Pattern mixture models for longitudinal quality of life studies in advanced stage disease

Analyses of longitudinal quality of life (QOL) for patients with advanced stage disease are frequently plagued by problems of non-random drop-out attributable to deteriorating health and/or death. As an example, Moinpour et al. cite specific challenges which limited their report and assessment of QOL for patients treated for advanced stage colorectal cancer in a clinical trial of several chemotherapeutic regimes performed by the Southwest Oncology Group. A particular source of confusion that arises in studies of advanced stage disease is whether or not to differentiate loss of follow-up due to death from drop-out where the patient is still alive but has dropped from the study. In this paper we examine exploratory data techniques for longitudinal QOL data with non-random missingness due to drop-out and censorship by death. We propose a pattern mixture model for longitudinal QOL, time of drop-out and survival, which allows for straightforward implementation of sensitivity analyses and explicit comparisons to the raw data. Our method is illustrated in the context of analysing the data and addressing the challenges posed by Moinpour et al.     

Time‐varying effect modeling with longitudinal data truncated by death: conditional models,interpretations, and inference

Recent studies found that infection‐related hospitalization was associated with increased risk of cardiovascular (CV) events, such as myocardial infarction and stroke in the dialysis population. In this work, we develop time‐varying effects modeling tools in order to examine the CV outcome risk trajectories during the time periods before and after an initial infection‐related hospitalization. For this, we propose partly conditional and fully conditional partially linear generalized varying coefficient models (PL‐GVCMs) for modeling time‐varying effects in longitudinal data with substantial follow‐up truncation by death. Unconditional models that implicitly target an immortal population is not a relevant target of inference in applications involving a population with high mortality, like the dialysis population. A partly conditional model characterizes the outcome trajectory for the dynamic cohort of survivors, where each point in the longitudinal trajectory represents a snapshot of the population relationships among subjects who are alive at that time point. In contrast, a fully conditional approach models the time‐varying effects of the population stratified by the actual time of death, where the mean response characterizes individual trends in each cohort stratum. We compare and contrast partly and fully conditional PL‐GVCMs in our aforementioned application using hospitalization data from the United States Renal Data System. For inference, we develop generalized likelihood ratio tests. Simulation studies examine the efficacy of estimation and inference procedures. Copyright © 2015 John Wiley & Sons, Ltd.     

Semiparametric regression models for repeated measures of mortal cohorts with non‐monotone missing outcomes and time‐dependent covariates

We propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non‐response to estimate regression parameters interpreted as conditioned on being alive. Our proposed method accommodates outcomes and time‐dependent covariates that are missing not at random with non‐monotone missingness patterns via inverse‐probability weighting. Missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse‐probability‐weighted estimating equation. Thus, we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates. The approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition, inflammation, and age. Copyright © 2010 John Wiley & Sons, Ltd.     

A dynamic trajectory class model for intensive longitudinal categorical outcome

This paper presents a novel dynamic latent class model for a longitudinal response that is frequently measured as in our prospective study of older adults with monthly data on activities of daily living for more than 10 years. The proposed method is especially useful when the longitudinal response is measured much more frequently than other relevant covariates. The trajectory classes are latent classes that represent distinct temporal patterns of the longitudinal response wherein an individual may remain in a trajectory class or switch to another as the class membership predictors are updated periodically over time. The identification of a common set of trajectory classes allows changes among the temporal patterns to be distinguished from local fluctuations in the response. Within a trajectory class, the longitudinal response is modeled by a class‐specific generalized linear mixed model. An informative event such as death is jointly modeled by class‐specific probability of the event through shared random effects with that for the longitudinal response. We do not impose the conditional independence assumption given the classes. We illustrate the method by analyzing the change over time in activities of daily living trajectory class among 754 older adults with 70,500 person‐months of follow‐up in the Precipitating Events Project. We also investigate the impact of jointly modeling the class‐specific probability of the event on the parameter estimates in a simulation study. The primary contribution of our paper is the periodic updating of trajectory classes for a longitudinal categorical response without assuming conditional independence. Copyright © 2014 John Wiley & Sons, Ltd.     

Joint modelling of longitudinal and multi‐state processes: application to clinical progressions in prostate cancer

Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate‐specific antigen (PSA) and time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post‐radiotherapy, or to predict the risk of one specific type of clinical recurrence post‐radiotherapy, from the PSA history. In this context, we present a joint model for a longitudinal process and a multi‐state process, which is divided into two sub‐models: a linear mixed sub‐model for longitudinal data and a multi‐state sub‐model with proportional hazards for transition times, both linked by a function of shared random effects. Parameters of this joint multi‐state model are estimated within the maximum likelihood framework using an EM algorithm coupled with a quasi‐Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer. Thanks to the classical covariates available at baseline and the repeated PSA measurements, we are able to assess the biomarker's trajectory, define the risks of transitions between health states and quantify the impact of the PSA dynamics on each transition intensity. Copyright © 2016 John Wiley & Sons, Ltd.     

Indirect estimation of a discrete‐state discrete‐time model using secondary data analysis of regression data

Multi‐state models of chronic disease are becoming increasingly important in medical research to describe the progression of complicated diseases. However, studies seldom observe health outcomes over long time periods. Therefore, current clinical research focuses on the secondary data analysis of the published literature to estimate a single transition probability within the entire model. Unfortunately, there are many difficulties when using secondary data, especially since the states and transitions of published studies may not be consistent with the proposed multi‐state model. Early approaches to reconciling published studies with the theoretical framework of a multi‐state model have been limited to data available as cumulative counts of progression. This paper presents an approach that allows the use of published regression data in a multi‐state model when the published study may have ignored intermediary states in the multi‐state model. Colloquially, we call this approach the Lemonade Method since when study data give you lemons, make lemonade. The approach uses maximum likelihood estimation. An example is provided for the progression of heart disease in people with diabetes. Copyright © 2009 John Wiley & Sons, Ltd.     

A marginal structural model for multiple‐outcome survival data:assessing the impact of injection drug use on several causes of death in the Canadian Co‐infection Cohort

It is often the case that interest lies in the effect of an exposure on each of several distinct event types. For example, we are motivated to investigate in the impact of recent injection drug use on deaths due to each of cancer, end‐stage liver disease, and overdose in the Canadian Co‐infection Cohort (CCC). We develop a marginal structural model that permits estimation of cause‐specific hazards in situations where more than one cause of death is of interest. Marginal structural models allow for the causal effect of treatment on outcome to be estimated using inverse‐probability weighting under the assumption of no unmeasured confounding; these models are particularly useful in the presence of time‐varying confounding variables, which may also mediate the effect of exposures. An asymptotic variance estimator is derived, and a cumulative incidence function estimator is given. We compare the performance of the proposed marginal structural model for multiple‐outcome data to that of conventional competing risks models in simulated data and demonstrate the use of the proposed approach in the CCC. Copyright © 2013 John Wiley & Sons, Ltd.     

A conditional estimating equation approach for recurrent event data with additional longitudinal information

Recurrent event data are quite common in biomedical and epidemiological studies. A significant portion of these data also contain additional longitudinal information on surrogate markers. Previous studies have shown that popular methods using a Cox model with longitudinal outcomes as time‐dependent covariates may lead to biased results, especially when longitudinal outcomes are measured with error. Hence, it is important to incorporate longitudinal information into the analysis properly. To achieve this, we model the correlation between longitudinal and recurrent event processes using latent random effect terms. We then propose a two‐stage conditional estimating equation approach to model the rate function of recurrent event process conditioned on the observed longitudinal information. The performance of our proposed approach is evaluated through simulation. We also apply the approach to analyze cocaine addiction data collected by the University of Connecticut Health Center. The data include recurrent event information on cocaine relapse and longitudinal cocaine craving scores. Copyright © 2016 John Wiley & Sons, Ltd.     

Blood pressure and the risk of chronic kidney disease progression using multistate marginal structural models in the CRIC Study

In patients with chronic kidney disease (CKD), clinical interest often centers on determining treatments and exposures that are causally related to renal progression. Analyses of longitudinal clinical data in this population are often complicated by clinical competing events, such as end‐stage renal disease (ESRD) and death, and time‐dependent confounding, where patient factors that are predictive of later exposures and outcomes are affected by past exposures. We developed multistate marginal structural models (MS‐MSMs) to assess the effect of time‐varying systolic blood pressure on disease progression in subjects with CKD. The multistate nature of the model allows us to jointly model disease progression characterized by changes in the estimated glomerular filtration rate (eGFR), the onset of ESRD, and death, and thereby avoid unnatural assumptions of death and ESRD as noninformative censoring events for subsequent changes in eGFR. We model the causal effect of systolic blood pressure on the probability of transitioning into 1 of 6 disease states given the current state. We use inverse probability weights with stabilization to account for potential time‐varying confounders, including past eGFR, total protein, serum creatinine, and hemoglobin. We apply the model to data from the Chronic Renal Insufficiency Cohort Study, a multisite observational study of patients with CKD.     

Model-based methodology for analyzing incomplete quality-of-life data and integrating them into the Q-TWiST framework.

BACKGROUND: The standard Q-TWiST approach defines a series of health states and weights each state's duration according to its quality of life (QOL) to calculate quality-adjusted lifetimes. However, a fixed weight may not adequately reflect time variations in QOL. METHODS: To account for measurements derived from irregular visits and informative missing data, the authors estimated the mean QOL profile using a mixed-effect growth curve model for the response, combined with a logistic regression model for the drop-out process. RESULTS: Using data from a clinical study of lymphoma patients, the authors demonstrated better readaptation to normal life for patients younger than 30. Sensitivity analyses and computer simulations demonstrated that modeling the drop-out probability as a function of the QOL measurements is necessary if conditioning by health state is not possible. CONCLUSION: Our model-based approach is useful to analyze studies with incomplete QOL data, especially when approximate QOL assessment by health state is not possible.     

Bayesian joint modeling of longitudinal and spatial survival AIDS data

Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for analyzing cancer and AIDS data. As both repeated measurements (longitudinal) and time‐to‐event (survival) outcomes are observed in an individual, a joint modeling is more appropriate because it takes into account the dependence between the two types of responses, which are often analyzed separately. We propose a Bayesian hierarchical model for jointly modeling longitudinal and survival data considering functional time and spatial frailty effects, respectively. That is, the proposed model deals with non‐linear longitudinal effects and spatial survival effects accounting for the unobserved heterogeneity among individuals living in the same region. This joint approach is applied to a cohort study of patients with HIV/AIDS in Brazil during the years 2002–2006. Our Bayesian joint model presents considerable improvements in the estimation of survival times of the Brazilian HIV/AIDS patients when compared with those obtained through a separate survival model and shows that the spatial risk of death is the same across the different Brazilian states. Copyright © 2016 John Wiley & Sons, Ltd.     

Time‐varying effect moderation using the structural nested mean model: estimation using inverse‐weighted regression with residuals

This article considers the problem of examining time‐varying causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and possible confounders are time varying. The structural nested mean model (SNMM) is used to specify the moderated time‐varying causal effects of interest in a conditional mean model for a continuous response given time‐varying treatments and moderators. We present an easy‐to‐use estimator of the SNMM that combines an existing regression‐with‐residuals (RR) approach with an inverse‐probability‐of‐treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time‐varying causal effects if the time‐varying moderators are also the sole time‐varying confounders. The proposed IPTW+RR approach provides estimators of the moderated time‐varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured time‐varying confounders. We use a small simulation experiment to compare IPTW+RR versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time‐varying moderators and time‐varying confounders. We illustrate the methodology in a case study to assess if time‐varying substance use moderates treatment effects on future substance use. Copyright © 2013 John Wiley & Sons, Ltd.     

A new linear model‐based approach for inferences about the mean area under the curve

Outcome versus time data are commonly encountered in biomedical and clinical research. A common strategy adopted in analyzing such longitudinal data is to condense the repeated measurements on each individual into a single summary statistic such as the area under the response versus time curve. Standard parametric or non‐parametric methods are then applied to perform inferences on the conditional area under the curve distribution. Disadvantages of this approach include the disregard of the within‐subject variation in the longitudinal profile. We propose a general linear model approach, accounting for the within‐subject variance, for estimation and hypothesis tests about the mean areas. Inferential properties of our approach are compared with those from standard methods of analysis using Monte Carlo simulation studies. The impact of missing data, within‐subject heterogeneity and homogeneity of variance, are also evaluated. A real working example is used to illustrate the methodology. It is seen that the proposed approach is associated with a significant power advantage over traditional methods, especially when missing data are encountered. Copyright © 2012 John Wiley & Sons, Ltd.     

Multi‐state models for colon cancer recurrence and death with a cured fraction

In cancer clinical trials, patients often experience a recurrence of disease prior to the outcome of interest, overall survival. Additionally, for many cancers, there is a cured fraction of the population who will never experience a recurrence. There is often interest in how different covariates affect the probability of being cured of disease and the time to recurrence, time to death, and time to death after recurrence. We propose a multi‐state Markov model with an incorporated cured fraction to jointly model recurrence and death in colon cancer. A Bayesian estimation strategy is used to obtain parameter estimates. The model can be used to assess how individual covariates affect the probability of being cured and each of the transition rates. Checks for the adequacy of the model fit and for the functional forms of covariates are explored. The methods are applied to data from 12 randomized trials in colon cancer, where we show common effects of specific covariates across the trials. Copyright © 2013 John Wiley & Sons, Ltd.     

A semiparametric joint model for terminal trend of quality of life and survival in palliative care research

Palliative medicine is an interdisciplinary specialty focusing on improving quality of life (QOL) for patients with serious illness and their families. Palliative care programs are available or under development at over 80% of large US hospitals (300+ beds). Palliative care clinical trials present unique analytic challenges relative to evaluating the palliative care treatment efficacy which is to improve patients’ diminishing QOL as disease progresses towards end of life (EOL). A unique feature of palliative care clinical trials is that patients will experience decreasing QOL during the trial despite potentially beneficial treatment. Often longitudinal QOL and survival data are highly correlated which, in the face of censoring, makes it challenging to properly analyze and interpret terminal QOL trend. To address these issues, we propose a novel semiparametric statistical approach to jointly model the terminal trend of QOL and survival data. There are two sub‐models in our approach: a semiparametric mixed effects model for longitudinal QOL and a Cox model for survival. We use regression splines method to estimate the nonparametric curves and AIC to select knots. We assess the model performance through simulation to establish a novel modeling approach that could be used in future palliative care research trials. Application of our approach in a recently completed palliative care clinical trial is also presented.     

Joint modeling of repeated multivariate cognitive measures and competing risks of dementia and death: a latent process and latent class approach

Joint models initially dedicated to a single longitudinal marker and a single time‐to‐event need to be extended to account for the rich longitudinal data of cohort studies. Multiple causes of clinical progression are indeed usually observed, and multiple longitudinal markers are collected when the true latent trait of interest is hard to capture (e.g., quality of life, functional dependency, and cognitive level). These multivariate and longitudinal data also usually have nonstandard distributions (discrete, asymmetric, bounded, etc.). We propose a joint model based on a latent process and latent classes to analyze simultaneously such multiple longitudinal markers of different natures, and multiple causes of progression. A latent process model describes the latent trait of interest and links it to the observed longitudinal outcomes using flexible measurement models adapted to different types of data, and a latent class structure links the longitudinal and cause‐specific survival models. The joint model is estimated in the maximum likelihood framework. A score test is developed to evaluate the assumption of conditional independence of the longitudinal markers and each cause of progression given the latent classes. In addition, individual dynamic cumulative incidences of each cause of progression based on the repeated marker data are derived. The methodology is validated in a simulation study and applied on real data about cognitive aging obtained from a large population‐based study. The aim is to predict the risk of dementia by accounting for the competing death according to the profiles of semantic memory measured by two asymmetric psychometric tests. Copyright © 2015 John Wiley & Sons, Ltd.     

Joint modeling of missing data due to non‐participation and death in longitudinal aging studies

Specific age‐related hypotheses are tested in population‐based longitudinal studies. At specific time intervals, both the outcomes of interest and the time‐varying covariates are measured. When participants are approached for follow‐up, some participants do not provide data. Investigations may show that many have died before the time of follow‐up whereas others refused to participate. Some of these non‐participants do not provide data at later follow‐ups. Few statistical methods for missing data distinguish between ‘non‐participation’ and ‘death’ among study participants. The augmented inverse probability‐weighted estimators are most commonly used in marginal structure models when data are missing at random. Treating non‐participation and death as the same, however, may lead to biased estimates and invalid inferences. To overcome this limitation, a multiple inverse probability‐weighted approach is presented to account for two types of missing data, non‐participation and death, when using a marginal mean model. Under certain conditions, the multiple weighted estimators are consistent and asymptotically normal. Simulation studies will be used to study the finite sample efficiency of the multiple weighted estimators. The proposed method will be applied to study the risk factors associated with the cognitive decline among the aging adults, using data from the Chicago Health and Aging Project (CHAP). Copyright © 2010 John Wiley & Sons, Ltd.     

Power calculations for delta‐adjusted pattern‐mixture models

Pattern‐mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data in longitudinal studies. The delta‐adjusted pattern‐mixture models handle missing data in a clinically interpretable manner and have been used as sensitivity analyses addressing the effectiveness hypothesis, while a likelihood‐based approach that assumes data are missing at random is often used as the primary analysis addressing the efficacy hypothesis. We describe a method for power calculations for delta‐adjusted pattern‐mixture model sensitivity analyses in confirmatory clinical trials. To apply the method, we only need to specify the pattern probabilities at postbaseline time points, the expected treatment differences at postbaseline time points, the conditional covariance matrix of postbaseline measurements given the baseline measurement, and the delta‐adjustment method for the pattern‐mixture model. We use an example to illustrate and compare various delta‐adjusted pattern‐mixture models and use simulations to confirm the analytic results. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimating cumulative probabilities from incomplete longitudinal binary responses with application to HIV vaccine trials

When describing longitudinal binary response data, it may be desirable to estimate the cumulative probability of at least one positive response by some time point. For example, in phase I and II human immunodeficiency virus (HIV) vaccine trials, investigators are often interested in the probability of at least one vaccine-induced CD8+ cytotoxic T-lymphocyte (CTL) response to HIV proteins at different times over the course of the trial. In this setting, traditional estimates of the cumulative probabilities have been based on observed proportions. We show that if the missing data mechanism is ignorable, the traditional estimator of the cumulative success probabilities is biased and tends to underestimate a candidate vaccine's ability to induce CTL responses. As an alternative, we propose applying standard optimization techniques to obtain maximum likelihood estimates of the response profiles and, in turn, the cumulative probabilities of interest. Comparisons of the empirical and maximum likelihood estimates are investigated using data from simulations and HIV vaccine trials. We conclude that maximum likelihood offers a more accurate method of estimation, which is especially important in the HIV vaccine setting as cumulative CTL responses will likely be used as a key criterion for large scale efficacy trial qualification.     

Multi‐state Markov models for disease progression in the presence of informative examination times: An application to hepatitis C

In many chronic diseases it is important to understand the rate at which patients progress from infection through a series of defined disease states to a clinical outcome, e.g. cirrhosis in hepatitis C virus (HCV)‐infected individuals or AIDS in HIV‐infected individuals. Typically data are obtained from longitudinal studies, which often are observational in nature, and where disease state is observed only at selected examinations throughout follow‐up. Transition times between disease states are therefore interval censored. Multi‐state Markov models are commonly used to analyze such data, but rely on the assumption that the examination times are non‐informative, and hence the examination process is ignorable in a likelihood‐based analysis. In this paper we develop a Markov model that relaxes this assumption through the premise that the examination process is ignorable only after conditioning on a more regularly observed auxiliary variable. This situation arises in a study of HCV disease progression, where liver biopsies (the examinations) are sparse, irregular, and potentially informative with respect to the transition times. We use additional information on liver function tests (LFTs), commonly collected throughout follow‐up, to inform current disease state and to assume an ignorable examination process. The model developed has a similar structure to a hidden Markov model and accommodates both the series of LFT measurements and the partially latent series of disease states. We show through simulation how this model compares with the commonly used ignorable Markov model, and a Markov model that assumes the examination process is non‐ignorable. Copyright © 2010 John Wiley & Sons, Ltd.