In this excellent review of the telomeres of 65,000 Danish people over seven years, they found that shorter telomeres were independently associated with about a 50% higher chance of dying after controlling for all confounding variables.
When you included the confounding factors such as age, smoking, hypertension, it was over 3X the risk.
Read the original paper here: http://jnci.oxfordjournals.org/content/107/6/djv074.short
The reason for this seems obvious to me. The shorter telomeres are causing the mortality because of the shortened telomeres are causing the mutations:
Read my book, TELOMERE TIMEBOMBS, to understand more.