Chasing the ghost of infection past: identifying thresholds of change during the COVID-19 infection in Spain

Luis Santamaria; Joaquin Hortal

It is also important to note that the relationship of the growth rates and breakpoints in the analysed data with the timeline provided in Figure 5 may be affected by both the variability in the time lags between the time of infection and the times of both diagnosis and death (see introduction), and the irregular reporting of both variables during weekends and among Spanish regions -particularly at the onset of the outbreak. However, the use of cumulative curves smoothes out considerably these effects, and provides in robust estimates of both breaking points and growth rates. Finally, the use of a family of models reaching a maximum of three breaking points, necessary to maintain model parsimony, may have also resulted in the lack of detection of additional breaking points. However, all models showed very high R 2 and adjusted R 2 values; and in three out of four models (all but the number of deaths in Spain), fitting an additional breaking point only resulted in slight, non-significant improvements in model fit. We might have also missed breaking points in the early stages of the infection, when values are lower and data more noisy. Indeed, heteroscedasticity in the original, untransformed data resulted in such a risk of underdetection; but using transformed data achieved homoscedasticity, and more breaking points were actually detected on earlier than on later dates.