Analysis of multi-arm tumor growth trials in xenograft animals using phase change adaptive piecewise quadratic models

Xenograft trials allow tumor growth in human cell lines to be monitored over time in a mouse model. We consider the problem of inferring the effect of treatment combinations on tumor growth. A piecewise quadratic model with flexible phase change locations is proposed to model the effect of change in therapy over time. Each piece represents a growth phase, with phase changes in response to change in treatment. Piecewise slopes represent phase-specific (log) linear growth rates and curvature parameters represent departure from linear growth. Trial data are analyzed in two stages: (i) subject-specific curve fitting (ii) analysis of slope and curvature estimates across subjects. A least-squares approach with penalty for phase change point location is proposed for curve fitting. In simulation studies, the method is shown to give consistent estimates of slope and curvature parameters under independent and AR (1) measurement error. The piecewise quadratic model is shown to give excellent fit (median R(2)=0.98) to growth data from a six armed xenograft trial on a lung carcinoma cell line.