Cancer metastasis networks and the prediction of progression patterns

Abstract

Background: Metastasis patterns in cancer vary both spatially and temporally. Network modelling may allow the incorporation of the temporal dimension in the analysis of these patterns.

Methods: We used Medicare claims of 2,265,167 elderly patients aged > or = 65 years to study the large-scale clinical pattern of metastases. We introduce the concept of a cancer metastasis network, in which nodes represent the primary cancer site and the sites of subsequent metastases, connected by links that measure the strength of co-occurrence.

Results: These cancer metastasis networks capture both temporal and subtle relational information, the dynamics of which differ between cancer types. Using these networks as entities on which the metastatic disease of individual patients may evolve, we show that they may be used, for certain cancer types, to make retrograde predictions of a primary cancer type given a sequence of metastases, as well as anterograde predictions of future sites of metastasis.

Conclusion: Improvements over traditional techniques show that such a network-based modelling approach may be suitable for studying metastasis patterns.

Figure 1

Metastasis incidence hazard functions. Each curve represents an anatomical location at which metastases may arise, showing the dynamics of metastatic progression at that site over time. Displayed are the metastatic progression profiles of six primary tumour types: (A), prostate, (B), breast, (C), colon, (D), lung, (E), melanoma, and (F), bladder. The vector of metastatic sites contains 27 locations, including the lymph nodes, organs, and other anatomical sites. Although labels for the corresponding curves are not shown, this vector of metastatic sites follows the same ordering among these four graphs, thus revealing distinct spatial and dynamical patterns.

Figure 2

The cancer metastasis network for colon cancer (chosen as a representative example) and the dynamics of its links. (A), network at t=0, or the time of diagnosis of the primary tumour. (B), network at t=48 months. Nodes correspond to anatomical sites of metastases, the size of which represents their respective incidence rates. The widths of the links represent the strength of metastasis co-occurrence for two anatomical sites. Yellow nodes represent lymph node metastases; red nodes represent organ metastases. The curves in Figure 1 represent the monthly growth of these nodes, whereas the following (phi) represents the monthly growth of the links: (C), metastasis site co-occurrence associations as measured by phi over time. All the possible associations are lined up on the x axis, and their temporal dynamics are represented by the y axis. Only phi with P-value <0.01 are shown. (D), metastasis site co-occurrence associations as measured by relative risk over time. Only RR values with 99% confidence interval or RR <0.1 are shown.

Figure 3

Clustergram of primary sites by characteristic sites of metastasis. (A), at t=0, the emergence of anatomical locality from this clustering is quite striking. (B), at t=48 months, a greater percentage of 2 cancers have progressed to more advanced stages, and thus the clustering is slightly different. Note: Larger high-resolution versions of these clustergrams can be found in the supplemental materials (Supplementary Figures S4 and S5).

Figure 4

Prediction of the primary cancer site from a sequence of metastases. The primary cancer types for which the true positive rates exceed 25% from each model are shown. The multinomial logistic regression (MLR) algorithm takes into account the number of patients in the respective categories, and therefore, a relatively rare cancer type will be classified as a common cancer type with similar metastasis patterns. The MLR algorithm and the network algorithm perform in different ways: the MLR classifies everything into a few common cancer types, whereas the network algorithm is able to differentiate between rarer cancer types.

Figure 5

Using the cancer metastasis networks to predict the temporal sequence of additional metastases. (A), diagram of how p¯_net is calculated, for the case of n_mets=2. To calculate the probability of developing a metastasis at site m2, given the primary cancer type represented in blue and a metastasis already having developed at site m1, the strength of the green links (represented by their widths) are summed, and divided by the summation of the strength of the red and green links. The grey links are ignored. (B), p¯_f vs p¯_net, for n_mets=2. (C), p¯_f vs p¯_net, for n_mets=3. (D), p¯_f vs p¯_net, for n_mets=4. Each point represents a primary cancer type. Red represents the primary cancer types for which p¯_net<p¯_f, and blue represents those for which p¯_net>p¯_f.