Continuous Time Markov Models for Binary Longitudinal Data

Bayesian Analysis of First-Order Markov Models for Autocorrelated Binary Responses

In many clinical trials, patient outcomes are often binary-valued which are measured asynchronously over time across various dose levels. To account for autocorrelation among such longitudinally observed outcomes, a first-order Markov model for binary data is developed. Moreover, to account for the asynchronously observed time points, nonhomogeneous models for the transition probabilities are proposed. The transition probabilities are modeled using B-spline basis functions after suitable transformations. Additionally, if the underlying dose-response curve is assumed to be non-decreasing, our model allows for the estimation of any underlying non-decreasing curve based on suitably constructed prior distributions. We also extended our model to the mixed effect model to incorporate individual-specific random effects. Numerical comparisons with traditional models are provided based on simulated data sets, and also practical applications are illustrated using real data sets.

Exposure-response modeling of peficitinib efficacy in patients with rheumatoid arthritis

The aim was to analyze the relationship between peficitinib exposure and efficacy response according to American College of Rheumatology (ACR) 20 criteria and 28‐joint disease activity score based on C‐reactive protein (DAS28‐CRP) in rheumatoid arthritis (RA) patients, and to identify relevant covariates by developing exposure–response models. The analysis incorporated results from three multicenter, placebo‐controlled, double‐blind studies. As an exposure parameter, individual post hoc pharmacokinetic (PK) parameters were obtained from a previously constructed population PK model. Longitudinal ACR20 response rate and individual longitudinal DAS28‐CRP measurements were modeled by a non‐linear mixed effect model. Influential covariates were explored, and their effects on efficacy were quantitatively assessed and compared. The exposure–response models of effect of peficitinib on duration‐dependent increase in ACR20 response rate and decrease in DAS28‐CRP were adequately described by a continuous time Markov model and an indirect response model, respectively, with a sigmoidal E_max saturable of drug exposure in RA patients. The significant covariates were DAS28‐CRP and total bilirubin at baseline for the ACR20 response model, and CRP at baseline and concomitant methotrexate treatment for the DAS28–CRP model. The covariate effects were highly consistent between the two models. Our exposure–response models of peficitinib in RA patients satisfactorily described duration‐dependent improvements in ACR20 response rates and DAS28‐CRP measurements, and provided consistent covariate effects. Only the ACR20 model incorporated a patient's subjective high expectations just after the start of the treatment. Therefore, due to their similarities and differences, both models may have relevant applications in the development of RA treatment.

Clinical trial registration

NCT01649999 (RAJ1), NCT02308163 (RAJ3), NCT02305849 (RAJ4).

Bayesian variable selection for multistate Markov models with interval-censored data in an ecological momentary assessment study of smoking cessation

The application of sophisticated analytical methods to intensive longitudinal data, collected with ecological momentary assessments (EMA), has helped researchers better understand smoking behaviors after a quit attempt. Unfortunately, the wealth of information captured with EMAs is typically underutilized in practice. Thus, novel methods are needed to extract this information in exploratory research studies. One of the main objectives of intensive longitudinal data analysis is identifying relations between risk factors and outcomes of interest. Our goal is to develop and apply expectation maximization variable selection for Bayesian multistate Markov models with interval-censored data to generate new insights into the relation between potential risk factors and transitions between smoking states. Through simulation, we demonstrate the effectiveness of our method in identifying associated risk factors and its ability to outperform the LASSO in a special case. Additionally, we use the expectation conditional-maximization algorithm to simplify estimation, a deterministic annealing variant to reduce the algorithm's dependence on starting values, and Louis's method to estimate unknown parameter uncertainty. We then apply our method to intensive longitudinal data collected with EMA to identify risk factors associated with transitions between smoking states after a quit attempt in a cohort of socioeconomically disadvantaged smokers who were interested in quitting.

Continuous time Markov chain approaches for analyzing transtheoretical models of health behavioral change: A case study and comparison of model estimations

Continuous time Markov chain models are frequently employed in medical research to study the disease progression but are rarely applied to the transtheoretical model, a psychosocial model widely used in the studies of health-related outcomes. The transtheoretical model often includes more than three states and conceptually allows for all possible instantaneous transitions (referred to as general continuous time Markov chain). This complicates the likelihood function because it involves calculating a matrix exponential that may not be simplified for general continuous time Markov chain models. We undertook a Bayesian approach wherein we numerically evaluated the likelihood using ordinary differential equation solvers available from the gnu scientific library. We compared our Bayesian approach with the maximum likelihood method implemented with the R package MSM. Our simulation study showed that the Bayesian approach provided more accurate point and interval estimates than the maximum likelihood method, especially in complex continuous time Markov chain models with five states. When applied to data from a four-state transtheoretical model collected from a nutrition intervention study in the next step trial, we observed results consistent with the results of the simulation study. Specifically, the two approaches provided comparable point estimates and standard errors for most parameters, but the maximum likelihood offered substantially smaller standard errors for some parameters. Comparable estimates of the standard errors are obtainable from package MSM, which works only when the model estimation algorithm converges.

Analysis of transtheoretical model of health behavioral changes in a nutrition intervention study--a continuous time Markov chain model with Bayesian approach

Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state.

Pharmacokinetic-pharmacodynamic modeling of fostamatinib efficacy on ACR20 to support dose selection in patients with rheumatoid arthritis (RA)

R788 (fostamatinib) is an oral prodrug that is rapidly converted into a relatively selective spleen tyrosine kinase (SYK) inhibitor R406, evaluated for the treatment of rheumatoid arthritis (RA). This analysis aimed at developing a pharmacodynamic model for efficacy using pooled ACR20 data from two phase II studies in patients with rheumatoid arthritis (TASKi1 and TASKi2), describing the effect of fostamatinib as a function of fostamatinib exposure (dose, R406 plasma concentration) and other explanatory variables. The exposure-response relationship of fostamatinib was implemented into a continuous time Markov model describing the time course of transition probabilities between the three possible states of ACR20 non-responder, responder, and dropout at each visit. The probability of transition to the ACR20 response state was linearly (at the rate constant level) related to average R406 plasma concentrations and the onset of this drug effect was fast. Further, increases of fostamatinib dose resulted in increased dropout and subsequent loss of efficacy. This analysis provided an increased understanding of the exposure-response relationship, and provided support for fostamatinib 100 mg BID an appropriate dose regimen for further clinical evaluation.

Outcome of pregnancy in women with inflammatory bowel disease treated with antitumor necrosis factor therapy

BACKGROUND

Infliximab (IFX) and adalimumab (ADA) are attractive treatment options in patients with inflammatory bowel disease (IBD) also during pregnancy but there is still limited data on the benefit/risk profile of IFX and ADA during pregnancy.

METHODS

This observational study assessed pregnancy outcomes in 212 women with IBD under antitumor necrosis factor alpha (TNF) treatment at our IBD unit. Pregnancy outcomes in 42 pregnancies with direct exposure to anti-TNF treatment (35 IFX, 7 ADA) were compared with that in 23 pregnancies prior to IBD diagnosis, 78 pregnancies before start of IFX, 53 pregnancies with indirect exposure to IFX, and 56 matched pregnancies in healthy women.

RESULTS

Thirty-two of the 42 pregnancies ended in live births with a median gestational age of 38 weeks (interquartile range [IQR] 37-39). There were seven premature deliveries, six children had low birth weight, and there was one stillbirth. One boy weighed 1640 g delivered at week 33, died at age of 13 days because of necrotizing enterocolitis. A total of eight abortions (one patient wish) occurred in seven women. Trisomy 18 was diagnosed in one fetus of a mother with CD at age 37 under ADA treatment (40 mg weekly) and pregnancy was terminated. Pregnancy outcomes after direct exposure to anti-TNF treatment were not different from those in pregnancies before anti-TNF treatment or with indirect exposure to anti-TNF treatment but outcomes were worse than in pregnancies before IBD diagnosis.

CONCLUSIONS

Direct exposure to anti-TNF treatment during pregnancy was not related to a higher incidence of adverse pregnancy outcomes than IBD overall.