gms | German Medical Science

A commonly used design in health, medical and biomedical research is the repeated measures design, where units, e.g. patients, are observed several times under different conditions. An unavoidable consequence in most repeated measures studies is the occurrence of missing data, for example, subjects may not be available for measurement at some time points. Many powerful statistical methods already exist under the assumption of multivariate normality and a specific covariance matrix structure of the error terms, e.g. linear mixed models. An often-suggested way to handle missing values is to use multiple imputation methods. However, if data is completely skewed or the sample size is small, it is better to use nonparametric methods instead of using multiple imputation methods for replacing the missing data, as these procedures are model based. Therefore, we propose a rank-based method for the general repeated measures design with missing values that assumes neither any specific data distribution nor identical covariance matrices across groups using all available data. The inference will be based on the so-called relative marginal effect, which can be interpreted as the probability that a randomly chosen observation from one time point is greater than a randomly chosen observation over all time points. This method allows for constructing confidence intervals, which is required when reporting to health authorities. The missing mechanism is considered to be completely at random. Using this methodology, continuous, discrete and even ordered categorical data can be analyzed in a unified way. Multiple contrast test procedures can be used within this framework, which unify the testing of the global hypothesis, testing arbitrary pairwise comparisons and calculating simultaneous confidence intervals. This avoids the common problem of incompatible results between an overall test, corresponding pairwise comparisons and confidence intervals. Simulation studies indicate a good performance of this procedure with respect to the type-I-error rate and the power with a missing rate up to 30%, also under non-normality and for small sample sizes. A real data example illustrates the application of the new methodology.

The authors declare that they have no competing interests.

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