Joint calibrated estimation of inverse probability of treatment and censoring weights for marginal structural models.

Marginal structural models (MSMs) with inverse probability weighted estimators (IPWEs) are widely used to estimate causal effects of treatment sequences on longitudinal outcomes in the presence of time-varying confounding and dependent censoring. However, IPWEs for MSMs can be inefficient and unstable if weights are estimated by maximum likelihood. To improve the performance of IPWEs, covariate balancing weight (CBW) methods have been proposed and recently extended to MSMs. However, existing CBW methods for MSMs are inflexible for practical use because they often do not handle dependent censoring, nonbinary treatments, and longitudinal outcomes (instead of eventual outcomes at a study end). In this paper, we propose a joint calibration approach to CBW estimation for MSMs that can accommodate (1) both time-varying confounding and dependent censoring, (2) binary and nonbinary treatments, (3) eventual outcomes and longitudinal outcomes. We develop novel calibration restrictions by jointly eliminating covariate associations with both treatment assignment and censoring processes after weighting the observed data sample (i.e., to optimize covariate balance in finite samples). Two different methods are proposed to implement the calibration. Simulations show that IPWEs with calibrated weights perform better than IPWEs with weights from maximum likelihood and the "Covariate Balancing Propensity Score" method. We apply our method to a natural history study of HIV for estimating the effects of highly active antiretroviral therapy on CD4 cell counts over time.

Standard and reference-based conditional mean imputation.

Clinical trials with longitudinal outcomes typically include missing data due to missed assessments or structural missingness of outcomes after intercurrent events handled with a hypothetical strategy. Approaches based on Bayesian random multiple imputation and Rubin's rules for pooling results across multiple imputed data sets are increasingly used in order to align the analysis of these trials with the targeted estimand. We propose and justify deterministic conditional mean imputation combined with the jackknife for inference as an alternative approach. The method is applicable to imputations under a missing-at-random assumption as well as for reference-based imputation approaches. In an application and a simulation study, we demonstrate that it provides consistent treatment effect estimates with the Bayesian approach and reliable frequentist inference with accurate standard error estimation and type I error control. A further advantage of the method is that it does not rely on random sampling and is therefore replicable and unaffected by Monte Carlo error.

A joint modelling approach for multistate processes subject to resolution and under intermittent observations.

Multistate processes provide a convenient framework when interest lies in characterising the transition intensities between a set of defined states. If, however, there is an unobserved event of interest (not known if and when the event occurs), which when it occurs stops future transitions in the multistate process from occurring, then drawing inference from the joint multistate and event process can be problematic. In health studies, a particular example of this could be resolution, where a resolved patient can no longer experience any further symptoms, and this is explored here for illustration. A multistate model that includes the state space of the original multistate process but partitions the state representing absent symptoms into a latent absorbing resolved state and a temporary transient state of absent symptoms is proposed. The expanded state space explicitly distinguishes between resolved and temporary spells of absent symptoms through disjoint states and allows the uncertainty of not knowing if resolution has occurred to be easily captured when constructing the likelihood; observations of absent symptoms can be considered to be temporary or having resulted from resolution. The proposed methodology is illustrated on a psoriatic arthritis data set where the outcome of interest is a set of intermittently observed disability scores. Estimated probabilities of resolving are also obtained from the model. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Trivariate mover-stayer counting process models for investigating joint damage in psoriatic arthritis.

In psoriatic arthritis, many patients do not develop permanent joint damage even after a prolonged follow-up. This has led several authors to consider the possibility of a subpopulation of stayers (those who do not have the propensity to experience the event of interest), as opposed to assuming the entire population consist of movers (those who have the propensity to experience the event of interest). In addition, it is recognised that the damaged joints process may act very differently across different joint areas, particularly the hands, feet and large joints. From a clinical perspective, interest lies in identifying possible relationships between the damaged joints processes in these joint areas for the movers and estimating the proportion of stayers in these joint areas, if they exist. For this purpose, this paper proposes a novel trivariate mover-stayer model consisting of mover-stayer truncated negative binomial margins, and patient-level dynamic covariates and random effects in the models for the movers and stayers, respectively. The model is then extended to have a two-level mover-stayer structure for its margins so that the nature of the stayer property can be investigated. A particularly attractive feature of the proposed models is that only an optimisation routine is required in their model fitting procedures. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Estimating drug concentration-response relationships by applying causal inference methods for continuous point exposures and time-to-event outcomes.

In clinical development, it is useful to characterize the causal relationship between individual drug concentrations and clinical outcomes in large phase III trials of new therapeutic agents because it can provide insights on whether increasing the currently administered drug dose may lead to better outcomes. However, estimating causal effects of drug concentration is complicated by the fact that drug concentration is a continuous measure and it is usually influenced by patient-level prognostic characteristics such as body weight and sex. In this article, we compare two approaches to estimate causal effects of continuous point exposures on time-to-event outcomes: (a) outcome regression (OR) and (b) weighting. In particular, we make the first direct comparison of the balancing weights, inverse probability weighting and OR methods for estimating the effects of continuous exposures on time-to-event outcomes in simulations and demonstrate that these methods can exhibit markedly different behaviours that subsequently lead to a change in the conclusions. To improve weighted exposure effect estimators, we also propose a new simple-to-apply diagnostic to detect when such estimators might be subject to severe bias, and demonstrate its effectiveness in simulations. Finally, we apply these methods to an example of multiple sclerosis drug development by providing causal effect estimates of average ocrelizumab concentrations on time-to-event disability progression outcomes.

Sensitivity analysis for calibrated inverse probability-of-censoring weighted estimators under non-ignorable dropout.

Inverse probability of censoring weighting is a popular approach to handling dropout in longitudinal studies. However, inverse probability-of-censoring weighted estimators (IPCWEs) can be inefficient and unstable if the weights are estimated by maximum likelihood. To alleviate these problems, calibrated IPCWEs have been proposed, which use calibrated weights that directly optimize covariate balance in finite samples rather than the weights from maximum likelihood. However, the existing calibrated IPCWEs are all based on the unverifiable assumption of sequential ignorability and sensitivity analysis strategies under non-ignorable dropout are lacking. In this paper, we fill this gap by developing an approach to sensitivity analysis for calibrated IPCWEs under non-ignorable dropout. A simple technique is proposed to speed up the computation of bootstrap and jackknife confidence intervals and thus facilitate sensitivity analyses. We evaluate the finite-sample performance of the proposed methods using simulations and apply our methods to data from an international inception cohort study of systemic lupus erythematosus. An R Markdown tutorial to demonstrate the implementation of the proposed methods is provided.

Predictors of treatment response in a lupus nephritis population: lessons from the Aspreva Lupus Management Study (ALMS) trial.

OBJECTIVES: To identify predictors of overall lupus and lupus nephritis (LN) responses in patients with LN. METHODS: Data from the Aspreva Lupus Management Study (ALMS) trial cohort was used to identify baseline predictors of response at 6 months. Endpoints were major clinical response (MCR), improvement, complete renal response (CRR) and partial renal response (PRR). Univariate and multivariate logistic regressions with least absolute shrinkage and selection operator (LASSO) and cross-validation in randomly split samples were utilised. Predictors were ranked by the percentage of times selected by LASSO and prediction performance was assessed by the area under the receiver operating characteristics (AUROC) curve. RESULTS: We studied 370 patients in the ALMS induction trial. Improvement at 6 months was associated with older age (OR=1.03 (95% CI: 1.01 to 1.05) per year), normal haemoglobin (1.85 (1.16 to 2.95) vs low haemoglobin), active lupus (British Isles Lupus Assessment Group A or B) in haematological and mucocutaneous domains (0.61 (0.39 to 0.97) and 0.50 (0.31 to 0.81)), baseline damage (SDI>1 vs =0) (0.38 (0.16 to 0.91)) and 24-hour urine protein (0.63 (0.50 to 0.80)). LN duration 2-4 years (0.43 (0.19 to 0.97) vs <1 year) and 24-hour urine protein (0.63 (0.45 to 0.89)) were negative predictors of CRR. LN duration 2-4 years (0.45 (0.24 to 0.83) vs <1 year) negatively predicted PRR. The AUROCs of models for improvement, CRR and PRR were 0.56, 0.55 and 0.51 respectively. CONCLUSIONS: Baseline variables predicted 6-month outcomes in patients with SLE. While the modest performance of models emphasises the need for new biomarkers to advance this field, the factors identified can help identify those patients who may require novel treatment strategies.

Covariate association eliminating weights: a unified weighting framework for causal effect estimation.

Weighting methods offer an approach to estimating causal treatment effects in observational studies. However, if weights are estimated by maximum likelihood, misspecification of the treatment assignment model can lead to weighted estimators with substantial bias and variance. In this paper, we propose a unified framework for constructing weights such that a set of measured pretreatment covariates is unassociated with treatment assignment after weighting. We derive conditions for weight estimation by eliminating the associations between these covariates and treatment assignment characterized in a chosen treatment assignment model after weighting. The moment conditions in covariate balancing weight methods for binary, categorical and continuous treatments in cross-sectional settings are special cases of the conditions in our framework, which extends to longitudinal settings. Simulation shows that our method gives treatment effect estimates with smaller biases and variances than the maximum likelihood approach under treatment assignment model misspecification. We illustrate our method with an application to systemic lupus erythematosus data.

Two-part models with stochastic processes for modelling longitudinal semicontinuous data: Computationally efficient inference and modelling the overall marginal mean.

Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.

Clustered multistate models with observation level random effects, mover-stayer effects and dynamic covariates: modelling transition intensities and sojourn times in a study of psoriatic arthritis.

In psoriatic arthritis, it is important to understand the joint activity (represented by swelling and pain) and damage processes because both are related to severe physical disability. The paper aims to provide a comprehensive investigation into both processes occurring over time, in particular their relationship, by specifying a joint multistate model at the individual hand joint level, which also accounts for many of their important features. As there are multiple hand joints, such an analysis will be based on the use of clustered multistate models. Here we consider an observation level random-effects structure with dynamic covariates and allow for the possibility that a subpopulation of patients is at minimal risk of damage. Such an analysis is found to provide further understanding of the activity-damage relationship beyond that provided by previous analyses. Consideration is also given to the modelling of mean sojourn times and jump probabilities. In particular, a novel model parameterization which allows easily interpretable covariate effects to act on these quantities is proposed.

Exploring the existence of a stayer population with mover-stayer counting process models: application to joint damage in psoriatic arthritis.

Many psoriatic arthritis patients do not progress to permanent joint damage in any of the 28 hand joints, even under prolonged follow-up. This has led several researchers to fit models that estimate the proportion of stayers (those who do not have the propensity to experience the event of interest) and to characterize the rate of developing damaged joints in the movers (those who have the propensity to experience the event of interest). However, when fitted to the same data, the paper demonstrates that the choice of model for the movers can lead to widely varying conclusions on a stayer population, thus implying that, if interest lies in a stayer population, a single analysis should not generally be adopted. The aim of the paper is to provide greater understanding regarding estimation of a stayer population by comparing the inferences, performance and features of multiple fitted models to real and simulated data sets. The models for the movers are based on Poisson processes with patient level random effects and/or dynamic covariates, which are used to induce within-patient correlation, and observation level random effects are used to account for time varying unobserved heterogeneity. The gamma, inverse Gaussian and compound Poisson distributions are considered for the random effects.