Cancer Survival Data Representation for Improved Parametric and Dynamic Lifetime Analysis

The need for speed in advanced non-small cell lung cancer: A population kinetics assessment

BACKGROUND

Systemic therapy prolongs overall survival (OS) in advanced non-small cell lung cancer (NSCLC), but diagnostic tests, staging and molecular profiling take time, and this can delay therapy initiation. OS approximates first-order kinetics.

METHODS

We used OS of chemo-naive NSCLC patients on a placebo/best supportive care trial arm to estimate % of patients dying while awaiting therapy. We digitized survival curves from eight studies, calculated OS half-life, then estimated the proportion surviving after different times of interest (t_n ) using the formula: X = exp - t n ∗ 0 .693 / t 1 / 2 , where EXP signifies exponential, * indicates multiplication, 0.693 is the natural log of 2, and t_1/2 is the survival half-life in weeks.

RESULTS

Across trials, the OS half-life for placebo/best supportive care in previously untreated NSCLC was 19.5 weeks. Hence, based on calculations using the formula above, if therapy were delayed by 1, 2, 3, or 4 weeks then 4%, 7%, 10%, and 13% of all patients, respectively, would die while awaiting treatment. Others would become too sick to consider therapy even if still alive.

CONCLUSIONS

This quantifies why rapid baseline testing and prompt therapy initiation are important in advanced NSCLC. It also illustrates why screening procedures for clinical trial inclusion must be faster. Otherwise, it is potentially hazardous for a patient to be considered for a trial due to risk of death or deterioration while awaiting eligibility assessment. It is also important to not delay initiation of systemic therapy for procedures that add relatively little value, such as radiotherapy for small, asymptomatic brain metastases.

Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

Pandemic curves, such as COVID-19, often show multiple and unpredictable contamination peaks, often called second, third and fourth waves, which are separated by wide plateaus. Here, by considering the statistical inhomogeneity of age groups, we show a quantitative understanding of the different behaviour rules to flatten a pandemic COVID-19 curve and concomitant multi-peak recurrence. The simulations are based on the Verhulst model with analytical generalized logistic equations for the limited growth. From the log–lin plot, we observe an early exponential growth proportional to et/τgrow. The first peak is often τgrow ≅ 5 d. The exponential growth is followed by a recovery phase with an exponential decay proportional to e−t/τrecov. For the characteristic time holds: τgrow< τrecov. Even with isolation, outbreaks due to returning travellers can result in a recurrence of multi-peaks visible on log–lin scales. The exponential growth for the first wave is faster than for the succeeding waves, with characteristic times, τ of about 10 d. Our analysis ascertains that isolation is an efficient method in preventing contamination and enables an improved strategy for scientists, governments and the general public to timely balance between medical burdens, mental health, socio-economic and educational interests.

Sporadic non-functioning pancreatic neuroendocrine tumours: multicentre analysis

BACKGROUND

Outcomes after surgery for sporadic pancreatic neuroendocrine neoplasms (Pan-NENs) were evaluated.

METHODS

This multicentre study included patients who underwent radical pancreatic resection for sporadic non-functioning Pan-NENs. In survival analysis, the risk of mortality in this cohort was analysed in relation to that of the matched healthy Italian population. Relative survival (RS) was calculated as the rate between observed and expected survival. Factors related to RS were investigated using multivariable modelling.

RESULTS

Among 964 patients who had pancreatic resection for sporadic non-functioning Pan-NENs, the overall RS rate was 91.8 (95 per cent c.i. 81.5 to 96.5) per cent. 2019 WHO grade (hazard ratio (HR) 5.75 (s.e. 4.63); P = 0.030) and European Neuroendocrine Tumour Society (ENETS) TNM stage (6.73 (3.61); P < 0.001) were independent predictors of RS. The probability of a normal lifespan for patients with G1, G2, G3 Pan-NENS, and pancreatic neuroendocrine carcinomas (Pan-NECs) was 96.7, 54.8, 0, and 0 per cent respectively. The probability of a normal lifespan was 99.8, 99.3, 79.8, and 46.8 per cent for those with stage I, II, III, and IV disease respectively. The overall disease-free RS rate was 73.6 (65.2 to 79.5) per cent. 2019 WHO grade (HR 2.10 (0.19); P < 0.001) and ENETS TNM stage (HR 2.50 (0.24); P < 0.001) significantly influenced disease-free RS. The probability of disease-free survival was 93.2, 84.9, 45.2, and 6.8 per cent for patients with stage I, II, III, and IV disease, and 91.9, 45.2, 9.4, and 0.7 per cent for those with G1, G2, G3 Pan-NENS, and Pan-NECs, respectively.

CONCLUSION

A surgical approach seems without benefit for Pan-NECs, and unnecessary for small G1 sporadic Pan-NENs. Surgery alone may be insufficient for stage III-IV and G3 Pan-NENs.

Similarities between pandemics and cancer in growth and risk models

Cancer and pandemics are leading causes of death globally, with severe socioeconomic repercussions. To better understand these repercussions, we investigate similarities between pandemics and cancer and describe the limited growth in number of infections or cancer cells, using mathematical models. For a pandemic, the analysis shows that in most cases, the initial fast growth is followed by a slower decay in the recovery phase. The risk of infection increases due to the airborne virus contact crossing a risk-threshold. For cancers caused by carcinogens, the increasing risk with age and absorbed dose of toxins that cross a risk-threshold, may lead to the disease onset. The time scales are different for both causes of death: years for cancer development and days to weeks for contact with airborne viruses. Contamination by viruses is on a time scale of seconds or minutes. The risk-threshold to get ill and the number-threshold in cancer cells or viruses, may explain the large variability in the outcome. The number of infected persons per day is better represented in log–lin plots instead of the conventional lin–lin plots. Differences in therapies are discussed. Our mathematical investigation between cancer and pandemics reveals a multifactorial correlation between both fragilities and brings us one step closer to understand, timely predict and ultimately diminish the socioeconomic hurdle of both cancer and pandemics.