48 Chapter 2 whether the increased numbers of NT1 in 2009–2011 were age-specific. Since delayed diagnosis is one of the major biases in the time series analyses as aforementioned, the ratios between the numbers of children and adult patients were calculated in each year. We used this artifice to find the genuine increase in either children or adult cases by cancelling out delayed diagnosis (i.e. we assumed that the delayed diagnosis equally influenced the numbers of children and adult patients in each year). We graphically analysed the changes of the ratios from 1995 to 2016 and used box plots to depict outliers. The outliers could confirm whether the increased NT1 were age-specific in specific years after removing the delay bias. Statistical analysis The ARIMA models were built using the R package forecast [143], in which the optimal models were selected automatically based on the bias-corrected Akaike information criterion (AICc) [144]. The LOESS models were 2-degree local polynomial regression and the model selections were done automatically based on AICc as well. They were built using the R package fANCOVA [145]. We used CIs rather than p-values to determine whether the prediction values of our models were significantly different from the real values in 2009–2011 (i.e. the results were significant if the 95% predictive CIs did not contain the real values), considering that p-values can only dichotomize significant or nonsignificant hypothesis testing while CIs could inform both the range of predictions and the statistical significance [146]. The data were expressed as means ± standard error (SE) unless indicated otherwise. Box plot was used in descriptive statistics to visually show the distribution of the data, including the median, interquartile range (IQR), the minimum (1st quartile −1.5 IQR), the maximum (3rd quartile + 1.5 IQR) and the outliers (data smaller than the minimum or larger than the maximum) of the data. All the analyses were done using R (version 3.5.3). Results Results of ARIMA models using data from 1995 to 2011 Combining all European countries, in total 39, 68, and 42 patients developed NT1 in 2009, 2010, and 2011, respectively. All tested patients (113 out of 149) who developed EDS in 2009–2011 were HLA DQB1*06:02 positive. The 68 patients in 2010 were significantly 2.34-fold higher (95% CI: [1.79, 3.41]) than the 29 cases that were anticipated by the ARIMA prediction model (Figure 1A).
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