely to occur. This analysis extends prior work by examining a variety of scenarios for the relationship between a biomarker and a health event of interest and the healthcare visit process.

RESULTS

Using biomarker values gathered at both informative and noninformative visits when estimating the effect of the biomarker on the event of interest resulted in minimal bias when the biomarker was relatively stable over time but produced substantial bias when the biomarker was more volatile. Adjusting analyses for the number of prior visits within a fixed look-back window was able to reduce but not eliminate this bias.

DISCUSSION

These results suggest that bias may arise frequently in commonly encountered scenarios and may not be eliminated by adjusting for prior visit intensity.

CONCLUSION

Depending on the context, the estimated effect from analyses using data from all visits available may diverge from the true effect. Sensitivity analyses using only visits likely to be informative or noninformative based on visit type may aid in the assessment of the magnitude of potential bias.

A Latent Disease Model to Reduce Detection Bias in Cancer Risk Prediction Studies

In studies of cancer risk, detection bias arises when risk factors are associated with screening patterns, affecting the likelihood and timing of diagnosis. To eliminate detection bias in a screened cohort, we propose modeling the latent onset of cancer and estimating the association between risk factors and onset rather than diagnosis. We apply this framework to estimate the increase in prostate cancer risk associated with black race and family history using data from the SELECT prostate cancer prevention trial, in which men were screened and biopsied according to community practices. A positive family history was associated with a hazard ratio (HR) of prostate cancer onset of 1.8, lower than the corresponding HR of prostate cancer diagnosis (HR = 2.2). This result comports with a finding that men in SELECT with a family history were more likely to be biopsied following a positive PSA test than men with no family history. For black race, the HRs for onset and diagnosis were similar, consistent with similar patterns of screening and biopsy by race. If individual screening and diagnosis histories are available, latent disease modeling can be used to decouple risk of disease from risk of disease diagnosis and reduce detection bias.

Clustered longitudinal data subject to irregular observation

Data collected longitudinally as part of usual health care is becoming increasingly available for research, and is often available across several centres. Because the frequency of follow-up is typically determined by the patient's health, the timing of measurements may be related to the outcome of interest. Failure to account for the informative nature of the observation process can result in biased inferences. While methods for accounting for the association between observation frequency and outcome are available, they do not currently account for clustering within centres. We formulate a semi-parametric joint model to include random effects for centres as well as subjects. We also show how inverse-intensity weighted GEEs can be adapted to account for clustering, comparing stratification, frailty models, and covariate adjustment to account for clustering in the observation process. The finite-sample performance of the proposed methods is evaluated through simulation and the methods illustrated using a study of the relationship between outdoor play and air quality in children aged 2-9 living in the Greater Toronto Area.

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: Patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with health care data, such assumptions unlikely hold. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.

Accounting for Informative Sampling in Estimation of Associations between Sexually Transmitted Infections and Hormonal Contraceptive Methods

The relationship between hormonal contraceptive method use and sexually transmitted infections (STIs) is not well understood. Studies that implement routine screening for STIs among different contraceptive users, such as the ASPIRE HIV-1 prevention trial, can be useful for identifying potential risk factors of STIs. However, the complex nature of non-random data can lead to challenges in estimation of associations for potential risk factors. In particular, if screening for the disease is not random (i.e. it is driven by symptoms or other clinical indicators), estimates of association can suffer from bias, often referred to as informative sampling bias. Time-varying predictors and potential stratification variables can further contribute to difficulty in obtaining unbiased estimates. In this paper, we estimate the association between time-varying contraceptive use and STI acquisition, in the presence of informative sampling, by extending the work Buzkova (2010). We use a two-step procedure to jointly model the non-random screening process and sexually transmitted infection risk. In the first step, inverse intensity rate ratios (IIRR) weights are estimated. In the second step, a weighted proportional rate model is fit to estimate the IIRR weighted hazard ratio. We apply the method to evaluate the relationship between hormonal contraception and risk of sexually transmitted infections among women participating in a biomedical HIV-1 prevention trial. We compare our results using the proposed weighted method to those generated using conventional approaches that do not account for potential informative sampling bias or do not use the full potential of the data. Using the IIRR weighted approach we found DMPA users have a significantly decreased hazard of T. vaginalis acquisition compared to IUD users (HR: 0.44, 95% CI: (0.25, 0.83)), which is consistent with the literature. We did not find significant increased or decreased hazard of other STIs for hormonal contraceptive users compared to non-hormonal IUD users.

Independence conditions and the analysis of life history studies with intermittent observation

Multistate models provide a powerful framework for the analysis of life history processes when the goal is to characterize transition intensities, transition probabilities, state occupancy probabilities, and covariate effects thereon. Data on such processes are often only available at random visit times occurring over a finite period. We formulate a joint multistate model for the life history process, the recurrent visit process, and a random loss to follow-up time at which the visit process terminates. This joint model is helpful when discussing the independence conditions necessary to justify the use of standard likelihoods involving the life history model alone and provides a basis for analyses that accommodate dependence. We consider settings with disease-driven visits and routinely scheduled visits and develop likelihoods that accommodate partial information on the types of visits. Simulation studies suggest that suitably constructed joint models can yield consistent estimates of parameters of interest even under dependent visit processes, providing the models are correctly specified; identifiability and estimability issues are also discussed. An application is given to a cohort of individuals attending a rheumatology clinic where interest lies in progression of joint damage.

Challenges and Opportunities for Using Big Health Care Data to Advance Medical Science and Public Health

Methodological advancements in epidemiology, biostatistics, and data science have strengthened the research world's ability to use data captured from electronic health records (EHRs) to address pressing medical questions, but gaps remain. We describe methods investments that are needed to curate EHR data toward research quality and to integrate complementary data sources when EHR data alone are insufficient for research goals. We highlight new methods and directions for improving the integrity of medical evidence generated from pragmatic trials, observational studies, and predictive modeling. We also discuss needed methods contributions to further ease data sharing across multisite EHR data networks. Throughout, we identify opportunities for training and for bolstering collaboration among subject matter experts, methodologists, practicing clinicians, and health system leaders to help ensure that methods problems are identified and resulting advances are translated into mainstream research practice more quickly.

Nonparametric analysis of dependently interval-censored failure time data

Failure time studies based on observational cohorts often have to deal with irregular intermittent observation of individuals, which produces interval-censored failure times. When the observation times depend on factors related to a person's failure time, the failure times may be dependently interval censored. Inverse-intensity-of-visit weighting methods have been developed for irregularly observed longitudinal or repeated measures data and recently extended to parametric failure time analysis. This article develops nonparametric estimation of failure time distributions using weighted generalized estimating equations and monotone smoothing techniques. Simulations are conducted for examination of the finite sample performance of proposed estimators. This research is motivated in part by the Toronto Psoriatic Arthritis Cohort Study, and the proposed methodology is applied to this study.

Analysis of longitudinal data from outcome-dependent visit processes: Failure of proposed methods in realistic settings and potential improvements

The timing and frequency of the measurement of longitudinal outcomes in databases may be associated with the value of the outcome. Such visit processes are termed outcome dependent, and previous work showed that conducting standard analyses that ignore outcome-dependent visit times can produce highly biased estimates of the associations of covariates with outcomes. The literature contains several classes of approaches to analyze longitudinal data subject to outcome-dependent visit times, and all of these are based on simplifying assumptions about the visit process. Based on extensive discussions with subject matter investigators, we identified common characteristics of outcome-dependent visit processes that allowed us to evaluate the performance of existing methods in settings with more realistic visit processes than have been previously investigated. This paper uses the analysis of data from a study of kidney function, theory, and simulation studies to examine a range of settings that vary from those where all visits have a low degree of missingness and outcome dependence (which we call "regular" visits) to those where all visits have a high degree of missingness and outcome dependence (which we call "irregular" visits). Our results show that while all the approaches we studied can yield biased estimates of some covariate effects, other covariate effects can be estimated with little bias. In particular, mixed effects models fit by maximum likelihood yielded little bias in estimates of the effects of covariates not associated with the random effects and small bias in estimates of the effects of covariates associated with the random effects. Other approaches produced estimates with greater bias. Our results also show that the presence of some regular visits in the data set protects mixed model analyses from bias but not other methods.

Semiparametric estimation of the accelerated mean model with panel count data under informative examination times

Panel count data arise when the number of recurrent events experienced by each subject is observed intermittently at discrete examination times. The examination time process can be informative about the underlying recurrent event process even after conditioning on covariates. We consider a semiparametric accelerated mean model for the recurrent event process and allow the two processes to be correlated through a shared frailty. The regression parameters have a simple marginal interpretation of modifying the time scale of the cumulative mean function of the event process. A novel estimation procedure for the regression parameters and the baseline rate function is proposed based on a conditioning technique. In contrast to existing methods, the proposed method is robust in the sense that it requires neither the strong Poisson-type assumption for the underlying recurrent event process nor a parametric assumption on the distribution of the unobserved frailty. Moreover, the distribution of the examination time process is left unspecified, allowing for arbitrary dependence between the two processes. Asymptotic consistency of the estimator is established, and the variance of the estimator is estimated by a model-based smoothed bootstrap procedure. Numerical studies demonstrated that the proposed point estimator and variance estimator perform well with practical sample sizes. The methods are applied to data from a skin cancer chemoprevention trial.

Longitudinal studies that use data collected as part of usual care risk reporting biased results: a systematic review

BACKGROUND

Longitudinal studies using data collected as part of usual care risk providing biased results if visit times are related to the outcome of interest. Statistical methods for mitigating this bias are available but rarely used. This lack of use could be attributed to a lack of need or to a lack of awareness of the issue.

METHODS

We performed a systematic review of longitudinal studies that used data collected as part of patients' usual care and were published in MEDLINE or EMBASE databases between January 2005 through May 13^th 2015. We asked whether the extent of and reasons for variability in visit times were reported on, and in cases where there was a need to account for informativeness of visit times, whether an appropriate method was used.

RESULTS

Of 44 eligible articles, 57% (n = 25) reported on the total follow-up time, 7% (n = 3) on the gaps between visits, and 57% (n = 25) on the number of visits per patient; 78% (n = 34) reported on at least one of these. Two studies assessed predictors of visit times, and 86% of studies did not report enough information to assess whether there was a need to account for informative follow-up. Only one study used a method designed to account for informative visit times.

CONCLUSIONS

The low proportion of studies reporting on whether there were important predictors of visit times suggests that researchers are unaware of the potential for bias when data is collected as part of usual care and visit times are irregular. Guidance on the potential for bias and on the reporting of longitudinal studies subject to irregular follow-up is needed.

Estimation of state occupancy probabilities in multistate models with dependent intermittent observation, with application to HIV viral rebounds

In follow-up studies on chronic disease cohorts, individuals are often observed at irregular visit times that may be related to their previous disease history and other factors. This can produce bias in standard methods of estimation. Working in the context of multistate models, we consider a method of nonparametric estimation for state occupancy probabilities that adjusts for dependent follow-up through the use of inverse-intensity-of-visit weighted estimating functions and smoothing. The methodology is applied to the estimation of viral rebound probabilities in the Canadian Observational Cohort on HIV-positive persons. Copyright © 2016 John Wiley & Sons, Ltd.

Longitudinal data subject to irregular observation: A review of methods with a focus on visit processes, assumptions, and study design

When data are collected longitudinally, measurement times often vary among patients. This is of particular concern in clinic-based studies, for example retrospective chart reviews. Here, typically no two patients will share the same set of measurement times and moreover, it is likely that the timing of the measurements is associated with disease course; for example, patients may visit more often when unwell. While there are statistical methods that can help overcome the resulting bias, these make assumptions about the nature of the dependence between visit times and outcome processes, and the assumptions differ across methods. The purpose of this paper is to review the methods available with a particular focus on how the assumptions made line up with visit processes encountered in practice. Through this we show that no one method can handle all plausible visit scenarios and suggest that careful analysis of the visit process should inform the choice of analytic method for the outcomes. Moreover, there are some commonly encountered visit scenarios that are not handled well by any method, and we make recommendations with regard to study design that would minimize the chances of these problematic visit scenarios arising.

Quantile regression analysis of censored longitudinal data with irregular outcome-dependent follow-up

In many observational longitudinal studies, the outcome of interest presents a skewed distribution, is subject to censoring due to detection limit or other reasons, and is observed at irregular times that may follow a outcome-dependent pattern. In this work, we consider quantile regression modeling of such longitudinal data, because quantile regression is generally robust in handling skewed and censored outcomes and is flexible to accommodate dynamic covariate-outcome relationships. Specifically, we study a longitudinal quantile regression model that specifies covariate effects on the marginal quantiles of the longitudinal outcome. Such a model is easy to interpret and can accommodate dynamic outcome profile changes over time. We propose estimation and inference procedures that can appropriately account for censoring and irregular outcome-dependent follow-up. Our proposals can be readily implemented based on existing software for quantile regression. We establish the asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulations suggest good finite-sample performance of the new method. We also present an analysis of data from a long-term study of a population exposed to polybrominated biphenyls (PBB), which uncovers an inhomogeneous PBB elimination pattern that would not be detected by traditional longitudinal data analysis.

Regression modeling of longitudinal data with outcome-dependent observation times: extensions and comparative evaluation

Conventional longitudinal data analysis methods assume that outcomes are independent of the data-collection schedule. However, the independence assumption may be violated, for example, when a specific treatment necessitates a different follow-up schedule than the control arm or when adverse events trigger additional physician visits in between prescheduled follow-ups. Dependence between outcomes and observation times may introduce bias when estimating the marginal association of covariates on outcomes using a standard longitudinal regression model. We formulate a framework of outcome-observation dependence mechanisms to describe conditional independence given observed observation-time process covariates or shared latent variables. We compare four recently developed semi-parametric methods that accommodate one of these mechanisms. To allow greater flexibility, we extend these methods to accommodate a combination of mechanisms. In simulation studies, we show how incorrectly specifying the outcome-observation dependence may yield biased estimates of covariate-outcome associations and how our proposed extensions can accommodate a greater number of dependence mechanisms. We illustrate the implications of different modeling strategies in an application to bladder cancer data. In longitudinal studies with potentially outcome-dependent observation times, we recommend that analysts carefully explore the conditional independence mechanism between the outcome and observation-time processes to ensure valid inference regarding covariate-outcome associations.

Comparison of predictor approaches for longitudinal binary outcomes: application to anesthesiology data

Longitudinal data with binary repeated responses are now widespread among clinical studies and standard statistical analysis methods have become inadequate in the answering of clinical hypotheses. Instead of such conventional approaches, statisticians have started proposing better techniques, such as the Generalized Estimating Equations (GEE) approach and Generalized Linear Mixed Models (GLMM) technique. In this research, we undertook a comparative study of modeling binary repeated responses using an anesthesiology dataset which has 375 patient data with clinical variables. We modeled the relationship between hypotension and age, gender, surgical department, positions of patients during surgery, diastolic blood pressure, pulse, electrocardiography and doses of Marcain-heavy, chirocaine, fentanyl, and midazolam. Moreover, parameter estimates between the GEE and the GLMM were compared. The parameter estimates, except time-after, Marcain-Heavy, and Fentanyl from the GLMM, are larger than those from GEE. The standard errors from the GLMM are larger than those from GEE. GLMM appears to be more suitable approach than the GEE approach for the analysis hypotension during spinal anesthesia.

Time-varying latent effect model for longitudinal data with informative observation times

In analysis of longitudinal data, it is not uncommon that observation times of repeated measurements are subject-specific and correlated with underlying longitudinal outcomes. Taking account of the dependence between observation times and longitudinal outcomes is critical under these situations to assure the validity of statistical inference. In this article, we propose a flexible joint model for longitudinal data analysis in the presence of informative observation times. In particular, the new procedure considers the shared random-effect model and assumes a time-varying coefficient for the latent variable, allowing a flexible way of modeling longitudinal outcomes while adjusting their association with observation times. Estimating equations are developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. One additional advantage of the procedure is that it provides a unified framework to test whether the effect of the latent variable is zero, constant, or time-varying. Simulation studies show that the proposed approach is appropriate for practical use. An application to a bladder cancer data is also given to illustrate the methodology.

Longitudinal data analysis for generalized linear models under participant-driven informative follow-up: an application in maternal health epidemiology

It is common in longitudinal studies for scheduled visits to be accompanied by as-needed visits due to medical events occurring between scheduled visits. If the timing of these as-needed visits is related to factors that are associated with the outcome but are not among the regression model covariates, naively including these as-needed visits in the model yields biased estimates. In this paper, the authors illustrate and discuss the key issues pertaining to inverse intensity rate ratio (IIRR)-weighted generalized estimating equations (GEE) methods in the context of a study of Kenyan mothers infected with human immunodeficiency virus type 1 (1999-2005). The authors estimated prevalences and prevalence ratios for morbid conditions affecting the women during a 1-year postpartum follow-up period. Of the 484 women under study, 62% had at least 1 as-needed visit. Use of a standard GEE model including both scheduled and unscheduled visits predicted a pneumonia prevalence of 2.9% (95% confidence interval: 2.3%, 3.5%), while use of the IIRR-weighted GEE predicted a prevalence of 1.5% (95% confidence interval: 1.2%, 1.8%). The estimate obtained using the IIRR-weighted GEE approach was compatible with estimates derived using scheduled visits only. These results highlight the importance of properly accounting for informative follow-up in these studies.