Comparing the benefits of screening for breast cancer and lung cancer using a novel natural history model

Abstract

To estimate the impact of early detection of cancer, knowledge of how quickly primary tumors grow and at what size they shed lethal metastases is critical. We developed a natural history model of cancer to estimate the probability of disease-specific cure as a function of tumor size, the tumor volume doubling time (TVDT), and disease-specific mortality reduction achievable by screening. The model was applied to non-small-cell lung carcinoma (NSCLC) and invasive ductal carcinoma (IDC), separately. Model parameter estimates were based on Surveillance Epidemiology and End Results (SEER) cancer registry datasets and validated on screening trials. Compared to IDC, NSCLC is estimated to have a lower probability of disease-specific cure at the same detected tumor size, shed lethal metastases at smaller sizes (median: 19 mm for IDC versus 8 mm for NSCLC), have a TVDT that is almost half as long (median: 252 days for IDC versus 134 days for NSCLC). Consequently, NSCLC is associated with a lower mortality reduction from screening at the same screen detection threshold and screening interval. In summary, using a similar natural history model of cancer, we quantify the disease-specific curability attributable to screening for breast cancer, and separately lung cancer, in terms of the TVDT and onset of lethal metastases.

Figure 1

Natural history model of cancer: The volume of the primary tumor V(t) grows exponentially with tumor volume doubling time, TVDT, and the treatment cure threshold occurs at size V_C. Patients detected and treated at or before V_C are cured of their disease; otherwise, lethal metastatic burden B(t) will grow exponentially from V_C in proportion (f) to the primary tumor and become the cause of cancer death at a maximal metastatic tolerance level B_D. The lethal metastatic burden becomes observable when it reaches a fraction (k₁) of B_D . A patient detected after this moment is regarded as having advanced staged. A patient is detected from either the primary tumor or metastasis, dependent on which prompts detection present first. The primary tumor is detected at size V_P, and the lethal metastatic burden is detected when it reaches a fraction (k₂) of B_D.

Figure 2

Model validation for non-small cell lung carcinoma (NSCLC), symptomatically detected in the absence of screening. (a) Distribution of tumor size (diameter in cm) predicted by model (grey) and observed in SEER (black). (b) Proportion of advanced stage diseases (stratified by tumor size) predicted by model and observed in SEER. (c) Disease-specific survival predicted by model (dashed curves) and observed in SEER (solid curves). The red, green and black curves represent early stage, advanced stage, and all cases, respectively. (d) Disease-specific survival predicted by model (red solid curve) vs. observed in the MLP control arm (black solid curve). The black dotted curves represent 95% confidence interval of MLP.

Figure 3

Model validation for invasive ductal carcinoma (IDC) symptomatically detected in the absence of screening. (a) Distribution of tumor size (diameter in cm) predicted by model (grey) and observed in SEER (black). (b) Proportion of advanced stage diseases (stratified by tumor size) predicted by model and observed in SEER. (c) Disease-specific survival predicted by model (dashed curves) and observed in SEER (solid curves). The red, green and black curves represent early stage, advanced stage, and all cases, respectively. (d) Disease-specific survival predicted by model (red solid curve) vs. observed in the HIP non-screened participants diagnosed from 1975 to 1979 (black solid curve). The black dotted curves represent 95% confidence interval of HIP.

Figure 4

Comparison of the model-based predictions of the impact of screening for non-small cell lung carcinoma (NSCLC) versus invasive ductal carcinoma (IDC), among patients who would have been symptomatically detected in the absence of screening. (a): Probability of disease-specific cure by tumor size at screen detection. (b): Distribution of tumor volume doubling time (TVDT) in days, represented as the 1^st quartile, median, and the 3^rd quartile. (c): Disease progression timeline, where the median length of the following time intervals are presented: progression from 2 mm to 5 mm, from 5mm to the treatment cure threshold, from the treatment cure threshold to clinical detection, and from clinical detection to disease-specific death. (d): Median length of opportunity window for early detection as a function of the screen detection threshold (mm).

Figure 5

Estimated probability of disease-specific cure for NSCLC (black curves) and IDC (red curves) in the absence of screening (dotted curves) and under two alternative screening detection thresholds (solid curves: 5mm; dashed curves: 15mm) and screening intervals (1 to 24 months). The disease-specific mortality reduction from screening is computed as difference between the probability of disease-specific cure in the presence and absence of screening divided by one minus the probability of disease-specific cure in the absence of screening. All estimates are limited to patients who would have been symptomatically detected in the absence of screening.