Semiparametric modeling of repeated measurements under outcome‐dependent follow‐up

In regression analysis of repeated measurements that are taken at subject‐specific times, the availability of the outcome data may be related to the past outcome and to other measured variables that are not in the intended regression model. In this paper we propose a natural extension of the semiparametric regression procedure of Lin and Ying (J. Am. Stat. Assoc. 2001; 96 :103–126) by building a class of ‘inverse‐intensity‐rate‐ratio’ weighted estimators that accommodate such outcome‐dependent follow‐up. The estimators have a closed form, are √n‐consistent, asymptotically normal, and do not require estimation of any infinite‐dimensional parameters. We give several simulations to demonstrate the estimator's performance and show a sensitivity study under follow‐up with various degrees of dependence on outcome‐related variables. We illustrate our approach using data from a randomized health services research study with noncompliance to scheduled visits. Copyright © 2008 John Wiley & Sons, Ltd.     

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. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of parametric failure time distributions based on interval‐censored data with irregular dependent follow‐up

Event history studies based on disease clinic data often face several complications. Specifically, patients may visit the clinic irregularly, and the intermittent observation times could depend on disease‐related variables; this can cause a failure time outcome to be dependently interval‐censored. We propose a weighted estimating function approach so that dependently interval‐censored failure times can be analysed consistently. A so‐called inverse‐intensity‐of‐visit weight is employed to adjust for the informative inspection times. Left truncation of failure times can also be easily handled. Additionally, in observational studies, treatment assignments are typically non‐randomized and may depend on disease‐related variables. An inverse‐probability‐of‐treatment weight is applied to estimating functions to further adjust for measured confounders. Simulation studies are conducted to examine the finite sample performances of the proposed estimators. Finally, the Toronto Psoriatic Arthritis Cohort Study is used for illustration. Copyright © 2017 John Wiley & Sons, Ltd.     

Parental satisfaction with follow‐up services for children with major anatomical congenital anomalies

Background Since 1999 a multidisciplinary follow‐up programme for parents and children with major anatomical congenital anomalies is in place in our hospital, run by a dedicated team. The aim of the present study was to evaluate the services of this team from a parental perspective. Methods Parents completed a questionnaire including open and closed questions about satisfaction with the various professional disciplines involved in the follow‐up, statements on usefulness of the follow‐up services and suggestions for improvement. Results Four hundred and sixty‐nine surveys were sent out, of which 71% were returned. Non‐responding parents included significantly more parents of non‐Dutch origin (P= 0.038) and parents who never responded to invitations for follow‐up examinations (P < 0.001). Parental satisfaction differed for the various disciplines. Eighty per cent of the parents were (very) satisfied with the social worker, compared with 92% with nurses. More than half of the parents agreed that the follow‐up services give peace of mind. Almost a quarter of parents, however, considered the follow‐up services as redundant. The children of these parents had significantly shorter intensive care unit stay (P= 0.02), were older at the time of the questionnaire (P= 0.04), of higher socio‐economic status (P= 0.001) and less likely to be of non‐Dutch origin (P= 0.008). Sixty‐one per cent of the parents had contacted the 24‐h helpline. Ninety per cent of the parents were satisfied with the intensive care unit, almost 80% with the general ward. Conclusion Overall, parents were satisfied with the services of the follow‐up team. Some parents, however, saw room for improvement related to better communication, recognizability of the team and better planning and organization.     

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.     

Distribution‐free models for longitudinal count responses with overdispersion and structural zeros

Overdispersion and structural zeros are two major manifestations of departure from the Poisson assumption when modeling count responses using Poisson log‐linear regression. As noted in a large body of literature, ignoring such departures could yield bias and lead to wrong conclusions. Different approaches have been developed to tackle these two major problems. In this paper, we review available methods for dealing with overdispersion and structural zeros within a longitudinal data setting and propose a distribution‐free modeling approach to address the limitations of these methods by utilizing a new class of functional response models. We illustrate our approach with both simulated and real study data. Copyright © 2012 John Wiley & Sons, Ltd.     

Generalized survival models for correlated time‐to‐event data

Our aim is to develop a rich and coherent framework for modeling correlated time‐to‐event data, including (1) survival regression models with different links and (2) flexible modeling for time‐dependent and nonlinear effects with rich postestimation. We extend the class of generalized survival models, which expresses a transformed survival in terms of a linear predictor, by incorporating a shared frailty or random effects for correlated survival data. The proposed approach can include parametric or penalized smooth functions for time, time‐dependent effects, nonlinear effects, and their interactions. The maximum (penalized) marginal likelihood method is used to estimate the regression coefficients and the variance for the frailty or random effects. The optimal smoothing parameters for the penalized marginal likelihood estimation can be automatically selected by a likelihood‐based cross‐validation criterion. For models with normal random effects, Gauss‐Hermite quadrature can be used to obtain the cluster‐level marginal likelihoods. The Akaike Information Criterion can be used to compare models and select the link function. We have implemented these methods in the R package rstpm2. Simulating for both small and larger clusters, we find that this approach performs well. Through 2 applications, we demonstrate (1) a comparison of proportional hazards and proportional odds models with random effects for clustered survival data and (2) the estimation of time‐varying effects on the log‐time scale, age‐varying effects for a specific treatment, and two‐dimensional splines for time and age.     

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.     

Non‐ignorable loss to follow‐up: correcting mortality estimates based on additional outcome ascertainment

Loss to follow‐up (LTFU) is a common problem in many epidemiological studies. In antiretroviral treatment (ART) programs for patients with human immunodeficiency virus (HIV), mortality estimates can be biased if the LTFU mechanism is non‐ignorable, that is, mortality differs between lost and retained patients. In this setting, routine procedures for handling missing data may lead to biased estimates. To appropriately deal with non‐ignorable LTFU, explicit modeling of the missing data mechanism is needed. This can be based on additional outcome ascertainment for a sample of patients LTFU, for example, through linkage to national registries or through survey‐based methods. In this paper, we demonstrate how this additional information can be used to construct estimators based on inverse probability weights (IPW) or multiple imputation. We use simulations to contrast the performance of the proposed estimators with methods widely used in HIV cohort research for dealing with missing data. The practical implications of our approach are illustrated using South African ART data, which are partially linkable to South African national vital registration data. Our results demonstrate that while IPWs and proper imputation procedures can be easily constructed from additional outcome ascertainment to obtain valid overall estimates, neglecting non‐ignorable LTFU can result in substantial bias. We believe the proposed estimators are readily applicable to a growing number of studies where LTFU is appreciable, but additional outcome data are available through linkage or surveys of patients LTFU. Copyright © 2013 John Wiley & Sons, Ltd.     

On performance of parametric and distribution‐free models for zero‐inflated and over‐dispersed count responses

Zero‐inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero‐inflated count responses. These models extend the Poisson and negative binomial (NB) to address excessive zeros in the count response. By adding a degenerate distribution centered at 0 and interpreting it as describing a non‐risk group in the population, the ZIP (ZINB) models a two‐component population mixture. As in applications of Poisson and NB, the key difference between ZIP and ZINB is the allowance for overdispersion by the ZINB in its NB component in modeling the count response for the at‐risk group. Overdispersion arising in practice too often does not follow the NB, and applications of ZINB to such data yield invalid inference. If sources of overdispersion are known, other parametric models may be used to directly model the overdispersion. Such models too are subject to assumed distributions. Further, this approach may not be applicable if information about the sources of overdispersion is unavailable. In this paper, we propose a distribution‐free alternative and compare its performance with these popular parametric models as well as a moment‐based approach proposed by Yu et al. [Statistics in Medicine 2013; 32 : 2390–2405]. Like the generalized estimating equations, the proposed approach requires no elaborate distribution assumptions. Compared with the approach of Yu et al., it is more robust to overdispersed zero‐inflated responses. We illustrate our approach with both simulated and real study data. Copyright © 2015 John Wiley & Sons, Ltd.     

Estimating the efficacy of an interstitial cystitis/painful bladder syndrome medication in a randomized trial with both non‐adherence and loss to follow‐up

We are motivated by a randomized clinical trial evaluating the efficacy of amitriptyline for the treatment of interstitial cystitis and painful bladder syndrome in treatment‐naïve patients. In the trial, both the non‐adherence rate and the rate of loss to follow‐up are fairly high. To estimate the effect of the treatment received on the outcome, we use the generalized structural mean model (GSMM), originally proposed to deal with non‐adherence, to adjust for both non‐adherence and loss to follow‐up. In the model, loss to follow‐up is handled by weighting the estimation equations for GSMM with one over the probability of not being lost to follow‐up, estimated using a logistic regression model. We re‐analyzed the data from the trial and found a possible benefit of amitriptyline when administered at a high‐dose level. Copyright © 2012 John Wiley & Sons, Ltd.     

Marginalized multilevel hurdle and zero‐inflated models for overdispersed and correlated count data with excess zeros

Count data are collected repeatedly over time in many applications, such as biology, epidemiology, and public health. Such data are often characterized by the following three features. First, correlation due to the repeated measures is usually accounted for using subject‐specific random effects, which are assumed to be normally distributed. Second, the sample variance may exceed the mean, and hence, the theoretical mean–variance relationship is violated, leading to overdispersion. This is usually allowed for based on a hierarchical approach, combining a Poisson model with gamma distributed random effects. Third, an excess of zeros beyond what standard count distributions can predict is often handled by either the hurdle or the zero‐inflated model. A zero‐inflated model assumes two processes as sources of zeros and combines a count distribution with a discrete point mass as a mixture, while the hurdle model separately handles zero observations and positive counts, where then a truncated‐at‐zero count distribution is used for the non‐zero state. In practice, however, all these three features can appear simultaneously. Hence, a modeling framework that incorporates all three is necessary, and this presents challenges for the data analysis. Such models, when conditionally specified, will naturally have a subject‐specific interpretation. However, adopting their purposefully modified marginalized versions leads to a direct marginal or population‐averaged interpretation for parameter estimates of covariate effects, which is the primary interest in many applications. In this paper, we present a marginalized hurdle model and a marginalized zero‐inflated model for correlated and overdispersed count data with excess zero observations and then illustrate these further with two case studies. The first dataset focuses on the Anopheles mosquito density around a hydroelectric dam, while adolescents’ involvement in work, to earn money and support their families or themselves, is studied in the second example. Sub‐models, which result from omitting zero‐inflation and/or overdispersion features, are also considered for comparison's purpose. Analysis of the two datasets showed that accounting for the correlation, overdispersion, and excess zeros simultaneously resulted in a better fit to the data and, more importantly, that omission of any of them leads to incorrect marginal inference and erroneous conclusions about covariate effects. Copyright © 2014 John Wiley & Sons, Ltd.     

Adherence to medical follow‐up recommendations reduces hospital admissions: Evidence from diabetic patients in France

The aim of this study was to document the extent to which diabetic patients who adhered to required medical follow‐ups in France experienced reduced hospital admissions over time. The main assumption was that enhanced monitoring and follow‐up of diabetic patients in the primary care setting could be a substitute for hospital use. Using longitudinal claim data of diabetic patients between 2010 and 2015 from MGEN, a leading mutuelle insurance company in France, we estimated a dynamic logit model with lagged measures of the quality of adherence to eight medical follow‐up recommendations. This model allowed us to disentangle follow‐up care in hospitals from other forms of inpatient care that could occur simultaneously. We found that a higher adherence to medical guidance is associated with a lower probability of hospitalization and that the take‐up of each of the eight recommendations may help reduce the rates of hospital admission. The reasons for the variation in patient adherence and implications for health policy are discussed.