Mortality Statistics and the Right to Life

For those who ventured to read the Mortality Statistics: ESA, IB and SDA released yesterday by the DWP, there is a very interesting claim / disclaimer, highlighted in bold in the introduction :

Any causal effect between benefits and mortality cannot be assumed from these statistics.
This is repeated again and again after each statistic is given.
The question is: Can the DWP be held responsible, under the ECHR, for these deaths?
The right to life, under Art. 2 ECHR, guarantees the right not to be unlawfully killed. As such, speaking in the abstract, WCA would not constitute lethal force. Neither would withdrawing IB.
But what about a case where a person with disability has her IB closed, and she starves to death? This does look like a violation of Art. 2 ECHR.
The obvious point therefore is that, even we assume, in good faith, that ‘no causal effect can be assumed from these statistics’, there is a procedural positive obligation to investigate deaths which come under the scope of Art. 2.What national authority is best placed to do this?
My argument is that, to the extent that the DWP is not collecting sufficient data about these deaths, the DWP is violating Art. 2 ECHR.