Abstract
Background: In longitudinal studies, observations are made over time. Hence, the single observations at each time point are dependent, making them a repeated measurement. In this work, we explore a different, counterintuitive setting: At each developmental time point, a lethal observation is performed on the pregnant or nursing mother. Therefore, the single time points are independent. Furthermore, the observation in the offspring at each time point is correlated with each other because each litter consists of several (genetically linked) littermates. In addition, the observed time series is short from a statistical perspective as animal ethics prevent killing more mother mice than absolutely necessary, and murine development is short anyway. We solve these challenges by using multiple contrast tests and visualizing the change point by the use of confidence intervals.Results: We used linear mixed models to model the variability of the mother. The estimates from the linear mixed model are then used in multiple contrast tests.There are a variety of contrasts and intuitively, we would use the Changepoint method. However, it does not deliver satisfying results. Interestingly, we found two other contrasts, both capable of answering different research questions in change point detection: i) Should a single point with change direction be found, or ii) Should the overall progression be determined? The Sequen contrast answers the first, the McDermott the second. Confidence intervals deliver effect estimates for the strength of the potential change point. Therefore, the scientist can define a biologically relevant limit of change depending on the research question.Conclusion: We present a solution with effect estimates for short independent time series with observations nested at a given time point. Multiple contrast tests produce confidence intervals, which allow determining the position of change points or to visualize the expression course over time. We suggest to use McDermott’s method to determine if there is an overall significant change within the time frame, while Sequen is better in determining specific change points. In addition, we offer a short formula for the estimation of the maximal length of the time series.
Air Force Space Programs: Comparing Estimates to Final Development Budgets
