Modelling a Spontaneously Reported Side Effect by Use of a Markov Mixed-Effects Model

Zingmark, Per-Henrik; Kågedal, Matts; Karlsson, Mats O.

doi:10.1007/s10928-005-0021-7

Cited by 31 publications

(28 citation statements)

References 13 publications

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“…The current logistic model assumes independence of two consecutive categorical observations measured as a function of time. To test that this assumption is reasonable, the posterior distribution of the number of different transitions19, 20 from the logistic model were generated for both lorazepam sleepiness and dizziness and overlaid on the observed mean value.…”

Section: Methodsmentioning

confidence: 99%

Pharmacodynamic Differentiation of Lorazepam Sleepiness and Dizziness Using an Ordered Categorical Measure

Kamal

Smith

Cook

et al. 2010

Journal of Pharmaceutical Sciences

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Categorical measures of lorazepam sleepiness and dizziness were modeled to identify differences in pharmacodynamic (PD) parameters between these adverse events (AEs). Differences in dataderived PD parameters were compared to relative incidence rates in the drug label (15.7% and 6.9%, respectively). Healthy volunteers (n=20) received single oral doses of 2 mg lorazepam or placebo in a randomized, double-blind, cross-over fashion. A 7-point categorical scale measuring the intensity of AEs was serially administered over 24 hr. The maximum score (MaxS), and area under the effect curve (AUEC) were determined by noncompartmental methods and compared using a paired t-test. Individual scores were modeled using a logistic function implemented in NONMEM. AUEC and MaxS for sleepiness were significantly higher than dizziness (20.35 vs. 9.76, p<0.01) and (2.35 vs.1.45, P<0.01). Model slope estimates were similar for sleepiness and dizziness (0.21 vs. 0.19 logits×ml/ng), but baseline logits were significantly higher for sleepiness (−2.81 vs. −4.34 logits). Data-derived PD parameters were in concordance with label incidence rates. The higher intensity of sleepiness may be directly related to baseline (no dug present) while the increase in intensity due to drug was relatively similar for both AEs.

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Section: Methodsmentioning

confidence: 99%

Pharmacodynamic Differentiation of Lorazepam Sleepiness and Dizziness Using an Ordered Categorical Measure

Kamal

Smith

Cook

et al. 2010

Journal of Pharmaceutical Sciences

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“…DTMM combines the PO model with a transition model. DTMM was first introduced into PKPD models by Karlsson et al to characterize sleep stages in insomnia patients treated with temazepam (2), and since then applied to various outcomes such as sedation scores in acute stroke (3), central nervous system side effects (4), improvement scores in rheumatoid arthritis (5), grades of proteinuria (6), fatigue, and hand-foot syndrome in cancer patients (7,8). In DTMM, the influence of the preceding state on the probability of the current score is assumed to be the same whatever the time interval is between the two assessments.…”

Section: Introductionmentioning

confidence: 99%

A Minimal Continuous-Time Markov Pharmacometric Model

Schindler

Karlsson

2017

AAPS J

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Abstract.In this work, an alternative model to discrete-time Markov model (DTMM) or standard continuous-time Markov model (CTMM) for analyzing ordered categorical data with Markov properties is presented: the minimal CTMM (mCTMM). Through a CTMM reparameterization and under the assumption that the transition rate between two consecutive states is independent on the state, the Markov property is expressed through a single parameter, the mean equilibration time, and the steady-state probabilities are described by a proportional odds (PO) model. The mCTMM performance was evaluated and compared to the PO model (ignoring Markov features) and to published Markov models using three real data examples: the four-state fatigue and hand-foot syndrome data in cancer patients initially described by DTMM and the 11-state Likert pain score data in diabetic patients previously analyzed with a count model including Markovian transition probability inflation. The mCTMM better described the data than the PO model, and adequately predicted the average number of transitions per patient and the maximum achieved scores in all examples. As expected, mCTMM could not describe the data as well as more flexible DTMM but required fewer estimated parameters. The mCTMM better fitted Likert data than the count model. The mCTMM enables to explore the effect of potential predictive factors such as drug exposure and covariates, on ordered categorical data, while accounting for Markov features, in cases where DTMM and/or standard CTMM is not applicable or conveniently implemented, e.g., non-uniform time intervals between observations or large number of categories.

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“…The placebo model was implemented as a step function (c ij =0 if j=1 and c ij =1 if j=2, 3,4), while the drug model was implemented as a linear function of the dose (d ij =0 if j=1 and d ij = 7.5,15,30 if j=1,2,3,4) respectively. The distribution of response categories was even (scenario D) and skewed (scenario E).…”

Section: Simulation Settingsmentioning

confidence: 99%

“…Mixed effect analyses are increasingly employed for the analysis of longitudinal efficacy or safety categorical data measured in clinical trials (1)(2)(3)(4)(5). For this purpose, proportional odds model are frequently used.…”

Section: Introductionmentioning

confidence: 99%

Implementation and Evaluation of the SAEM Algorithm for Longitudinal Ordered Categorical Data with an Illustration in Pharmacokinetics–Pharmacodynamics

Savic

Mentré

Lavielle

2010

AAPS J

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Abstract. Analysis of longitudinal ordered categorical efficacy or safety data in clinical trials using mixed models is increasingly performed. However, algorithms available for maximum likelihood estimation using an approximation of the likelihood integral, including LAPLACE approach, may give rise to biased parameter estimates. The SAEM algorithm is an efficient and powerful tool in the analysis of continuous/ count mixed models. The aim of this study was to implement and investigate the performance of the SAEM algorithm for longitudinal categorical data. The SAEM algorithm is extended for parameter estimation in ordered categorical mixed models together with an estimation of the Fisher information matrix and the likelihood. We used Monte Carlo simulations using previously published scenarios evaluated with NONMEM. Accuracy and precision in parameter estimation and standard error estimates were assessed in terms of relative bias and root mean square error. This algorithm was illustrated on the simultaneous analysis of pharmacokinetic and discretized efficacy data obtained after a single dose of warfarin in healthy volunteers. The new SAEM algorithm is implemented in MONOLIX 3.1 for discrete mixed models. The analyses show that for parameter estimation, the relative bias is low for both fixed effects and variance components in all models studied. Estimated and empirical standard errors are similar. The warfarin example illustrates how simple and rapid it is to analyze simultaneously continuous and discrete data with MONOLIX 3.1. The SAEM algorithm is extended for analysis of longitudinal categorical data. It provides accurate estimates parameters and standard errors. The estimation is fast and stable.

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Modelling a Spontaneously Reported Side Effect by Use of a Markov Mixed-Effects Model

Abstract: This approach of incorporating Markov elements in an analysis of spontaneously reported categorical side-effect data could adequately predict the observed side-effect time course and could be considered in analyses of categorical data where dependence between observations is an issue.

Cited by 31 publications

References 13 publications

Pharmacodynamic Differentiation of Lorazepam Sleepiness and Dizziness Using an Ordered Categorical Measure

Pharmacodynamic Differentiation of Lorazepam Sleepiness and Dizziness Using an Ordered Categorical Measure

A Minimal Continuous-Time Markov Pharmacometric Model

Implementation and Evaluation of the SAEM Algorithm for Longitudinal Ordered Categorical Data with an Illustration in Pharmacokinetics–Pharmacodynamics

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