## Understanding uncertainty: Microlives

Submitted by mf344 on January 11, 2012Speeding towards death.

Acute risks, such as riding a motorbike or going skydiving, may result in an accident — a natural unit for comparing such risks is the *micromort*, which is a 1-in-a-million chance of sudden death, for some defined activity (see our previous article Small but lethal).

However many risks we take don't kill you straight away: think of all the lifestyle frailties we get warned about, such as smoking, drinking, eating badly, not exercising and so on. The *microlife* aims to make all these chronic risks comparable by showing how much life we lose on average when we're exposed to them:

**A**

*microlife*is 30 minutes off your life expectancyLife expectancy for a man aged 22 in the UK is currently about 79 years, which is an extra 57 years, or 20,800 days, or 500,000 hours, or 1 million half hours. So, a young man of 22 typically has 1 million half-hours ahead of him, the same as a 26 year-old woman. We define a microlife as a chronic risk that shortens life on average by just one of the million half hours that they have left.

Here are some things that would, on average, cost a 30-year-old man one microlife:

- Smoking two cigarettes
- Drinking 7 units of alcohol (e.g. 2 pints of strong beer)
- Each day of being 5 Kg overweight

Details of the derivations of these quantities are given below.

Of course this is not a precise consequence of each cigarette smoked or drink drunk: it comes from accumulating the effects of a lifetime of behaviour and averaging it over a whole population. And these are very rough figures, based on many assumptions. If you just smoke two cigarettes and then stop, it is impossible to say what long-term effect it will have on you, for a number of reasons. First, microlives are usually based on comparisons between different people (e.g. people who smoke and people who don't smoke) rather than people who have changed behaviour (although below we consider evidence from people who stop smoking). Second, we can never know what would have happened had an individual done something different, the *counterfactual*.

There is a simple relationship between change in life expectancy and microlives per day. Consider a person aged around 30 with a life expectancy of 50 years, or 18,000 days. Then a daily behaviour or status that leads them to lose a year of life expectancy (17,500 microlives) means they are using up around one microlife every day of their lives.

### The speed of living your life

Microlives encourage the metaphor that people go through their lives at different speeds according to their lifestyle. For example, someone who smokes 20 a day is using up around 10 microlives, which could be loosely interpreted as their rushing towards their death at around 29 hours a day instead of 24. This idea of premature ageing has been found to be an effective metaphor in encouraging behaviour change. An example is your "lung age" — the age of a healthy person who has the same lung function as you (see 1). "Heart age" is also becoming a popular concept.

An interesting issue is that life expectancy has been increasing by around 3 months every year (that's 12 microlives per day) for the last 25 years. This could be interpreted as follows: although just by living we are using up 48 microlives a day, our death is also moving away from us at 12 microlives a day. Essentially our health care system and healthier life-styles are giving us a bonus pay-back of 12 microlives per day.

### What is the relation between a micromort and a microlife?

It turns out that exposing ourselves to a micromort, a 1-in-a-million chance of death, corresponds to a reduction of our life expectancy by a millionth. Hence a young adult taking a micromort's acute risk is almost exactly exposing themselves to a microlife (recall that a young man of 22 is expected to have 1 million half-hours ahead of him). An older person taking the same risk, while still reducing their life-expectancy by a millionth, is only perhaps losing 15 minutes life-expectancy. However, acute risks from dangerous activities are not well expressed as changes in life expectancy, and so different units appear appropriate.

There is one big difference between micromorts and microlives. If you survive your motorbike ride, then your micromort slate is wiped clean and you start the next day with an empty account. But if you smoke all day and live on pork pies, then your microlives accumulate. It's like a lottery where the tickets you buy each day remain valid forever — and so your chances of winning increase every day. Except that, in this case, you really don't want to win.

### What is the official value of a microlife and a micromort?

Slurp down those microlives.

Governments also put a value on microlives. The UK National Institute for Health and Clinical Excellence (NICE) has guidelines which suggest the National Health Service pay up to £30,000 if a treatment is expected to prolong life by one healthy year. That's around 17,500 microlives. This means that NICE prices a microlife at around £1.70 (see the *Plus* article The economics of health for more on NICE's methods of evaluating life). The UK Department of Transport prices a "value of a statistical life" at £1,600,000, which means they are willing to pay £1.60 to avoid a 1-in-a-million chance of death, or a micromort. So two government agencies put similar value on a microlife and a micromort.

### How to derive the values: Smoking

A very basic analysis has estimated a 6.5 years difference in life-expectancy between smokers and non-smokers, which is 3,418,560 minutes (see 2). They considered median consumption of 16 cigarettes a day from ages 17 to 71, which comes to 311,688 cigarettes. Making the simplifying assumption that each cigarette contributes equally to the risk, this comes to 11 minutes a cigarette or around 3 cigarettes for a microlife.

Smokers, however, may have lower life-expectancy anyway because of the type of person they are and other life-style factors. So a more sophisticated analysis would look at the effect of stopping smoking. Another study (see 3) analysed data on 40,000 UK doctors, many of whom gave up smoking during the period of the study from 1951 to 2001. They estimate a 40-year-old man who stopped smoking gained 9 years in life-expectancy, or 4,700,000 minutes. If he carried on smoking he only expected to live another 30 years or 11,000 days, during which he smoked 325,000 cigarettes (assuming the higher consumption of 30 a day in 1950s and 1960s). This works out at 15 minutes lost per cigarette smoked, or around 2 cigarettes for a microlife.

### How to derive the values: Alcohol

One study (see 4) provides spreadsheets for the annual risk of all-cause mortality for different ages and quantities of alcohol drunk per week, in UK units. Consider a 20 year-old man who drinks 28 units a week (which is officially considered "hazardous"), rather than seven units a week. His life expectancy is decreased by six months to 55 years, which works out at a loss of 4,400 hours or 8,800 microlives. During this period he will drink three units extra a day, which is 60,000 extra units of alcohol. Thence he loses one microlife per seven units of alcohol consumed, which is about two pints of strong beer.

### How to derive the values: Weight

Shed microlives by piling on pounds.

One way of quantifying someone's body fat is to look at their body mass index (BMI), which is defined to be their weight in kilograms divided by their height in metres squared. A recent paper (see 5) estimates a relative annual risk of 1.29 for all-cause mortality per 5 kg/m^{2} increase in BMI over the optimum of 22.5 to 25 kg/m^{2}. For a man of average height (1.75m), this corresponds to a relative risk of 1.09 per 5 kg overweight, where the optimal weight is taken as between 69 and 77 kg. Using the formula derived from relative risks (see below), this corresponds to a loss of around 0.95 years life-expectancy for a man aged 35 who is 5 kg overweight. He is expected to live around another 40 years or 15,000 days. This means he is losing around 350 days life-expectancy, 16,500 microlives, for every day he is overweight. This corresponds roughly to one microlife lost for each day being 5 kg overweight.

### Mathematical appendix: A simple way of obtaining change in life-expectancy from epidemiological studies

There are two quantities that measure the excess risk of someone engaging in a particular activity, for example smoking. One is the *standardised mortality ratio* (SMR): the ratio between observed deaths among people who smoke to expected deaths in the general population. The other is the *hazard ratio*: the ratio between the daily risk of death for smokers to the daily risk of death for the general population.

John Haybittle (who was a very fine but modest statistician) describes very nicely how to approximate changes in life-expectancy from standardised mortality ratios or hazard ratios (see 6).

Haybittle’s method is based on the *Gompertz approximation* to human survival risk, which approximates the annual risk of dying at age by a function

where and are constants. Assuming that the Gompertz model is correct, the life-expectancy at age is given by

For current survival, for both men and women.

When is small compared with , which holds for ages below 40, the second term in the life expectancy becomes negligible, and the life expectancy can be approximated by

An SMR or hazard ratio throughout the whole life leads to a change in life-expectancy at age . This can be obtained by using the above formula but substituting for .

Now

So the change in life expectancy from a lifetime excess risk is , giving roughly for For small excess risks this is roughly So something that raises your daily mortality risk by 1% () will on average take around 0.11 years or 40 days off your life.

Very roughly, a person in their 30s facing, from some cause, a daily relative risk of death of 1.09 throughout their life is losing around 1 microlife per day. This follows as they expect to lose around 0.95 years in life-expectancy, or 17000 microlives, and yet expect to live another 50 years or so which is around 18000 days.

### References

1. Parkes G, Greenhalgh T, Griffin M, Dent R. Effect on smoking quit rate of telling patients their lung age: the Step2quit randomised controlled trial. BMJ. 2008 Mar 15;336(7644):598–600.

2. Shaw M, Mitchell R, Dorling D. Time for a smoke? One cigarette reduces your life by 11 minutes. BMJ. 2000 Jan 1;320(7226):53.

3. Doll R. Mortality in relation to smoking: 50 years’ observations on male British doctors. BMJ. 2004 Jun 26;328:1519–0.

4. White IR, Altmann DR, Nanchahal K. Alcohol consumption and mortality: modelling risks for men and women at different ages. BMJ. 2002 Jul 27;325(7357):191.

5. Prospective Studies Collaboration. Body-mass index and cause-specific mortality in 900 000 adults: collaborative analyses of 57 prospective studies. The Lancet. 2009 Mar;373:1083–96.

6. Haybittle JL. The use of the Gompertz function to relate changes in life expectancy to the standardized mortality ratio. International Journal of Epidemiology. 1998 Oct 1;27(5):885–9.

### About the author

David Spiegelhalter

David Spiegelhalter is Winton Professor of the Public Understanding of Risk at the University of Cambridge. David and his team run the *Understanding uncertainty* website, which informs the public about issues involving risk and uncertainty.