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Tales (and heads) of statistics in large genetic studies

Ken Rice

Associate Professor

Analysis Committee Chair, CHARGE consortium

http://faculty.washington.edu/kenrice

Q. What do you do?

Like most faculty, my time is split;

• Teaching courses• Advising students (Training Grant)• Developing new statistical methods• … and Cardiovascular disease research

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Q. What do you do in GWAS?

p < 5x10-8?

Y

G

Basically, it’s embarrassingly simple…

Q. What does 5x10-8 mean?

5x10-8 is 0.00000005; a 1-in-20-million chance, or a 5-millionths of 1 percent. Which of these are more/less likely?

A. You are struck by lightning, this year

B. Your 1 ticket wins WA’s Lottery Jackpot

C. You (born today) live to 110 years old

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1 in 7 million

1 in a m

illion

1 in 250 million

Q. What’s it mean that’s familiar?

• Someone is tossing coins; who?

6Nice, ineffectual Causes deaths!

Q. Dudley D-R or Snidely W?

Suppose we see;• 2 heads in a row;

p=1/4• 3 heads in a row;

p=1/8

7Neither of these would be very suspicious

Q. Dudley or Snidely, in a GWAS?

How many heads in a row gives p<5x10-8 ?

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p=

• In GWAS, seeing ‘only’ 24 heads in a row isn’t enough to make us suspicious (!)

Q. Dudley or Snidely? (harder)

Suppose, unknown to us and the coin-tosser, the coin was a little biased?

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Heads comes up more often than usual; we’d be suspicious too soon

Q. Dudley or Snidely? (harder)

How much does it matter? If the coin actually has a 55% chance of heads;• 3 heads in a row;

=16.6%

• but we’d think; = 12.5%

We’d be 1.33 too suspicious – about the same as extra 4/10 Heads, from a fair coin

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Q. How does this affect GWAS?

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We thought 3+0.4 heads, not 3

We’d think 29.9 heads, not 25 (!)

We’d think 26.7 heads, not 23 (!!!)

Q. How does this affect GWAS?

Inflation exactly like this happens in GWAS;• If many tests are only slightly ‘wrong’, there

will be many spurious signals• E.g. some variants

are more common in Scots…

• We can fix it, by ‘angling down’ the line so it behaves correctly at p=0.5 (i.e. at 1 head)

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Q. Is that the only problem? (no)

Back to our cartoon – and a fair coin;

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Computers work out p;…actually, they* just work out the approximate value of p

*…even the cool stylish ones

Q. What’s the right answer?

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132

132

532

1032

1032

532 = 0.031

Q. What’s the approximate answer?

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p = 0.031Area = 0.033

(i.e. 4.9 heads)

Q. What happens in GWAS?

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For 25/25 heads; p = 3x10-8

Area = ???

Q. What happens in GWAS?

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At 25/25 heads; p = 3x10-8

Area = 1.3x10-12

i.e. 39.5 heads (!)

Claiming 25 H’s worth of suspicion when should claim 18 (!!!)

No problem, at 5 H’s

Q. How does this affect GWAS?

Inflation exactly like this happens in GWAS;• The data is fine, but the approximate

calculations are too approximate• The ‘angling down’ fix doesn’t work, here• In GWAS we can’t do perfect calculations

– but are now using better approximations• More accurate results & better science

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Q. Are you going to stop now?

In summary; • “Omics” data a huge statistical

challenge… even to do familiar stuff• We want people who are;

– Smart – Inquisitive about statistics– Care about doing good science