On the analysis of count data of birth-and-death process type: With application to molecularly targeted cancer therapy

For molecularly targeted cancer therapy, potency of a novel monoclonal antibody is typically studied in vitro in order to observe directly the effect of the antibody on a malignant tumour cell population. Numbers of viable cells of the population are counted over time to evaluate how the antibody may change the population growth pattern. Usually, such count data is analysed by a log-linear model to estimate the average antibody effects, but it is based on a Poisson-like process and is not appropriate for modelling the growth pattern of the tumour cells. In this paper, we propose to analyse the count data from the point of view of a birth-and-death process, which is a more natural description of the biological process in these experiments. Assuming a simple birth-and-death process and a naïve regression model for the birth rate and death rate, we show that the log-linear relationship still holds for the average count and the covariates, although the linear predictor needs to satisfy a specific functional form. The estimation can be based on the quasi-likelihood method. The variance is not a simple function of the mean, but can be adequately approximated by a function of mean of either quadratic form or linear form, available in most standard statistical packages. We perform a simulation study to show that the proposed method provides consistent and robust estimations. The utility of the method is demonstrated by the analysis of a data set for experiment for anti-lymphoma monoclonal antibodies.