Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis.

This paper is concerned with modern approaches to mechanistic modeling of the process of cancer detection. Measurements of tumor size at diagnosis represent a valuable source of information to enrich statistical inference on the processes underlying tumor latency. One possible way of utilizing this information is to model cancer detection as a quantal response variable. In doing so, one relates the chance of detecting a tumor to its current size. We present various theoretical results emerging from this approach and illustrate their usefulness with numerical examples and analyses of epidemiological data. An alternative approach based on a threshold type mechanism of tumor detection is briefly described.

Statistical comparison of dissolution curves.

The purpose of this investigation was to develop statistical procedures to determine if two sets of dissolution curves could have come from the same population of curves. The f(2)statistic developed by the Food and Drug Administration, FDA, has been shown to have many limitations and is too liberal in concluding similarity between dissolution profiles. The procedure currently used by the FDA involves computing the mean amount dissolved at each time and then comparing the two mean curves. This approach ignores all of the variability within sets of profiles, which, from a statistical viewpoint, is a serious limitation. This investigation presents three different statistics for comparison of dissolution curves with associated decision rules and power functions. These three statistics are extensions of existing procedures: (1) an extension of the Mann--Whitney test which compares the variability within each set of profiles and between the two sets; (2) an extension of the Kolmogorov--Smirnov D statistic which compares three empirical cumulative distribution functions; and (3) an adaptation of the well known chi-squared test. A computer program, which includes the algorithm for each of the three statistics and varying sample sizes, is also available.

Construction of best confidence intervals for half-lives.

This paper presents a method of determining a confidence interval for the drug half-life based on statistical properties of the estimates of the disappearance rate constant of the drug. This interval is shown to be of minimum length which indicates it is a more precise estimate than others currently in use. A computer program to construct these intervals is available upon request.

Estimation of human tumor growth rate from distribution of tumor size at detection.

Methods are presented for estimating the growth curve of a tumor (up to an unknown scale factor of time) from the distribution of volumes at detection on the basis of two assumptions: 1) the existence of a common growth curve and 2) the assumption that the probability of detecting a tumor in a period of time is proportional to the tumor volume. These methods can accommodate variation between individuals in speed of traversal of the growth curve. The methods are applied to volumes of tumor at detection of a large series of breast cancers. The simplest, adequate description is exponential growth with great individual-to-individual variation in tumor doubling time. The data are consistent with bounded growth (Gompertzian or logistic form) as well as exponential growth. However, there is no evidence that the bound on growth is within the range of the data. The shape of the distribution of volumes does not yield an effective lower limit on such a bound.