Exploring the Usefulness of Functional Data Analysis for Health Surveillance

Abstract

Health surveillance is the process of ongoing systematic collection, analysis, interpretation, and dissemination of health data for the purpose of preventing and controlling disease, injury, and other health problems. Health surveillance data is often recorded continuously over a selected time interval or intermittently at several discrete time points. These can often be treated as functional data, and hence functional data analysis (FDA) can be applied to model and analyze these types of health data. One objective in health surveillance is early event detection. Statistical process monitoring tools are often used for online event detecting. In this paper, we explore the usefulness of FDA for prospective health surveillance and propose two strategies for monitoring using control charts. We apply these strategies to monthly ovitrap index data. These vector data are used in Hong Kong as part of its dengue control plan.

Appendices

Appendix A: Choosing Smooth Parameters

The generalized cross-validation method, developed by Craven and Wahba (2013), is used to determine the smoothing parameter in (2). The GCV for one curve is defined as

$$\begin{aligned} GCV(\lambda )=\Big (\frac{n}{n-df(\lambda )}\Big )\Big (\frac{SSE}{n-df(\lambda )}\Big ) \,, \end{aligned}$$

(14)

where SSE is the sum of squared error calculated by

$$\begin{aligned} SSE(x)=\sum _{j}^{n}[y_{j}-x(t_{j})]^{2} \end{aligned}$$

and where $df(\lambda )$ is the degree of freedom of the fit defined by $\lambda$ and computed as $df(\lambda )=trace[\boldsymbol{H}(\lambda )]$. Where $\boldsymbol{H}(\lambda )=\varPhi (\varPhi ^{T}\varPhi +\lambda \boldsymbol{R})^{-1}\varPhi ^{T}$, and $\boldsymbol{R}=\int L\phi (t)L\phi '(t) dt$ is the symmetric roughness penalty matrix with order K.

In the case study, we predefined $K=7$, and choose $\lambda$ subject to it minimized the GCV as given in (14). Figure 9 illustrates how to choose smoothing parameter $\lambda$ given the GCV values. Based on this, we select $\lambda =10^{-1.4}$ (as $log(\lambda )=-1.4$).

Fig. 9

The value of the GCV as a function of $\lambda$ the smoothing parameter for fitting the MOI curve

Appendix B: Verify the Signal in Q Chart

We plot the mean cure shown in Fig. 3b and the fitted MOI curve of 2013 on Fig. 10. We can see the significant differences between these two lines showed in July and August, but reviewing the principal components in Fig. 5, it seems none of three principal components can capture the shifts in 2013 perfectly.

Fig. 10

The comparison between mean curve and fitted MOI in 2013