gms | German Medical Science

Background: Laubender et al. [1] introduce the LML model, a trinormal model for two potential treatment responses in parallel group randomized clinical trials (RCTs) using a baseline biomarker measurement and reconstruct the invisible correlation between both responses. Their main assumption is a linear dependence between biomarker and the sum of the potential outcomes. We apply this approach to right-censored log-normally distributed time to event data by log-transforming the event times and combining the LML model with the EM-algorithm.

The main aim of this contribution is to assess potential bias in the relevant model parameters and to determine their confidence intervals. Furthermore, we would like to apply the model to a real RCT. Finally, the relevance of log-normal event data in specific clinical settings is explored.

Methods: We performed an extensive simulation study. The data was produced by the LML model combined with an independent censoring mechanism. The EM algorithm provided a log-likelihood estimation on the simulated data set based on imputed (multiple) right-censored survival data. Rubin's rules were applied to pool the results of the multiple imputations. Bias and standard errors for the parameters between the full informative data without censoring and the censored data were calculated.

Results: We varied sample size (5), correlation between responses and biomarkers (8), percentage of censoring (3) within 120 simulation scenarios. Bias in parameters was given if in both treatment groups correlations between biomarker and event times were similar, by low (<100) group size, or relevant censoring in small groups. Relative efficiency was also influenced by sample size and censoring, but was acceptable in the setting of a typical RCT.

We applied the method to an RCT from the field of chronic myeloid leukaemia. Large group size and a high censoring rate are typical for RCTs in this area. We present an example where age is a relevant biomarker and survival under bone marrow transplantation versus medical therapy (Interferon) are the outcomes. The example shows several drawbacks of the censored log-LML model caused by small correlation coefficients between age and log-transformed survival in both treatment groups.

Conclusion: The simulation studies showed a good performance of the censored log-LML model in typical RCT settings if the normality assumptions are met. The clinical example teaches the need to check these assumptions carefully before applying the proposed model. The Doornik-Hansen test seems to be appropriate for these assessments.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.