This is a systematic error due to the differences in response rates of participants in a study [1], and happens when participation in the study is related to the exposure status.

In a case-control study it is sometimes difficult to identify controls. Some don't respond either because they refuse, because they cannot be contacted, or because their exposure cannot be documented. The assumption is then that controls not included in the study (non-respondents) have the same history of exposure as controls who respond. However, if this is not true - and non-respondents exhibit exposures or outcomes which differ from those of respondents - the exposure among controls may be either overestimated or underestimated, leading to a lower or higher odds ratio. Efforts must be made to achieve high response rates (i.e. a low 'non-response rate') and prevent non-response bias.  

The antithetical bias is called 'volunteer bias' (i.e. volunteers from a specified sample may exhibit exposures or outcomes (e.g. be healthier) different to those of non-volunteers e.g. volunteers for screening [2]).

Example: the following example illustrates the consequences of non-response linked to exposure in a case-control study (non-response occurs among controls).

All cases and controls are responding
Exposure Cases Controls OR
Yes 150 50 9.0
No 50 150 reference
Total 200 200  
 
30% of controls are not responding (respectively 30% of exposed and 30% of unexposed controls)
Exposure Cases Controls OR
Yes 150 35 9.0
No 50 105 reference
Total 200 140  

i.e. if the proportion of non-response is equal among exposed and unexposed controls, the OR is unchanged.

This second example illustrates the effect on the estimation of the OR when the proportion of non-response differs among exposed and unexposed controls, although the overall non-response rate among controls is still 30%, as in the first example.

30% of controls are not responding (respectively 70% of exposed and 17% of unexposed controls)
Exposure Cases Controls OR
Yes 150 15 25
No 50 125 reference
Total 200 140  
 
30% of controls are not responding (respectively 10% of exposed and 37% of unexposed controls)
Exposure Cases Controls OR
Yes 150 45 6.3
No 50 95 reference
Total 200 140  

i.e. if the proportion of non-response is not equal among exposed and unexposed controls, the estimated OR is biased.

The same consequence can be observed if non-response occurs among cases.

Example: a case-control study to assess the association between smoking and myocardial infarction (MI) was done using a postal questionnaire. Non-response was higher among exposed than unexposed MI cases, leading to an underestimation of the strength of association between smoking and MI.