Statistics for Dummies
This chapter brings up some basic statistical concepts and is written for a reader with little or no knowledge of statistics – other readers should skip it. Odds ratios and risk ratios are presented and how their statistical significance can be evaluated,
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Statistics for Dummies
9.1
Risk Estimates
In order to epidemiologically investigate if an exposure (e.g., maternal use of a drug) causes an outcome (e.g., infant congenital malformations), one first has to look for an association between the two; if the outcome occurs more often than expected after the exposure. If so, the next step is to see if it is likely that the excess probably is random or if it is “statistically significant.” The crucial point is then to determine the number of outcomes after the exposure and to get an estimate of how many one would have had if the exposure had not affected the outcome, that is, the expected number. You sometimes hear that you don’t expect a baby to be malformed (which is true), but “expected” here means what number you would expect if the exposure had no effect. The expected number has to be estimated from some sort of a control material, for instance, from the occurrence of the malformation in non-exposed infants. If the observed number of outcomes exceeds the expected number, this indicates the presence of a risk associated with the exposure. In order to quantify this risk, one can use a risk ratio, that is, the ratio between the risk after exposure divided with the risk after non-exposure. We can go back to the simple 2 × 2 table shown already in the introduction. It consists of four central cells and the rand sums (totals). Exposed Unexposed Total
Outcome
No outcome
N1 N3 N1 + N3
N2 N4 N2 + N4
Total N1 + N2 N3 + N4 N1 + N2 + N3 + N4
The risk after exposure is thus N1/(N1 + N2) and after non-exposure N3/(N3 + N4) where N’s represent numbers in each cell and the risk ratio will be N1/(N1 + N2) divided by N3/(N3 + N4). If the risk ratio = 1, the risks are identical, and the exposure has no effect – if it is over 1, the exposure may increase the risk of outcome; if it is
© Springer International Publishing Switzerland 2016 B. Källén, Drugs During Pregnancy, DOI 10.1007/978-3-319-40697-8_9
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9 Statistics for Dummies
lower than 1, the exposure may protect against the outcome. Note thus that at null risk, the risk ratio estimate is 1.0, not 0. The expected number in the “exposed, outcome” cell will be a product of the number of exposed infants and the risk in the total material, thus (N1 + N2)*(N1 + N3)/ (N1 + N2 + N3 + N4). Such risk estimates are difficult or impossible to calculate from case-control studies as the proportion between outcome and no outcome is already defined, for instance, two controls for each case. The odds for exposure in the outcome is N1/N3 and in the non-outcome N2/N4 and the odds ratio is (N1/N3)/(N2/N4). Note that this will be the same if one instead divides the odds for outcome in the exposed with the odds for outcome in the non-exposed. The odds ratio will with necessity always be larger than the risk ratio (because you divide with a smaller number), but when outcomes are relatively rare (like congenital malformations) and exposures are relatively rare (like most drug use), the difference between the odds ratio and the risk ra
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