News “cycling to work can halve cancer risk” - from a statistical perspective

Holiday Special Update III

Today’s blog gives a statistical perspective on the article published in BBC health news on 20 April 2017 titled “Cycling to work halves cancer risk”.

Risk to a disease means the probability of catching that disease. Catching of a disease in an individual’s life time is a random event and it is a function of time. So denoting X(t) as a random variable denoting the state of having a disease (say cancer) at time t takes two values 0 and 1. x (t) = 0 implies a disease free state with some probability P(x (t) = 0) denoted by  p1 and x(t) = 1 implies the existence of a disease at time t with probability P(x(t) = 1) denoted by p2. Here p1+p2=1, because either an individual is in a state of health or he/she has a disease at time t and these two states are exhaustive and mutually exclusive. This disease could be as common as common cold or not as common as cancer. For a healthy and young individual p1>p2 and as time progresses implying that as an individual become older and older p2 becomes closer and closer to 1. These probabilities can be explained by a probability distribution. Diseases those are common in modern day life like high blood pressure and sugar can be explained by Binomial probability distribution. This distribution tends to normal distribution when the size of population is large. The incidence of not so common diseases/rare diseases can be explained by Poisson distribution and Negative binomial distribution. Normal distribution is a limiting case for these distributions as well. As the news says ”Cycling to work can halve the cancer risk”, this implies that p2, which is the probability of catching a disease (cancer) at time t is reduced by half when people cycle to their places of work. Similarly regular exercise and consumption of balanced diet can also reduce p2. p2 is a function of time/age and it increases as age increases. But its growth can be checked by cycling to work.

Human life is governed by several random events. These occurrences can be statistically analyzed by the probability distribution of random variables that explain these random events.  Clinical trials and data based research give us an idea of values of these p1 and p2.  This is an evidence/data based approach of estimating p1 and p2. This kind of research complements laboratory based research. If time and energy is invested in making a  foundation of good quality data, then breakthrough results can be obtained with much less time and money.