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Research Article

Multiyear Climate Variability and Dengue—El Niño Southern Oscillation, Weather, and Dengue Incidence in Puerto Rico, Mexico, and Thailand: A Longitudinal Data Analysis

  • Michael A. Johansson mail,

    mjohansson@cdc.gov

    Affiliations: Dengue Branch, Division of Vector-Borne Infectious Diseases, Centers for Disease Control and Prevention, San Juan, Puerto Rico, United States of America, W. Harry Feinstone Department of Molecular Microbiology and Immunology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

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  • Derek A. T. Cummings,

    Affiliation: Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

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  • Gregory E. Glass

    Affiliation: W. Harry Feinstone Department of Molecular Microbiology and Immunology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

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  • Published: November 17, 2009
  • DOI: 10.1371/journal.pmed.1000168

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Wavelet Analysis of Multiyear Climate Variability and Dengue: The crucial influence of data transformation and null hypothesis tested

Posted by cazelles on 01 May 2010 at 21:59 GMT

Wavelet Analysis of Multiyear Climate Variability and Dengue: The crucial influence of data transformation and null hypothesis tested

Bernard Cazelles, Mario Chavez

In an interesting work, Johansson et al [1] examine the dynamic relationship between climate variables and the incidence of dengue in Thailand, Mexico and Puerto Rico using wavelet analysis. The strength of this work is the comparison between countries in contrasted environment, and they find no systematic significant association between multi-annual dengue outbreaks and El Niño. But one of the main findings of Johansson et al [1] is that dengue incidence oscillations are dominated by a marked seasonal component in these three countries. They also emphasize the weakness of multiyear oscillations contrarily to previous studies [2,3]. Rohani [4] commented the paper underlying that this strong seasonality is a clear fingerprint of the influence of local weather variables on disease incidence and may have important consequences in term of prediction. Significant predictors of dengue epidemic risk, such as local climatic drivers (e.g. rainfall, humidity and temperature) may be usefully employed in early warning systems. Moreover the absence of a significant influence of El Niño on dengue transmission reported by the authors also seems to be important information for the development of predictive tools [4].
Nevertheless, the results obtained by Johansson et al [1] are strongly relied on the methodological choices associated with the wavelet analysis done. The authors have used a log-transformation of the dengue cases and for testing the wavelet patterns obtained they have used an AR(p) process. As the obtained results are not in the line of previous published works where the important role of the 2-3 year periodic components is highlighted [2,3], it is crucial to point out the weakness of their methodological choices. Firstly, it is well know that the log-transformation greatly homogenizes the variance of time series and thus gives more weight to the dominant oscillations. For this reason, in epidemiology there is more and more works that prefer the square-root-transformation (e.g. [5]). To simply illustrate the effect of these transformations we have applied wavelet analysis to the dengue dataset of Thailand with no-transformation, square-root-transformation and log-transformation (Fig. S1). This figure clearly demonstrates that compared to the results obtained with no-transformation, those with log-transformation give more emphasis to the seasonal component. This can be easily explained because a homogenization of amplitude of the time series by a log-transformation induces an important reduction of the variance.
The second methodological drawback is the choice of an AR(p) stochastic process (without specifying the p order used in their paper) to test the statistical significance of the wavelet patterns. As stressed by the authors, it is clear that the use of white noise is frequently insufficient and red noise (AR(1) process) appears not always supported by the spectral characteristics of ecological and epidemiological time series. Similarly, AR(p) with higher order considerably reduce the discrimination power of the hypothesis testing in case of pseudo-periodic data. We think that a bootstrapping approach driven by the data allowing null stochastic processes in accordance with the characteristics of the dataset is preferable. We then suggested using a class of bootstrapped series that models the underlying statistical structure of the time series as 1/(ƒ^β) noise i.e. bootstrapped series with a similar slope (β) as the raw series in their power spectra [6]. The Fig S2 illustrates our comment. White noise gives equal importance to all the periodic components, red noise gives significance only to periodic component lesser than 15 months, and our proposed 1/(ƒ^β) process gives importance to larger periodic bands in greater adequation with the apparent reality.
These two methodological shortcomings greatly weaken the presented findings [1]. Contrarily our results (see Fig S2B) support the fact that the multi-year components of dengue epidemics are more important than claimed by the authors [1]. Particularly with a better detection of multiyear components both in dengue and climatic time series, one can expect to find more clear statistical association, event discontinuous, between these series as its bas been stressed in previous works [2,3]. This may greatly modify the different conclusions drawn based on this study even in terms of prediction [4].
A deeper understanding of infectious disease dynamics is important in order to forecast the effects of environmental changes. Nonstationarity of relationships between climate and disease could induce problems for disease prediction. Conventional statistical methods may fail to reveal a relationship between climate and health when discontinuous associations are present. Wavelet approaches [7,8] appear particularly appropriate and have been used for both descriptions of epidemiological time series and quantification of nonstationary relationships between epidemiological and environmental time series. Nevertheless some cautions have to be considered for a straightforward interpretation of the obtained results.

Bernard Cazelles (E-mail: cazelles@biologie.ens.fr)
UMR 7625, UPMC-CNRS-ENS, Ecole Normale Supérieure, 46 rue d’Ulm, 75230 Paris cedex 05, France and UMMISCO UMI 209 IRD-UPMC, 93142 Bondy, France

Mario Chavez (E-mail: mario.chavez@upmc.fr)
UMR 7225 UPMC-CNRS, Hôpital de La Pitié-Salpêtrière, 47 Bd. de l'Hôpital, 75651 Paris cedex 13, France.

1. Johansson MA, Cummings DAT, Glass GE (2009) Multi-year variability and dengue: El Nino Southern Southern Oscillation, weather, and dengue incidence in Puerto Rico, Mexico, and Thailand. PLoS Med 6: e168. doi:10.1371/journal.pmed.1000168.
2. Cummings DA, Irizarry RA, Huang NE, Endy TP, Nisalak A, et al. (2004) Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand. Nature 427: 344–347.
3. Cazelles B, Chavez M, McMichael AJ, Hales S (2005) Nonstationary influence of El Niño on the synchronous dengue epidemics in Thailand. PLoS Med 2: e106. doi:10.1371/journal.pmed.0020106.
4. Rohani P (2009) The link between dengue incidence and El Niño Southern Oscillation. PLoS Med 6: e185. doi:10.1371/journal.pmed.1000185.
5. Grenfell BT, Bjørnstad ON, Kappey J (2001) Travelling waves and spatial hierarchies in measles epidemics. Nature 414: 716–723.
6. Rouyer T, Fromentin JM, Stenseth NC, Cazelles, B (2008) Analysing multiple time series and extending significance testing in wavelet analysis. Marine Ecology Progress Series, 359: 11-23.
7. Cazelles B, Chavez M, Magny GC, Guégan JF, Hales S (2007) Time-dependent spectral analysis of epidemiological time-series with wavelets. J R Soc Interface 4: 625–636.
8. Cazelles B, Chavez M, Berteaux D, Ménard F, Vik JO, Jenouvrier S, Stenseth NC (2008) Wavelet analysis of ecological time series. Oecologia: 156, 287-304.



Figure S1 Influence of data transformation on the wavelet analysis. (A-C-E) The dengue hemorrhagic fever cases in Thailand: the row data (A), the square-root-transformed data (C) and log-transformed (E). (B-D-F) The wavelet power spectrum of the 3 transformed time series respectively. The colors code for power values from dark blue, low values, to dark red, high values. The black lines show the 5% significant levels computed based on 1000 bootstrapped series based on an AR(1) process (red noise). The dashed lines show the cone of influence, which indicates the region not influenced by edge effects, and the white lines show the local maxima of the wavelet power spectra.

Figure S2 Influence of the null stochastic process employed for testing the wavelet power spectra. The dengue hemorrhagic fever cases in Thailand with log-transformation have been used. The significant levels have been computed based on 1000 bootstrapped series with: (A) white noise process; (B) 1/(ƒ^β) noise process; (C) red noise process, AR(1). The colors code for power values from dark blue, low values, to dark red, high values. The black lines the show the 5% significant levels computed based on 1000 bootstrapped series based on a given process. The dashed lines show the cone of influence, which indicates the region not influenced by edge effects, and the white lines show the local maxima of the wavelet power spectra.


No competing interests declared.

RE: Wavelet Analysis of Multiyear Climate Variability and Dengue: The crucial influence of data transformation and null hypothesis tested

mjohansson replied to cazelles on 07 Jul 2010 at 21:17 GMT

We thank Cazelles and Chavez for their comments on our manuscript. We agree that careful consideration of the statistical significance of our findings is critical. However, we disagree with some of the assertions regarding our findings.

First, we did not intend to imply that inter-annual variability is not an important part of dengue dynamics. Rather, we believe that it is extremely important. What our analysis shows is that the inter-annual variation does not exhibit strong stationarity and is not strongly associated with the assessed climate variables. Although not statistically significant here, the generally high power at long periods in the transforms is consistent with other analyses [1-4].

Cazelles and Chavez also bring up two important methodological issues: the data transformation choice and the definition of the null hypothesis. We used wavelet analysis to analyze periodic components within dengue time series. To elucidate these components, it is often necessary to reduce skewing in the data by transformation and standardize the mean and variance by normalization. Histograms of all three dengue time series studied here show significant skewing which can be reduced effectively by log transformation, but not the square-root transformation.

As Cazelles and Chavez report, if we had analyzed the skewed, square-root transformed data, we would have found slightly different results in some cases. However, even then, the only significance found at multi-year scales was transient and thus supports the assertion that inter-annual variability is important but does not represent a stationary periodic. In coherence analysis, the square-root transformation slightly altered the shape and area of significance, but again did not qualitatively affect the conclusions.

In our manuscript we stated that our null hypothesis for wavelet significance was “the variability of the observed time-series is equivalent to the expected variability of a random process with similar first-order autocorrelation.” That is, a red noise, AR(1) process. As suggested, we reanalyzed the data using a pink-noise (1/(ƒ^β)) process. Regardless of data transformation (log or square-root), using pink rather than red noise did not result in notably different characterization of significance in any of the wavelet transforms.

In conclusion, we appreciate the attention of Cazelles and Chavez to the details of wavelet analysis for epidemiological data. We agree that a pink-noise is a reasonable null hypothesis and disagree that a square-root transformation is adequate for the data in question. Most importantly, neither of these components affects our conclusions about the non-stationarity of multi-year fluctuation in dengue incidence and the lack of evidence for a strong, biologically-plausible relationship between multi-year climate variability and dengue.

Michael A. Johansson
Division of Vector-Borne Infectious Diseases, Centers for Disease Control and Prevention, San Juan, Puerto Rico

Derek A. T. Cummings
Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

Gregory E. Glass
W. Harry Feinstone Department of Molecular Microbiology and Immunology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America

1. Hay SI, Myers MF, Burke DS, Vaughn DW, Endy T, et al. (2000) Etiology of interepidemic periods of mosquito-borne disease. Proc Natl Acad Sci U S A 97:9335–9339.

2. Cummings DA, Irizarry RA, Huang NE, Endy TP, Nisalak A, et al. (2004) Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand. Nature 427: 344–347.

3. Cazelles B, Chavez M, McMichael AJ, Hales S (2005) Nonstationary influence of El Niño on the synchronous dengue epidemics in Thailand. PLoS Med 2: e106.doi:10.1371/journal.pmed.0020106.

4. Nagao Y, Koelle K (2008) Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever. Proc Natl Acad Sci U S A 105: 2238–2243.

No competing interests declared.