Chronological bias in randomized clinical trials arising from different types of unobserved time trends

In clinical trials patients are commonly recruited sequentially over time incurring the risk of chronological bias due to (unobserved) time trends. To minimize the risk of chronological bias, a suitable randomization procedure should be chosen.

Considering different time trend scenarios, we aim at a detailed evaluation of the extent of chronological bias under permuted block randomization in order to provide recommendations regarding the choice of randomization at the design stage of a clinical trial and to assess the maximum extent of bias for a realized sequence in the analysis stage.

For the assessment of chronological bias we consider linear, logarithmic and stepwise trends illustrating typical changes during recruitment in clinical practice. Bias and variance of the treatment effect estimator as well as the empirical type I error rate when applying the t-test are investigated. Different sample sizes, block sizes and strengths of time trends are considered.

Using large block sizes, a notable bias exists in the estimate of the treatment effect for specific sequences. This results in a heavily inflated type I error for realized worst-case sequences and an enlarged mean squared error of the treatment effect estimator. Decreasing the block size restricts these effects of time trends. Already applying permuted block randomization with two blocks instead of the random allocation rule achieves a good reduction of the mean squared error and of the inflated type I error. Averaged over all sequences, the type I error of the t-test is far below the nominal significance level due to an overestimated variance.

Unobserved time trends can induce a strong bias in the treatment effect estimate and in the test decision. Therefore, already in the design stage of a clinical trial a suitable randomization procedure should be chosen. According to our results, small block sizes should be preferred, but also medium block sizes are sufficient to restrict chronological bias to an acceptable extent if other contrary aspects have to be considered (e.g. serious risk of selection bias). Regardless of the block size, a blocked ANOVA should be used because the t-test is far too conservative, even for weak time trends.