A KPD Model for ordered categorical data: application to toxicity score in colorectal cancer patients treated with capecitabine
Hénin, Emilie(1), Klaas P. Zuideveld (2), Céline Dartois (1), Brigitte Tranchand (1,3), Gilles Freyer (1,4), Pascal Girard (1,5)
(1) EA3738, Faculté de Médecine LyonSud, Oullins, Fance ; (2) F. HoffmanLa Roche Ltd., Basel, Switzerland ; (3) Centre Léon Bérard, Lyon, France ; (4) Service d'Oncologie Médicale, Hôpital LyonSud, PierreBénite, France ; (5) INSERM, Lyon, France
Objectives: To model the longitudinal toxicity score experienced by patients affected with a colorectal cancer, and treated by an oral cytotoxic agent, capecitabine. This model for ordered categorical data includes the effect of the quantity of drug accumulated throughout the treatment without any pharmacokinetic information, and the score experienced at previous time.
Patients & Data: 1207 patients were randomised in two large phase III studies (1,4), which compared the efficacy and the toxicity of 5FU administered intravenously versus oral capecitabine, as first line treatment of metastatic colorectal cancer. Patients were treated over 32 weeks or until disease progression; in responding patients, treatment duration was up to 48 weeks. The median duration of capecitabine treatment was 146 days. Given treatment interruptions at the end of treatment period for many patients, only the first 30 weeks of treatment were modelized. Since very few occurrences of grade 3 were observed, grades 2 and 3 were grouped to a single category. Therefore 3 different scores (0, 1, and ≥2) were considered into the model. Covariates such as age, sex, height, weight, body surface area and type of cancer were considered. Among the 595 patients in capecitabine arm we randomly selected 400 patients to build the model (“building” data set) while 195 were assigned for model qualification (“qualification” data set).
Methods: The probability of experiencing a score of HFS was modelled with an extension of proportional odds ratio model as proposed by Lewis Sheiner (3). The extensions concerned the use of a KPD model for drug exposure and conditional probabilities (Markov model) on transitions from one score to another. Since no pharmacokinetic information was available in those patients, a drug accumulation in the body and a monoexponential elimination were assumed, which is the principle of the KPD model (2). The parameters of the model were estimated by the Laplacian method implemented in NONMEM software. In the model building process, predictive checks guided the choice of best model as follows: confidence intervals of timedependant predicted probabilities were compared to observed probabilities. Predicted probabilities were computed by simulating the HFS scores in 100 new building datasets using a degenerate posterior distribution (5).
Once the final model was established, it was qualified by predictive check. We simulated 500 times the toxicity profiles from qualification data set, using the model and likelihood estimates obtained from the building data set. Comparisons were performed between the distribution of number of transitions from one grade to another computed in each simulated data set, and the observed one in the qualification data set.
Results:
Model specification: The final model was a longitudinal proportional odds ratio model with KPD and Markovian component, ie the probability of experiencing a HFS grade was related to the amount of capecitabine administered and to the HFS grade experienced the week before. Tests for covariates effect were performed, and only AGE was significant. Final model is:
Logit{P(Y = 0)} = B_{0}   E_{MAX} * (Q*K)
(Q*K) + ED_{50} 
+ θ_{AGE}*(AGE64) + η_{i} 
Logit{P(Y ≤ 1)} = B_{0} + B_{1}   E_{MAX} * (Q*K)
(Q*K) + ED_{50} 
+ θ_{AGE}*(AGE64) + η_{i} 
P(Y = 2) = 1  P(Y ≤ 1) 

Q is the accumulated dose with an elimination rate constant K (monoexponential elimination);

B_{0} and B_{1} > 0 are the logit intercepts for ordered model;

E_{MAX} and ED_{50} are the maximum effect and apparent dose producing 50% decrease of Emax;

(AGE64) is the difference of the AGE with the population median age;

η_{i}, η_{K} are interindividual variabilities on logit and K.

the parameters B_{0}, B_{1} and E_{MAX} are dependent of the score at the previous time, which introduces the Markov assumption.
Model qualification: The model constructed on building data set was used to simulate 500 times the HFS profiles of patients in the qualification data set. Predictive check has been performed and the observed probabilities were found to be within the 90% CI obtained from simulations. Also, the number of transitions from one grade to another was compared to the number of transitions observed in the original data set. The observed values from the qualification data set are all included in the interval defined by the quantiles 5% and 95% of the simulated distribution. The distributions (from the simulated sets) of the number of days the patients spend in one given grade were compared to the observed distribution. Based on those simulations the model was accepted.
Conclusions: A longitudinal doseeffect model including a Markov and KPD components from real toxicity longitudinal data was built. The model was qualified by data splitting using a predictive check and qualification criteria. Future use of the model will be firstly developing individual optimal dosing regimen and secondly assessing the impact of noncompliance on HFS. As long as no patient compliance data is available in the case of treatment of cancer by an oral cytotoxic chemotherapy, an in silico study of noncompliance will be performed in order to quantify its impact on the HandandFoot syndrome.
References:
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