Baseline Risk and Absolute Genotype Risks

Why a Baseline Risk Is Needed

A genotype effect stated only as a difference does not tell us the probability of the phenotype. For example, a difference of 4 percentage points could correspond to a change from 2% to 6%, or from 40% to 44%. To describe the probability for a particular genotype, we need both a reference risk and the difference from that reference.

This calculation is meaningful only when the risk and the difference refer to the same outcome, population context, and time horizon. A risk of developing a condition within five years cannot be combined with a difference defined for lifetime risk. Likewise, a baseline risk in one age group should not be combined mechanically with a genotype contrast defined for a different age group.

Here, “absolute” means that the result is a probability on the zero-to-one scale, rather than just a contrast between groups. The baseline is the risk in the stated reference group; it is not automatically the risk in the whole population, and it is not necessarily a risk that would occur if all genetic effects were absent. The reference group can be a genotype, such as \(AA\), with other conditions held fixed or otherwise defined.

A risk difference is an additive change in probability. For instance, a difference of \(0.04\) means an increase of 0.04 in probability, or 4 percentage points. It does not mean a 4% increase relative to baseline. The latter would involve a different calculation. Keep the scale explicit: a probability of \(0.12\) is 12%, and a difference of \(0.04\) is 4 percentage points.

Calculating Genotype-Specific Absolute Risks

The calculation is direct: add the genotype-specific difference to the baseline risk. A positive difference raises the risk above baseline; a negative difference lowers it. For the reference genotype itself, the difference is zero by definition, so its absolute risk is the baseline risk.

The inputs must be on the probability scale and refer to a common target context. If a table gives a risk difference in percentage points, convert it to a probability before adding it to a baseline written as a proportion. For example, 3 percentage points is \(0.03\), not \(3\).

Probability Bounds and Consistency

A probability must lie between zero and one. Consequently, an absolute risk calculated from a baseline and a difference must satisfy \(0\leq p_g\leq 1\). Substituting \(p_g=p_0+\delta_g\) gives a useful check on any proposed contrast:

The lower bound says a negative difference cannot reduce risk below zero. The upper bound says a positive difference cannot raise risk above one. A contrast outside these limits is incompatible with the stated baseline if it is intended to describe an actual probability in that same context. This check does not establish that the values are accurate; it only identifies an arithmetic or modeling inconsistency with the probability scale.

The values in such a calculation are specific to the defined context. If risks are conditional on age, environment, or another variable, then \(p_0\) and \(\delta_g\) must refer to the same value or distribution of that variable. If they do not, adding them may combine quantities that describe different groups. A population-average risk can also differ from a risk conditional on a particular context, because the groups being averaged over may differ.

Changing the Reference Genotype

The choice of reference genotype changes the baseline and the numerical contrasts. It does not change the underlying absolute risks when the same genotype risks and context are being described. This is a re-expression of the same set of probabilities, not a change in the phenotype risks themselves.

Deriving the Reference-Change Formula

The reference-change rule follows directly from the definition of a risk difference. With original reference \(g_0\), the contrast for genotype \(g\) is \(\delta_g=p_g-p_0\), and the contrast for a newly selected reference \(h\) is \(\delta_h=p_h-p_0\). Subtract the second equality from the first:

Therefore the contrast for \(g\) relative to \(h\) is \(\delta_g-\delta_h\). The new baseline is \(p_h=p_0+\delta_h\). Combining them gives

This identity is useful when reporting effects with a different reference genotype: update both the baseline and the contrasts together. Changing only the contrast labels, or only the baseline, will generally produce incorrect absolute risks.

Interpretation, Scope, and Common Pitfalls

A genotype-specific absolute risk is a probability for a defined outcome, time horizon, and target context. It is not necessarily the overall risk for all people in a population. The overall risk depends on how common each genotype is and on the risks across those genotypes; the genotype frequencies alone do not replace the genotype-specific probabilities.

The arithmetic also does not establish that genotype causes a change in risk. It translates a stated baseline and stated genotype-specific differences into probabilities. Interpretation as an association or a causal effect depends on how those quantities were obtained and on the study design and assumptions. For this calculation, do not attach a causal interpretation merely because the difference is labelled a genotype effect.

• Wrong reasoning: “A difference of 4 means add 4.” A risk difference is often given as a proportion or in percentage points. Convert it to the probability scale first: 4 percentage points is \(0.04\), not \(4\).
• Wrong reasoning: “A 4-point difference means the risk is 4%.” The difference is not the absolute risk. Add it to the baseline; for example, \(0.08+0.04=0.12\), or 12%.
• Wrong reasoning: “Any population risk can be used as the baseline.” Use the risk for the explicitly named reference group in the same target context and over the same period.
• Wrong reasoning: “A calculated value is valid even if it is negative or above 1.” Such a value cannot be a probability. Check the units, reference group, context, and arithmetic; a contrast may also be incompatible with the baseline.
• Wrong reasoning: “Changing the reference changes the genotype risks.” It changes the baseline and the contrasts. When they are re-expressed consistently, the absolute risks remain the same.