Time series data collected in clinical trials can have varying degrees of missingness, adding challenges during statistical analyses. An additional layer of complexity is introduced for missing data in randomized controlled trials (RCT), where researchers must remain blinded between intervention and control groups. Such restriction severely limits the applicability of conventional imputation methods that would utilize other participants' data for improved performance. This paper explores and compares various methods to impute high-resolution temperature logger data in RCT settings. In addition to the conventional non-parametric approaches, we propose a spline regression (SR) approach that captures the dynamics of indoor temperature by time of day that is unique to each participant. We investigate how the inclusion of external temperature and energy use can improve the model performance. Results show that SR imputation results in 16% smaller root mean squared error (RMSE) compared to conventional imputation methods, with the gap widening to 22% when more than half of data is missing. The SR method is particularly useful in cases where missingness occurs simultaneously for multiple participants, such as concurrent battery failures. We demonstrate how proper modelling of periodic dynamics can lead to significantly improved imputation performance, even with limited data.
