Revealing and addressing length bias and heterogeneous effects in frequency case-crossover studies

The case-crossover design is useful for assessing whether a recurrent exposure (e.g., drug) triggers an event (e.g., myocardial infarction), using only cases, when finding good controls is impractical. In the basic frequency design, the observed exposure odds among cases, during a period immediately before the event, are compared with the expected exposure odds, based on their usual frequency of past exposures. This is equivalent to comparing observed gap times between the event and the last exposure with the expected gap times based on the subjects' exposure experience under the null hypothesis of no exposure-event relation. Such a comparison reveals two problems in the usual-frequency analyses: 1) length bias that exists even under the null hypothesis; and 2) loss of efficiency when exposure effects do exist. The first problem arises because the event will more likely fall on a longer-than-average period between exposures, even under the null hypothesis, resulting in a systematic downward bias of risk ratios. The second problem arises from categorizing cases as exposed or unexposed and from not fully using the data on gap times between events and preceding exposures. A new method of analysis is presented that is free from length bias and that efficiently uses gap time data.