bias is a systematic distortion in measuring the true
frequency of a phenomenon due to the way in which the data are
collected. In genetics, ascertainment bias is an important factor
in the use of family pedigrees to establish modes of inheritance.
Consider the inheritance of the genetic condition Alkaptonuria, characterized by excretion of high amounts of "alkapton" (homogentisic acid) in the urine. We know that this is a rare autosomal recessive condition, so that almost all persons born with the condition (aa) will be the offspring of unaffected carrier (Aa) parents. Thus, among a large group of Aa x Aa crosses, 1/4 of offspring are expected to show the condition. Recognition of such a ratio would be an important clue to the pattern of inheritance. In the first inquiry into the genetics of this condition, Garrod (1902) reported the following data:
Given the birth of
offspring with alkaptonuria (aa) to "normal" parents, the parents
may be assumed to all be carriers (Aa). Then, among a total
of 48 offspring of such parents, the expected ratio should be 1:3 or 12
alkaptonuric : 36 normal members. The observed ratio is 19 : 29, that is, significantly more alkaptonurics
are present in the sample than expected from the genetic model.
Why is this? [Homework: Test the deviation between observed and
expected results by the Chi-Square test]. The
answer is the way in which Garrod collected his data.
One source of ascertainment bias is that
Garrod was a physician: his table includes data only from
families in which at least one child has alkaptonuria.
Note that for 3/4 of Aa
parents with one child, that child will be unaffected, and the
family has no reason to consult him. Thus a large number of
families with Aa parents,
and 1, 2, 3, or more unaffected
children are excluded from his counts.
A second source is the greater likelihood that families with a higher number of alkaptonuric children will consult Garrod: they are more likely to seek advice than families in which the condition is confined to a single child. In the table, 6 of 9 families reported have more than one affected child, and in all of these (except family #7) the observed ratio of affected children exceeds 1:3. [Indeed, without family #7, the observed proportion would be 18:20, effectively 1:1]. This will again systematically bias the data towards a higher proportion of affected children.
A classroom demonstration of
ascertainment bias is a survey for the primary sex ratio in humans. Ask all women present to report
the number of male and female siblings in their families. Ask
the same question of men present. The women will report
collectively a higher ratio of females: the survey method is
biased towards families in which there is at least one woman
(themselves), includes many families in which they are
only-children, and excludes families with no female and multiple males. The reverse bias exists in
the male survey, which will report an excess number of males.