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# Date of Breakthrough in Cancer Treatment

### Question

Every sixth death in the world is due to cancer, making it the second leading cause of death (second only to cardiovascular diseases). In 2016, 8.9 million people are estimated to have died from the various forms of cancer.

Some cancers are harder to survive than others. Common cancer sites with low 5 year survival rates include the brain and nervous system (35.9%), stomach (31.1%), oesophagus (21%), lungs and bronchus (19.5%), liver (18.5%) and pancreas (8.7%) (all rates for both sexes, all races from 2013 in the U.S.).

When will we see a doubling of the odds of survival (relative to 2013 rates) in the U.S. for cancers in any two of the following sites for both sexes and all races: brain and nervous system, stomach, oesophagus, lungs and bronchus, liver, or the pancreas?

Positive resolution requires any two of the following reported average rates for both sexes and all races in the U.S.

1. $\gt 52.8$% 5-year survival rates for brain and nervous system cancer,
2. $\gt 47.4$% 5-year survival rates for stomach cancer,
3. $\gt 34.7$% 5-year survival rates for oesophagus cancer,
4. $\gt 32.6$% 5-year survival rates for lungs and bronchus cancer,
5. $\gt 31.2$% 5-year survival rates for liver cancer,
6. $\gt 16$% 5-year survival rates for pancreatic cancer,

as reported by the National Cancer Institute, or any other reputable provider of medical statistics.

Historical of survival rates from all listed cancers are catalogued in Our World in Data.

To pinpoint a particular date, we will linearly interpolate between the first day of the year when the last threshold was breached, and the first day of the prior year (see fine-print).

In particular, suppose survival rate for the second cancer of the two was met in year $t_k$, at which point the survival rate was $s_k$. Moreover, the relevant threshold is denoted as $s^*$ Then the resolution date will be given by:

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