Periodogram Analysis of Censored Time Series from a Designed Experiment

Growth hormone plasma concentrations vary rhythmically between high and low values. Radioimmunoassay measurements of low values are often indistinguishable from low controls, and are reported as a censored value, the 'minimum detectable dose'. This paper reports such a dataset from a designed experiment with about 60% of the values censored but large distinct signals for the remainder of the data. The ordinates of the average periodogram for each treatment group are independently gamma distributed, with distribution depending on the underlying spectrum and the replication for that group. This situation can lead to an analysis for common spectral shape using a gamma generalized linear model with log link, and the hypothesis of common spectral shape is rejected here. Since such a level of censoring reduces the variance of each profile, the periodogram, which is a partition of the variance, is also reduced in overall magnitude. A simulation study shows that this reduction is not necessarily uniform over the frequency domain, but may be more pronounced at lower or higher ordinates depending on the underlying model. Therefore it is possible that the rejection of common spectral shape is an artefact of the censoring.