Emma C. Martin (1), Leon Aarons (1), James W.T. Yates (2)
(1) University of Manchester, Centre for Applied Pharmacokinetic Research, Manchester Pharmacy School, the University of Manchester, M13 9PT, U.K. (2) AstraZeneca, Innovative Medicines, Oncology, Modelling and Simulation, Li Ka Shing Centre, Robinson Way, Cambridge CB2 0RE, U.K
Purpose: Xenograft studies are commonly used to assess the efficacy of new compounds and characterise their dose response relationship [1]. Analysis often involves comparing the final tumour sizes across dose groups [2]. This can cause bias, as often in xenograft studies a tumour burden limit (TBL) is imposed for ethical reasons [3], leading to the animals with the largest tumours being excluded from the final analysis. This means the average tumour size, particularly in the control group, is underestimated, leading to an underestimate of the treatment effect.
Methods: Four methods to account for dropout due to the TBL are proposed, as outlined below, which use all the available data instead of only final observations. The methods were applied to both a simulated data set, and a real example.
- Modelling – a tumour growth model was fitted to all available data, ignoring drop out, then population estimates of the response at each dose were used to estimate the dose response curve.
- Pattern mixture – the mice were treated as belonging to different drop out patterns depending on the day they dropped out of the study [4], missing data was then imputed for each drop out pattern based on models fitted to the patterns which were most similar.
- Censoring – the M3 method was used [5] which is often applied to data below the limit of quantification. The likelihood for missing values is replaced by the likelihood of the missing value truly being above the tumour burden limit, given that the observation is missing due to drop out.
- Joint modelling – the tumour growth data and the missing data were jointly modelled through shared random effects. A logistic model was used to model the drop out, with the only covariate being the expected tumour size from the tumour growth model.
Results: All four proposed methods led to an improvement in the estimate of treatment effect in the simulated data. The joint modelling method performed most strongly, with the censoring method also providing a good estimate of the treatment effect, but with higher uncertainty. In the real data example, the dose response estimated using the censoring and joint modelling methods was higher than the very flat curve estimated from average final measurements.
Conclusions: Accounting for dropout using the proposed censoring or joint modelling methods allows the treatment effect to be recovered in studies where it may have been obscured due to dropout caused by the TBL.
References:
[1] Tan, M., et al., Repeated-measures models with constrained parameters for incomplete data in tumour xenograft experiments. Stat Med, 2005. 24(1): p. 109-19.
[2] Hather, G., et al., Growth rate analysis and efficient experimental design for tumor xenograft studies. Cancer Inform, 2014. 13(Suppl 4): p. 65-72.
[3] Workman, P., et al., Guidelines for the welfare and use of animals in cancer research. Br J Cancer, 2010. 102(11): p. 1555-77.
[4] Yuen, E., I. Gueorguieva, and L. Aarons, Handling missing data in a duloxetine population pharmacokinetic/pharmacodynamic model – imputation methods and selection models. Pharm Res, 2014. 31(10): p. 2829-43.
[5] Beal, S.L., Ways to fit a PK model with some data below the quantification limit. J Pharmacokinet Pharmacodyn, 2001. 28(5): p. 481-504.
Reference: PAGE 25 (2016) Abstr 5721 [www.page-meeting.org/?abstract=5721]
Poster: Methodology - New Modelling Approaches