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Explicit formulae for modelling the trend of resident and non-resident monthly TB risk are given below.
From an application point of view this technique of modelling the trend and cyclical components can be perceived as a regression of the data Yt on periodic covariates, which are functions of time, while the stochastic dependence of the data, on its past including seasonality, is modelled by fitting SARIMA models to the residuals of this regression.
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We considered linear, quadratic, and cubic terms for the time variable to model the trend.
We modeled the trend in fitness over 7 years for each man using simple linear regression.
The DP model identified the epidemic curve as being distinct from those in the library and was also able to accurately model the trend of the curve.
The cubic term was not significant (p > 0.05), but the others were; therefore, we included both linear and quadratic terms in order to model the trend.
We did not attempt to model the trend component parametrically as estimating the pattern of the trend components globally by a closed mathematical function of time may severely misestimate the true trend beyond the range of fitting period.
Therefore, an exponential decay function, R e (t), is used to model the trends.
For example, some authors modelled the secular trend with a smoothing spline fitted on summer months [ 12, 29].
Our empirical approach is to fit a polynomial to model the age trends when restrictions are in place.
Age in days and absolute day of birth were fitted with random smoothing splines to model the temporal trends.
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