They concluded that there was a dose-dependent relationship between all causes of dying and shorter telomeres. The “p-value” is the estimate that this relationship was due to random chance. That p-value was 0.000000000000002 or 2 in 1,000,000,000,000,000 odds.
cells from prostate cancer patients with short telomeres and hypervariable lengths were 14X more likely to die of their disease
Anderson et al showed a significant association with shorter telomeres and risk of dementia and mortality. But they call for more research and decline to state the two are causally related.