C-reactive protein (CRP) is an acute-phase plasma protein that can be used as a biomarker for activation of the immune system. A spectral analysis of CRP level over time for patients with gynaecological tumours has been reported by Madondo et al., using a periodogram method, suggesting that there is no significant periodicity in the data. In our study, we investigate the impact of low sample number on periodogram analysis, for non-uniform sampling intervals—we conclude that data of Madondo et al. cannot rule out periodic behaviour. The search for patterns (periodic or otherwise) in the CRP time-series is of interest for providing a cue for the optimal times at which cancer therapies are best administered. In this paper we show (i) there is no evidence to rule out periodicity in CRP levels, and (ii) we provide a prescription for the minimum data sample rate required in future experiments for improved testing of a periodic CRP signal hypothesis. The analysis we provide may be used for establishing periodicity in any short time-series signal that is observed without a priori information.

C-reactive protein (CRP) is a biomarker of inflammation and is widely considered as an indicator of cancer prognosis, risk, and recurrence in clinical experiments. Investigating the properties and behaviors of CRP time series has recently emerged as an area of significant interest in informing clinical decision making. The area of cancer immunotherapy is a key application where CRP forecasting is critically needed. Therefore, predicting the future values of a CRP time series can provide useful information for clinical purposes. In this paper, we focus on CRP time series forecasting, comparing autoregressive integrated moving average (ARIMA) modeling with deep learning. The CRP data are obtained from 24 patients with melanoma. This paper using CRP data indicates that deep learning provides significantly reduced prediction error compared to ARIMA modeling.

The eye may perceive a significant trend in plotted time-series data, but if the model errors of nearby data points are correlated, the trend may be an illusion. We examine generalized least-squares (GLS) estimation, finding that error correlation may be underestimated in highly correlated small datasets by conventional techniques. This risks indicating a significant trend when there is none. A new correlation estimate based on the Durbin–Watson statistic is developed, leading to an improved estimate of autoregression with highly correlated data, thus reducing this risk. These techniques are generalized to randomly located data points in space, through the new concept of the nearest new neighbour path. We describe tests on the validity of the GLS schemes, allowing verification of the models employed. Examples illustrating our method include a 40-year record of atmospheric carbon dioxide, and Antarctic ice core data. While more conservative than existing techniques, our new GLS estimate finds a statistically significant increase in background carbon dioxide concentration, with an accelerating trend. We conclude with an example of a worldwide empirical climate model for radio propagation studies, to illustrate dealing with spatial correlation in unevenly distributed data points over the surface of the Earth. The method is generally applicable, not only to climate-related data, but to many other kinds of problems (e.g. biological, medical and geological data), where there are unequally (or randomly) spaced observations in temporally or spatially distributed datasets.

Prediction of the severity of multipath fading is fundamental to the design of point-to-point terrestrial fixed microwave links at frequencies below 10 GHz, but error in this prediction may be significant in countries such as Australia, not represented in the dataset used to generate existing empirical models. We take advantage of recently collected worst-month fading data from Australia, and find new parameters particularly useful in predicting the severe fading experienced in Northern Australia. These parameters are from very irregularly spaced weather stations, so we investigate various interpolation techniques for this situation, including a new version of natural neighbour interpolation. Conventional multipath prediction models are based on ordinary least squares (OLS) regression, but we refine this, taking spatial correlation into account with generalised least squares (GLS) regression. We then demonstrate further improvement in regions well populated by measured data, by employing universal kriging.

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