Ascertainment 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 pedigree data 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. Alkaptonuria is an autosomal recessive trait, such that almost all persons born with the condition (aa) will be the offspring of two unaffected heterozygous carrier (Aa) parents. Thus, according to ordinary Mendelian principles, among a large group of Aa x Aa crosses, 1/4 of offspring are expected to show the condition. Recognition of the 3:1 ratio would be an important clue to the pattern of inheritance.

    Alkaptonuria was the first human medical trait to be identified as genetic. In the first inquiry into the genetics of this condition, Garrod (1902) reported the following data:

    Given the birth of alkaptonuric offspring with (aa) to unaffected "normal" parents, the parents must 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, significantly more alkaptonurics are present in the sample than expected from the genetic model. Why is this? The answer is the way in which Garrod collected his data, which results in ascertainment bias.

    One source of ascertainment bias is that Garrod as a physician saw people who consulted him medically. His data tables includes only families in which at least one child has alkaptonuria. Because there is a 3/4 chance that any single child born to Aa parents will not have alkaptonuria, they will not consult Garrod, and he will not count this "zero class". The same is true for (3/4)² = 9/16 and (3/4)³ = 27/64 of two- & three-child families. Thus, large numbers of families with two Aa parents and 1, 2, 3, or more unaffected children are excluded from his counts, and are underrepresented in 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 occurs only 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, which would support a model of autosomal dominant inheritance in which Aa x aa => 50% Aa: 50% aa. Ascertainment bias skews the data towards a higher number of affected children.

  A classroom demonstration of ascertainment bias is a survey for the primary sex ratio in humans.

Homework: (1) Test the deviation between the observed and expected results by the Chi-Square test.
                    (2) Suggest some methods to correct Garrod's data to test the hypothesis of recessive inheritance.