M. Cerou [1,2,3], K. Brendel[3], E. Comets[1,2,4,5] and M.Chenel[3]
[1] - Inserm, IAME, UMR 1137, F-75018, Paris, France [2] – University Paris diderot, IAME, UMR 1137, 75008, Paris [3] - Division of Clinical Pharmacokinetics and Pharmacometrics, Institut de Recherches Internationales Servier, Suresnes, France [4] – Inserm, CIC 1414, 35000 Rennes, France [5] – University Rennes-1, 35000 Rennes, France
Objectives: Item Response Theory (IRT) is increasingly used in Pharmacometrics to model the disease progression using the whole available item-level information [1]. As a first step, our aim was to analyze and evaluate the time course of response to placebo of patients with major depressive disorder using this approach.
Methods:
Data
The dataset includes 2136 patients where we had longitudinal observation for 626 patients under placebo and information at baseline for 1510 patients in the treatment arm. The data was collected from one phase II and seven phase III clinical studies where the tested drug was Agomelatine, which was marketed in 2009. At each observation time, item information of the Hamilton depression rating scale (HAM-D) [2] which contains 17 items was collected. The number of visits by patient ranges from 3 to 42 (9 in median) and the follow-up period was 14 days in median. Study duration was decomposed as one short term study (2 months), five midterm studies (6 months), and two long term studies (12 months) and the number of patients among studies was very similar (around 120). Dropout information in the studies was recorded and the causes were mainly due to lack of effect, adverse event or at random. Approximately 60% of patients dropped out in a year.
HAM-D IRT model
The first step was to estimate the item-specific parameters, implemented as fixed effect of ordered categorical models and latent depression disability as random effect and for that purpose we used all available information.
Longitudinal model
The second step was to estimate the evolution of the hidden depression disability over time by fixing the item-specific parameters and using several mixed-effect models.
Longitudinal model with dropout
To take into account the dropout, we used a time-to-event (TTE) parametric model and several distributions of the baseline hazard model were tested. To characterise the relationship between dropout and the latent depression disability (LDD), several forms of link were explored.
Model selection and evaluation
Model selection was done based on the AIC. Model evaluation was done through graphical diagnostics based on both item and summary levels (mirror plot) and also to Visual predictive check (VPC) based on the HAM-D score. VPC of Kaplan-Meier was computed to evaluate the dropout model. The best model was selected on the basis of all these numerical and graphical diagnostics, but also on uncertainty of the parameters, a relevant interpretation of the parameters and a clinically pertinent model.
Results:
HAM-D IRT model
A total of 92 parameters was estimated with 10 ordinal categorical sub-models of 5 scores, and 8 ordinal categorical sub-models of 3 scores. The mirror plot and summary level checks showed good agreement with observations.
Longitudinal model
Depression time course based on the HAMD corresponds to a strong diminution (remission) and it can be associated with a relapse. Several models were tested: linear (AIC: 197655), Weibull [3] (AIC: 188348), Bateman [4] (AIC: 189045), a modified inverse Bateman (AIC: 188277) and a second modified inverse Bateman (AIC: 188519). Based on AIC and the graphical diagnostics, the model of the latent depression disability which best described the data was the first modified Bateman model, where the shape of the diminution corresponds to a Weibull like model.
Joint model with longitudinal and TTE sub-models
Patients with high value of LDD were strongly associated with a dropout. A Weibull model for the hazard was tested and several forms of link were explored: no link (AIC: 138073), link with the current value of the LDD (AIC: 137711), link with a logit transformation of the current value of the LDD (AIC: 138714). A lognormal model for the hazard with a link with the current value of the LDD was also tested (AIC: 138895). Based on numerical and graphical diagnostics, the selected model was a Weibull model for the hazard with a link with the current value of the LDD. The relative standard error for this model was under 5% for all parameters, and VPC of the HAMD-D score was in good agreement with the observations.
Conclusion:
A longitudinal IRT model has been developed and is a suitable method to describe the disease progression of depressed patients. This model will be used and adapted to take into account treatment effect. This work could be used later as a basis for the study of the normalised prediction distribution errors, a metric used in model evaluation, adapted to this type of data.
References:
[1] Sebastian Ueckert, Improved utilization of ADAS-Cog assessment data through Item Response Theory based pharmacometric modeling, 2014 Aug, 31(8):2152-65
[2] HAM-D score: http://healthnet.umassmed.edu/mhealth/HAMD.pdf
[3] Krekels, E. H., Novakovic, A. M., Vermeulen, A. M., Friberg, L. E., & Karlsson, M. O. (2017). Item response theory to quantify longitudinal placebo and paliperidone effects on PANSS scores in schizophrenia. CPT: pharmacometrics & systems pharmacology.
[4] Holford N (2005) The time course of placebo response in clinical trials—do antidepressants really take two weeks to work? In: AAPS annual meeting and exposition, Nashville, TN. http://www.aapspharmaceutica.com/inside/focus_groups/ModelSim/imagespdfs/Holford05.pdf. Accessed 15 Oct 2008
Reference: PAGE 27 (2018) Abstr 8567 [www.page-meeting.org/?abstract=8567]
Poster: Drug/Disease Modelling - Other Topics