Graph models of oncogenesis with an application to melanoma.

We describe several analytical techniques for use in developing genetic models of oncogenesis including: methods for the selection of important genetic events, construction of graph models (including distance-based trees, branching trees, contingency trees and directed acyclic graph models) from these events and methods for interpretation of the resulting models. The models can be used to make predictions about: which genetic events tend to occur early, which events tend to occur together and the likely order of events. Unlike simple path models of oncogenesis, our models allow dependencies to exist between specific genetic changes and allow for multiple, divergent paths in tumor progression. A variety of genetic events can be used with the graph models including chromosome breaks, losses or gains of large DNA regions, small mutations and changes in methylation. As an application of the techniques, we use a recently published cytogenetic analysis of 206 melanoma cases [Nelson et al. (2000), Cancer Genet. Cytogenet.122, 101-109] to derive graph models for chromosome breaks in melanoma. Among our predictions are: (1) breaks in 6q1 and 1q1 are early events, with 6q1 preferentially occurring first and increasing the probability of a break in 1q1 and (2) breaks in the two sets [1p1, 1p2, 9q1] and [1q1, 7p2, 9p2] tend to occur together. This study illustrates that the application of graph models to genetic data from tumor sets provide new information on the interrelationships among genetic changes during tumor progression.

Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood.

The germinal center reaction (GCR) of vertebrate immunity provides a remarkable example of evolutionary succession, in which an advantageous phenotype arises as a spontaneous mutation from the parental type and eventually displaces the parental type altogether. In the case of the immune response to the hapten (4-hydroxy-3-nitrophenyl)acetyl (NP), as with several other designed immunogens, the process is dominated by a single key mutation, which greatly simplifies the modeling of and analysis of data. We developed a two-stage model of this process in which the primary stage represents the appearance and establishment of the mutant population as a stochastic process while the second stage represents the growth and dominance of the clone as a deterministic process, conditional on its time of establishment from stage one. We applied this model to the analysis of population samples from several germinal center (GC) reactions and used maximum-likelihood methods to estimate the waiting times to arrival and to dominance of the mutant clone. We determined the sampling properties of the maximum-likelihood estimates using Monte Carlo methods and compared them to their asymptotic distributions. The methods we present here are well-suited for use in the analysis of other systems, such as tumor growth and the experimental evolution of bacteria.

Chromosome abnormalities in malignant melanoma: clinical significance of nonrandom chromosome abnormalities in 206 cases.

We report the cytogenetic abnormalities from a series of 206 primary malignant melanoma specimens referred to a single institution. A total of 169 out of 206 unique cases had chromosome breakpoints. A previously described statistical method was used to detect nonrandom distribution of chromosome breakpoints at the level of chromosome regions. Nonrandom occurrence of chromosome breakpoints (indicating that the observed number of breaks significantly exceeded the expected number of breaks) was detected in 28 regions, suggesting a hierarchy of genetic abnormalities in melanoma. Clinical variables and tumor characteristics were analyzed for associations with the presence of any nonrandom chromosome breakpoints; with individual, nonrandomly involved chromosome regions; and with paired, nonrandomly involved chromosome regions. No nonrandomly involved chromosome regions or pairs of regions appeared to significantly affect survival. These results identify recurring, nonrandom chromosome abnormalities in malignant melanoma. These results suggest that recurring, nonrandom chromosome alterations play a key role in the etiology and/or progression of malignant melanoma and identify targets within the genome for molecular genetic studies.

Estimation of tamoxifen's efficacy for preventing the formation and growth of breast tumors.

BACKGROUND: Several randomized clinical trials have tested the hypothesis that tamoxifen is effective in preventing breast cancer. The largest such trial, the National Surgical Adjuvant Breast and Bowel Project's Breast Cancer Prevention Trial (BCPT), reported a 49% reduction in risk of invasive breast cancer for the tamoxifen group. However, it is unclear whether the effect of tamoxifen in this trial was mainly due to prevention of newly forming tumors or to treatment of occult disease. METHODS: We used various tumor growth models (i.e., exponential and Gompertzian [growth limited by tumor size]) and a computer simulation to approximate the percentage of detected tumors that were initiated after study entry. Maximum likelihood techniques were then used to estimate separately the efficacy of tamoxifen in treating occult disease and in preventing the formation and growth of new tumors. RESULTS: Under the assumptions of most of the growth models, the trial was sufficiently long for substantial numbers of new tumors to form, grow, and be detected during the trial. With the Gompertzian model and all available incidence data from the BCPT, it was estimated that 60% (95% confidence interval [CI] = 40%-80%) fewer new tumors were detected in the tamoxifen group than in the placebo group. Likewise, 35% (95% CI = 6%-63%) fewer occult tumors were detected in the tamoxifen group. With this model, the estimated incidence rate of invasive breast cancer among women in the placebo group of the BCPT was 7.7 (95% CI = 6.6-8.9) per 1000 women per year. Similar results were obtained with three exponential tumor growth models. CONCLUSIONS: These results support the concept that tamoxifen reduced cancer incidence in the BCPT through both treatment of occult disease and prevention of new tumor formation and growth. However, data from prevention trials may never be sufficient to completely distinguish prevention of new tumor formation from treatment of occult disease.

Predicted and inferred waiting times for key mutations in the germinal centre reaction: evidence for stochasticity in selection.

The germinal centre reaction (GCR) is a fundamental component of the immune response to T-dependent antigens, during which the immunoglobulin (Ig) genes of B cells experience somatic hypermutation and selection. A maximum-likelihood method on DNA sequence data from 16 individual germinal centres was used to infer that the waiting time for position 33 key (high-affinity) mutations in the anti-(4-hydroxy-3-nitrophenyl) acetyl (NP) response is 8.3 days. This is in marked contrast to the prediction of a key mutant each generation (waiting time about 1/3 day) obtained from a simple model and parameters available in the literature. This disagreement is resolved in part by the finding that the targeted base occurs in a cold spot for hypermutation, raising the predicted waiting time to 2.3 days, although this value remains significantly lower than that inferred from the sequence data. It is proposed that the remaining disparity is attributable to some further stochastic process in the GCR: many early key mutations arise but fail to 'take root' within the GC, either due to emigration or failure of cognate T cell/B cell interaction. Furthermore, it is argued that the frequency with which position 33 mutations are found in secondary responses to NP indicates the presence of selection after the GCR.