Clinical and Biological Interpretation of Survival Curves of Cancer Patients, Exemplified With Stage IV Non-Small Cell Lung Cancers With Long Follow-up

Abstract

Worldwide, 18.1 million new invasive cancers and 9.9 million cancer deaths occurred in 2020. Lung cancer is the second most frequent (11.4%) and, with 1.8 million deaths, remains the leading cause of cancer mortality. About 1.7 million of lung cancers are of the non-small cell lung cancer (NSCLC) subtype, and of these, 60%-70% are in advanced stage IV at the time of diagnosis. Thus, the annual worldwide number of new NSCLC stage IV patients is about 1 million, and they have a very poor prognosis. Indeed, 25%-30% die within 3 months of diagnosis. However, the survival duration of the remaining 700,000 new patients per year surviving >3 months varies enormously. Surprisingly, little research has been done to explain these survival differences, but recently it was found that classical patient, tumour and treatment features cannot accurately distinguish short- and very long-term survivors. What then are the causes of these bewildering survival variations amongst "the same cancers"? Clonality, proliferation differences, neovascularization, intra-tumour heterogeneity, genetic inhomogeneity and other cancer hallmarks play important roles. Considering each of these, single or combined, can greatly improve our understanding. Another technique is analysis of the survival curve of a seemingly homogeneous group of cancer patients. This can give valuable information about the existence of subgroups and their biological characteristics. Different basic survival curves and what their shapes tell about the biological properties of these invasive cancers are discussed. Application of this analysis technique to the survival curve of 690 stage IV NSCLC patients with a 3.2-120.0-month survival suggests that this seemingly homogeneously group of patients probably consists of 4-8 subgroups with a very different survival. A subsequent detailed mathematical analysis shows that a model of 8 subgroups gives a very good match with the original survival curve of the whole group. In conclusion, the survival curve of a seemingly homogeneous group of cancer patients can give valuable information about the existence of subgroups and their biological characteristics. Application of this technique to 690 NSCLC Stage IV patients makes it probable that 8 different subgroups with very different survival rates exist in this group of cancers.

Keywords: detection of different subgroups; metastatic cancer; non-small cell lung cancer; stage IV; survival curve analysis.

Figure 1

Invasive cancer group A. Survival curve with long follow-up. None of the patients develop/die from metastatic disease.

Figure 2

Invasive cancer group B All patients have died from metastatic disease within 24 months.

Figure 3

Survival curve of the two patient groups A and B together. Note the initial rather steep decline, followed by an increasingly more horizontal plateau.

Figure 4

Survival curve type 4. At no point is a horizontal plateau found. This means that all patients had (occult) metastases at the time of diagnosis. However, the growth speeds vary greatly, resulting in continuous deaths from lethal metastatic load.

Figure 5

Left: Survival curve of the whole group of 690 stage IV NSCLC patients with a 3.2–120.0-month follow-up, who had received conventional radiotherapy, platinum-based chemotherapy and tyrosine kinase inhibitor-targeted therapy.

Figure 6

Right: Hypothetical delineation of the curved shape of the survival curve. See the text for details. For the sake of clarity, we have only drawn 4 tangent lines instead of 8.

Figure 7

The survival curve of the 690 patients starts at Point P at 100% survival and 3 months of follow-up, as 261 other patients had already died within 3 months and are excluded from this study. From point P, the survival line shows a curved slope downward to the last point at 4% survival and 120 months of follow-up. At specific points in the survival curve, the slope shows a subtle change (i.e., becomes less steep). These points are denoted as Q, R, S and T. For details of these points, see text.

Figure 8

Linear lines between points P–Q, Q–R, R–S, S–T. These lines are slightly shifted up and down, and to the left and right in the figure, to make them more visible.

Figure 9

The original curved survival line is shown as small vertical black lines. The linear tangent lines of the curved survival line from Figures 7 and 8 , between points P–Q, Q–R, R–S and S–T, are extrapolated from where they originally begun, at point P.

Figure 10

The actual observed survival curve (light blue continuous line) with the results of the combination of the model with 4 hypothetical straight lines (dark blue broken line). Note that the match is not perfect.

Figure 11

The survival curves of the 8 hypothetical subgroups.

Figure 12

The actual observed survival curve (light blue continuous line) with the results of the combination of the model with 8 hypothetical straight lines (dark blue broken line). The similarity between the Actual Observed survival curve and the Hypothetical Calculated survival curve from the 8 hypothetical subgroups, with the linear survival curves from Figure 11 , is remarkable.