Bad statistics – cancer edition

Are two-thirds of cancer due to bad luck as many recent headlines have stated? Well, we don’t really know.

The paper that triggered these headlines found that two-thirds of the variation in log of cancer risk can be explained by the number of cell divisions. More cell divisions – more opportunity for “bad luck”.

But, as pointed out by Bob O’Hara and GrrlScientist, an explanation for variation in incidence is not an explanation for the absolute numbers. As they state, although all variation in the depth of the Marianas trench might be due to tides, tides are not the explanation for the depth of the trench itself. There might be some underlying factor X affecting all cancers.

My reason for drawing attention to this misinterpretation is that a similar confusion occurs in discussions of heritability. Heritability is the proportion of variation in phenotype – an organism’s observable traits – due to genes. If heritability of height is 0.8, 80 per cent of variation in height is due to genetic variation. But your height is not “80 per cent due to genes”.

To make this distinction clear, consider the number of fingers on your hand. Heritability of the number of fingers on your hand is close to zero. This is because most variation is due to accidents where people lose a finger or two. But does this mean that the number of fingers on your hand is almost entirely due to environmental factors? No, it’s almost entirely genetic – those five fingers are an expression of your genes. There is an underlying factor X – our genes – that are responsible for the major pattern.

Turning back to the cancer paper, as PZ Myer points out, there may be no underlying factor X affecting cancer and the two-thirds figure could be correct. Extrapolating one chart hints that might be the case. But that’s not what the paper states.

As an endnote, a recent study pointed out that most errors in scientific reporting start in the research centre press release. This case looks like no exception. From the initial John Hopkins press release (underlining mine):

Scientists from the Johns Hopkins Kimmel Cancer Center have created a statistical model that measures the proportion of cancer incidence, across many tissue types, caused mainly by random mutations that occur when stem cells divide. By their measure, two-thirds of adult cancer incidence across tissues can be explained primarily by “bad luck,” when these random mutations occur in genes that can drive cancer growth, while the remaining third are due to environmental factors and inherited genes.

And from their updated press release:

Scientists from the Johns Hopkins Kimmel Cancer Center have created a statistical model that measures the proportion of cancer risk, across many tissue types, caused mainly by random mutations that occur when stem cells divide. By their measure, two-thirds of the variation in adult cancer risk across tissues can be explained primarily by “bad luck,” when these random mutations occur in genes that can drive cancer growth, while the remaining third are due to environmental factors and inherited genes.

Good on them for updating, but it would have been nice if they had clarified why their first release was problematic.

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