Slowly cycling tumor cells that may be present in human tumors may evade cytotoxic therapies, which tend to be more efficient at destroying cells with faster growth rates. However, the proportion and growth rate of slowly cycling tumor cells is often unknown in preclinical model systems used for drug discovery. Here, we report a quantitative approach to quantitate slowly cycling malignant cells in solid tumors, using a well-established mouse model of Kras-induced lung cancer (Kras(G12D/+)). 5-Bromo-2-deoxyuridine (BrdUrd) was administered to tumor-bearing mice, and samples were collected at defined times during pulse and chase phases. Mathematical and statistical modeling of the label-retention data during the chase phase supported the existence of a slowly cycling label-retaining population in this tumor model and permitted the estimation of its proportion and proliferation rate within a tumor. The doubling time of the slowly cycling population was estimated at approximately 5.7 weeks, and this population represented approximately 31% of the total tumor cells in this model system. The mathematical modeling techniques implemented here may be useful in other tumor models where direct observation of cell-cycle kinetics is difficult and may help evaluate tumor cell subpopulations with distinct cell-cycling rates.

One of the most important research areas in case-control Genome-Wide Association Studies is to determine how the effect of a genotype varies across the environment or to measure the gene-environment interaction (G × E). We consider the scenario when some of the "healthy" controls actually have the disease and when the frequency of these latent cases varies by the environmental variable of interest. In this scenario, performing logistic regression with the clinically diagnosed disease status as an outcome variable and will result in biased estimates of G × E interaction. Here, we derive a general theoretical approximation to the bias in the estimates of the G × E interaction and show, through extensive simulation, that this approximation is accurate in finite samples. Moreover, we apply this approximation to evaluate the bias in the effect estimates of the genetic variants related to mitochondrial proteins a large-scale prostate cancer study.