key: cord-1006952-pk3vh1n2
authors: Saâdaoui, Foued; Rabbouch, Hana; Saadaoui, Hayet; Dutheil, Frédéric
title: Multiscaled causality of infections on viral testing volumes: The case of COVID‐19 in Tunisia
date: 2022-02-12
journal: Int J Health Plann Manage
DOI: 10.1002/hpm.3427
sha: 4eba6cd89990e8d4b3adeeca21b8625106e51cdf
doc_id: 1006952
cord_uid: pk3vh1n2

OBJECTIVES: Coronavirus disease (COVID‐19) is one of the most detrimental pandemics that affected the humanity throughout the ages. The irregular historical progression of the virus over the first year of the pandemic was accompanied with far‐reaching health and social damages. To prepare logistically against this worsening disaster, many public authorities around the world had set up screening and forecasting studies. This article aims to analyse the time‐frequency co‐evolution of the number of confirmed cases (NCC) in Tunisia and the related number of performed polymerase chain reaction (PCR) tests over the COVID‐19 first year. Accurately predicting such a relationship allows Tunisian authorities to set up an effective health prevention plan. STUDY DESIGN: In order to keep pace with the speed of evolution of the virus, we used uninterrupted daily time series from the Tunisian Ministry of Public Health (TMPH) recorded over the COVID‐19 first year. The objective is to: (1) analyse the time‐frequency progress of the NCC in relationship with the number of PCR tests, (2) identify a multi‐scale two‐factor stochastic model in order to develop a robust bivariate forecasting technique. METHODS: We assume a bivariate stochastic process which is projected onto a set of wavelet sub‐spaces to investigate the scale‐by‐scale co‐evolvement the NCC/PCR over the COVID‐19 first year. A wavelet‐based multiresolutional causality test is then performed. RESULTS: The main results recommend the rejection of the null hypothesis of no instantaneous causality in both directions, while the statistics of the Granger test suggest failing to reject the null hypothesis of non‐causality. However, by proceeding scale‐by‐scale, the Granger causality is proven significant in both directions over varying frequency bands. CONCLUSIONS: It is important to include the NCC and PCR variables in any time series model intended to predict one of these variables. Such a bivariate and multi‐scale model is supposed to better predict the needs of the public health sector in screening tests. On this basis, testing campaigns with multiple periodicities can be planned by the Tunisian authorities.

Over the few last decades, medical practices have known significant changes, which altered the demand for supplies/ service and the ways they are employed. These changes therefore have, in fact, budgetary requirements, especially in terms of capital investment and revenue requirements. With the onset of Coronavirus disease 2019 (COVID-19), this equation has become even more complicated, hence the need for effective management plans to avoid stockout of medical supplies. Thus, accurately planning health care needs is an important issue, yet existing forecasting models are often inadequate. On this basis, there is a need to methods whereby the optimum level of provision can be predicted and the likely effects of changes proposed can be evaluated. 1 An effective multiresolutional forecasting model, [2] [3] [4] [5] for instance, should enable health planners/managers to minimise costs and maximise the use of projected capital and investment. In all of this, the role of the authorities would therefore be to plan with certainty the necessary financial resources by the request for additional budgets intended for the public health sector over COVID-19.

COVID-19 is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).

Since identified in 2019 in Wuhan (China), COVID-19 has generated much fear due to its relatively high mortality rate. Today, the current pandemic caused by the highly contagious SARS-CoV-2 and its effects on the global economy is of major global concern. 6-8 Preventive and organisational measures have been taken at the global and regional • Screening campaigns with multiple periodicities can be conducted by Tunisian MOH levels to limit and control the spread of the pandemic and its repercussions. 9,10 Tunisia, in particular, was not only among the first north-African countries to be affected by the virus, but also the among the firsts to know how to fight it effectively. The Tunisian Public Health Ministry (TPHM) had in fact opted for protectionist and proactive strategies based upon effective screening and forecasting plans. This had immediately succeeded in stopping the scourge in a very effective manner, despite the fact that the North African nation is situated in a Mediterranean zone of great liveliness, and in particular in the neighbourhoods of Italy, which was one of the most affected by the pandemic during the first year.

On the other hand, the COVID-19 pandemic is a powerful reminder of the importance of having health services that are effective and just-in-time. For the public authorities, predicting the instantaneous evolution of the number of cases affected by this disease is both a delicate and important mission in the sense that its success allows to accurately determine in advance the material and logistic needs in order to protect themselves from severe viral waves. 11 The most popular models used in a wide range are based on a single factor model developed in a continuous-time setting, which provides a rich framework for specifying the dynamic behaviour in the short-term. 12 However, the most known models does not capture important information about nonstationary processes. Therefore, wavelets are commonly used to decompose data into a sum of orthogonal sub-signals. 3, 4, 13, 14 Wavelets are known as very practical and accurate mathematical tools for dealing with nonlinearities and problems where phenomena of very different scales occur.

In the wavelet-decomposed signals, the finest time-scales represent the short-run dynamics (corresponding to the very high-and high-frequency components), the coarsest time scales characterise cycles (epidemic waves), while the trend is associated to approximation components corresponding to the long-run elements.

In this paper, a wavelet-based bivariate time series methodology is proposed for analysing the relationship between the daily COVID-19 infections and the number of polymerase chain reaction (PCR) tests in Tunisia. The idea of such a relationship has in fact recently been spread in some research directions. 15 The main interest of this conjoint modelling is to allow health authorities in Tunisia to prepare logistically against the arrival of new COVID-19 waves in order to optimise their needs in terms of PCR tests. To keep pace with the speed of evolution of the virus during its first year, uninterrupted daily time series are used in our study. The strength of the wavelet-based multiresolution analysis (MRA), in comparison with classical approaches, is that it offers a powerful way to decompose the dynamics of the signals over a variety of different time horizons. Such a framework could therefore represent the cornerstone of a multi-periodic screening plan. The main results recommend the rejection of the null hypothesis of no instantaneous causality in both directions, while the statistics of the Granger test suggest failing to reject the null hypothesis of non-causality also in both directions. By proceeding rather scale-by-scale, the Granger causality is proven significant in both directions over varying frequency bands. The implication of such results is that it is important to include both variables in any model intended to predict one of the variables. Such a bivariate and multi-scale model is supposed to better predict the needs of the public health sector in screening tests.

The wavelet transform 3,4,13,14 decomposes a signal f(t) into some regular functions called daughter wavelets ψ s,τ (t),

where c 0,k summarise the general form of the function and the d j,k represent the local details. These coefficients, known as scaling and wavelets coefficients, are calculated as  . and

The coefficients of a Maximal Overlap Discrete Wavelet Transform (MODWT) can be defined as:

, mod , , mod 0 0 ( ) and ( ),

new wavelet filter for level j. Finally, the MODWT algorithm provides a MRA of f, which is represented as follows:

,

S are respectively the detail and smooth components.

where ~ denotes the equivalence in distribution. At each scale j, the two alternative hypotheses are expressed as follows:

:

where the crossed out arrow in the null hypothesis means

Similarly, inverting the arrows'

directions implies that the causality is tested in the opposite direction.

The objective of this experiment is to test the uni-and multi-scaled causalities between the number of COVID-19 (Geweke-Porter-Hudak GPH test), are the common facts for the two variables. These statistics are also confirmed by the histograms of the two variables as well as the cross-correlation function between the same variables ( Figure 1 ).

The significance of these statistics is a sign that a multiresolutional decomposition method can lead to a better appreciation of the interplay between the two variables.

The causality analysis between these two variables will in fact allow us to measure whether one of these variables have a significant effect on the other or not. Furthermore, the main interest of such a conjoint empirical study is to allow health authorities in Tunisia to prepare logistically against the arrival of new COVID-19 waves in order to optimise their needs in terms of PCR tests. In the other direction, it would also be possible for academia to re-predict the evolution of the number of cases according to the number of tests, especially in relationship with the credibility of the results announced by the authorities. To examine the causality assumption, we use the daily data ranging between

March 2020 and March 2021 (see Figure 2 ). Three types of tests are conducted: the Granger test of causality, 16 instantaneous test of causality, 17 and multiscaled causality test. 3 Since the simple principle of the multiscaled causality is to perform a scale-by-scale Granger test, we rely on the same rule as the classical test, which is to calculation an empirical information criterion to determine the order of autoregression lags.

The results reported in Table 2 The time series chart in Figure 2 , however, shows signs of local stationarity and persistence, which could be interpreted as a type of long-range co-dependence. 18 For this reason, the causality hypothesis is addressed in more depth by employing wavelets. As explained above, wavelets allow to restructure the causality test on ordered frequency T A B L E 1 Descriptive statistics and goodness-of-fit tests F I G U R E 1 Cross-correlation and histogram plots of the daily changes (ΔX t = X t − X t−1 ) of COVID-19 confirmed cases and polymerase chain reaction (PCR) tests

sub-bands. As detailed in Table 3 , on a decomposition level J = 3, the non-causal hypothesis is rejected in both directions at all scales. This implies that a bidirectional multiscaled forecasting model 4 can be used with potential success.

Proving such a significant causal relationship between the number of infected cases and the number of performed PCR tests can in fact be one of the levers of a national COVID screening strategy, and therefore, a reliable informational advantage for an efficient public health logistics. This also means that it is possible to use data from the two factors to forecast the values of one of them. Forecasts that can be of great interest, especially if they are sufficiently accurate. Moreover, given the dynamics of the virus's progression and the NCC, showing several types of irregularities, it was crucial to use a sophisticated tool to better understand the relationship. It was for this reason that we have used wavelet techniques to also measure scale-by-scale causality. Recorded T A B L E 3 MODWT-based multiscaled causality. A Daubechies least asymmetric wavelet filter of length L = 5 is used for the MODWT with a decomposition level of J = 3

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We would like to thank the anonymous reviewers for their insightful and constructive comments that greatly contributed to improving the paper. Our many thanks go also to the editorial staff for their generous support and assistance during the review process. This work has not received any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

The authors declare no conflicts of interest.

Data were publicly available and did not include individual identities and thus did not require ethics approval.

The data that support the findings of this study are openly available at the websites of the Tunisian Ministry of Public Health (http://www.santetunisie.rns.tn/) and the Tunisian Observatory for New and Emerging Diseases (http://www.

https://orcid.org/0000-0002-0574-2922