Conditions for Bias from Differential Left Truncation

Spontaneous abortion studies that recruit pregnant women are left truncated because an unknown proportion of the source population experiences losses prior to enrollment. Unconditional logistic regression, commonly used in such studies, ignores left truncation, whereas survival analysis can accommodate left truncation and is therefore more appropriate. This study assessed the magnitude of bias introduced by fitting logistic versus Cox models using left-truncated data from a 1998 US pregnancy cohort study (n = 5,104) of trihalomethanes and spontaneous abortion. In addition, the conditions producing bias were explored by using simulated exposure data. The odds ratios and hazard ratios from the actual study differed by 10% or less. However, when the exposed women entered observation earlier on average than those unexposed, the hazard ratio was closer to the null than the odds ratio, whereas the reverse was true when the exposed entered later. The simulation suggests that bias in the odds ratio will exceed 20% when average gestational age at entry for the exposed versus the unexposed differs by 10 days or more, as has been observed regarding some socioeconomic factors, such as education and ethnicity. Cox regression can correct for left truncation and is no more difficult to perform than logistic regression.