Wednesday, 2 April 2014

Statistics of Poverty

Norman Fenton, 2 April 2014

I was one of two plenary speakers at the Winchester Conference on Trust, Risk, Information and the Law yesterday (slides of my talk: "Improving Probability and Risk Assessment in the Law" are here).

The other plenary speaker was Matthew Reed (Chief Executive of the Children's Society) who spoke about "The role of trust and information in assessing risk and protecting the vulnerable". In his talk he made the very dramatic statement that
"one in every four children in the UK today lives in poverty"
He further said that the proportion had increased significantly over the last 25 years and showed no signs of improvement.

When questioned about the definition of child poverty he said he was using the Child Poverty Act 2010 definition which defines a child as living in poverty if they lived in a household whose income (which includes benefits) is less than 60% of the national median (see here).

Matthew Reed has a genuine and deep concern for the welfare of children. However, the definition is purely political and is as good an example of poor measurement and misuse of statistics as you can find. Imagine if every household was given an immediate income increase of 1000%  - this would mean the very poorest households with, say, a single unemployed parent and 2 children going from £18,000 to a fabulously wealthy £180,000 per year. Despite this, one in every four children would still be 'living in poverty' because the number of households whose income is less than 60% of the median has not changed.  If the median before was £35,000, then it is now £350,000 and everybody earning below  £210,000 is, by definition, 'living in poverty'.

At the other extreme if you could ensure that every household in the UK earns a similar amount, such as in Cuba where almost everybody earns $20 per month then the number of children 'living in poverty' is officially zero (since the median is $240 per year and nobody earns less than $144).

In fact, in any wealthy free-market economy whichever way you look at the definition it is loaded not only to exaggerate the number of people living in poverty but also to ensure (unless there is massive wealth redistribution to ensure every household income is close to the median level) there will always be a 'poverty' problem:
  • Households with children are much more likely to have one, rather than two, wage earners, so by definition households with children will dominate those below the median income level.
  • Over the last 20 years people have been having fewer children and having them later in life, which again means that an increasing proportion of the country's children inevitably live in households whose income is below the median (hence the 'significant increase in the proportion of children living in poverty over the last 25 years').
  • Families with large numbers of children (> 3) increasingly are in the immigrant community (Asia/Africa) whose households are disproportionately below the median income. 
Unless the plan is stop households on below median income from having children (also known as eugenics), the only way to achieve the stated objective of 'making child poverty history' (according to this definition) is to redistribute wealth so that no household income is less than 60% of the median (also known as communism). Judging by some of the people who have been pushing the 'poverty' definition and agenda it would seem the latter is indeed their real objective.

Bayesian network approach to Drug Economics Decision Making

Consider the following problem:
A relatively cheap drug (drug A) has been used for many years to treat patients with disease X. The drug is considered quite successful since data reveals that 85% of patients using it have a ‘good outcome’ which means they survive for at least 2 years. The drug is also quite cheap, costing on average $100 for a prolonged course. The overall “financial benefit” of the drug (which assumes a ‘good outcome’ is worth $5000 and is defined as this figure minus the cost) has a mean of $4985.

There is an alternative drug (drug B) that a number of specialists in disease X strongly recommend. However, the data reveals that only 65% of patients using drug B survive for at least 2 years (Fig. 1(b)). Moreover, the average cost of a prolonged course is $500. The overall “financial benefit” of the drug has a mean of just $2777.
On seeing the data the Health Authority recommends a ban against the use of drug B. Is this a rational decision?

The answer turns out to be no. The short paper here explains this using a simple Bayesian network model that you can run (by downloading the free copy of AgenaRisk)