Sequential analysis of latent variables using mixed-effect latent variable models: Impact of non-informative and informative missing data

Sequential methods allowing for early stopping of clinical trials are widely used in various therapeutic areas. These methods allow for the analysis of different types of endpoints (quantitative, qualitative, time to event) and often provide, in average, substantial reductions in sample size as compared with single-stage designs while maintaining pre-specified type I and II errors. Sequential methods are also used when analysing particular endpoints that cannot be directly measured, such as depression, quality of life, or cognitive functioning, which are often measured through questionnaires. These types of endpoints are usually referred to as latent variables and should be analysed with latent variable models. In addition, in most clinical trials studying such latent variables, incomplete data are not uncommon and the missing data process might also be non-ignorable. We investigated the impact of informative or non-informative missing data on the statistical properties of the double triangular test (DTT), combined with the mixed-effects Rasch model (MRM) for dichotomous responses or the traditional method based on observed patient's scores (S) to the questionnaire. The achieved type I errors for the DTT were usually close to the target value of 0.05 for both methods, but increased slightly for the MRM when informative missing data were present. The DTT was very close to the nominal power of 0.95 when the MRM was used, but substantially underpowered with the S method (reduction of about 23 per cent), irrespective of whether informative missing data were present or not. Moreover, the DTT using the MRM allowed for reaching a conclusion (under H(0) or H(1)) with fewer patients than the S method, the average sample number for the latter increasing importantly when the proportion of missing data increased. Incorporating MRM in sequential analysis of latent variables might provide a more powerful method than the traditional S method, even in the presence of non-informative or informative missing data.