The Numbers in the video trailer for "Tails You Win: the Science of Chance"

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understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

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Submitted by david on Tue, 09/10/2012 - 1:00pm

Here are brief background notes and links for the numbers used in the video trailer for "Tails You Win: the Science of Chance"

  • “I was born in the 1950s and back then my expected lifespan was just 67 years.”

    See Social Trends 41 - Health

  • “The average lifespan is actually rising by 3 months a year”

    See Social Trends 41 - Health “Between 1930 and 2009 period life expectancy at birth in the UK increased by around 20 years for both sexes”

  • “If I were born today, I could expect to live to 78.” .... “So at my age now, I can expect to live to …. 82”

    See 2010 Interim Life Tables for England and Wales

The various statements about “expecting to lose ½ an hour” are based on the following procedure (see our Microlives page for a full description).

  1. Use epidemiological studies to estimate the annual excess risk for all-cause mortality (hazard ratio) associated with a life-long behaviour
  2. Translate the hazard ratios into changes in life-expectancy using the current life-tables for England and Wales
  3. Calculate the ratio (change in life-expectancy)/(number of days post 35 years old) obtain a pro-rata loss/gain associated with each day with a habit or behaviour post 35 years old.

An annual excess risk of around 9% (hazard ratio 1.09) translates to an approximate loss of ½ an hour each day past 35. Of course we cannot know or measure the precise effect of, say, smoking 2 cigarettes – the “1/2 hour” is a mathematical construct that averages over populations and lifetimes. We also cannot conclude that changes in behaviour will result in subsequent benefits.

  • “Research tells us that for every day you’re five kilos overweight – like I am – you can expect to lose half an hour off your life.”

    A recent meta-analysis based on over 66,000 deaths estimated a hazard ratio of 1.29 for all-cause mortality per 5 kg/sqm increase in body mass index (BMI) over the optimum of 22.5 to 25 kg/sqm. For a man/woman of average height (1.75m/1.62m), this corresponds to a hazard ratio of around 1.09/1.10 per 5 kg overweight.

  • “Sad to say, if you’re a man sinking three pints a day then that’s also half an hour. “

    In a recent meta-analysis of studies involving over 1,000,000 subjects and 94,000 deaths, one drink (10g of alcohol) per day was associated with an adjusted hazard ratio of around 0.83 for men. Each successive daily drink was associated with a hazard ratio of around 1.06, up to 6 drinks a day. The protective effect of alcohol on all-cause mortality is controversial due to the possibility of residual confounding and ex-drinkers having stopped due to ill-health: Di Castelnuovo and colleagues consider a cautious hazard ratio for low consumption is 0.9, which we have assumed. This for a man, 3 pints of low-strength beer (3.5%) per day, containing around 6 UK units (48g of alcohol), would be associated with a hazard ratio of around 0.9 x 1.06 x 1.06 x 1.06 x 1.06 = 1.13, corresponding to around ½ hour each day loss in life-expectancy.

  • “A regular run of half an hour' and you can expect to live longer – half an hour longer.”

    We assume this regular exercise is on top of being reasonably active. A meta-analysis of 22 studies and over 52,000 deaths estimated an adjusted all-cause hazard ratio of 0.81 for 2.5 hours per week (20 minutes a day) of moderate exercise compared to no activity. There were strong diminishing marginal returns, with 7 hours a week associated with a hazard ratio of 0.76, or 0.76/0.81 = 0.94 when compared to 2.5 hours a week. So the extra ½ hour a day of exercise was associated with slightly less than ½ hour average gain in life expectancy.

    Also, in a study of over 400,000 people in Taiwan, an extra 15 minutes of activity each day was associated with a hazard reduction of 4%, so ½ hour was associated with a hazard ario of 0.92, corresponding to around ½ hour gain in life-expectancy.

    These results are for ‘moderate exercise’, and so the ‘run’ is more of the ‘brisk walk’ variety.

  • “Two cigarettes costs half an hour.”

    Doll and Peto estimated a Standardised Mortality Ratio of 2.17 for smoking 15-24 cigarettes per day. If we assume a hazard ratio of 2.2 for 20 cigarettes, and a constant effect of each cigarette on the risk, then pro-rata this translates to a hazard ratio of 1.08 per 2 cigarettes, which translates to 1/2 a day loss of life-expectancy.

  • “I’m 58 now. As the years roll by, in more and more of these possible futures I die, until by the age of 82 about half of my future selves will be dead and about half still alive”

    Numbers surviving derived from 2010 Interim Life Tables for England and Wales

    For smokers, a hazard ratio of 2 is assumed.

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