The temporal lagged association between meteorological factors and malaria in 30 counties in south-west China: a multilevel distributed lag non-linear analysis

Malaria is an important cause of death and illness in children and adults in tropical countries. Globally, the World Health Organization estimates that in 2010, 219 million clinical cases of malaria occurred, and 660,000 people died of malaria [1]. Despite significant reductions in the overall burden of malaria in the 20th century, malaria remains a significant public health issue in China, especially in the southern part of the mainland. Particularly, Yunnan Province used to be the highest endemic province [2]. For south-west China, the majority of previous studies focused on spatiotemporal pattern for mortality or morbidity [3‐5], or pathogenic classifications of reported cases [6].

Malaria is transmitted by female mosquitoes of the genus Anopheles, and the transmission and prevalence of malaria are influenced by many factors, in which meteorological factors are considered to play a crucial role. However, researchers still have a poor understanding of the mechanistic link between climate and malaria risk [7‐10]. Many studies were conducted to explore the link with inconsistent findings reported, and the nature and extent of the link remains highly controversial [11‐14]. See [7] for a recent review of existing studies supporting and rebutting the role of climatic change as a driving force for highland invasion by malaria. Some existing studies in China made contradictory conclusions [15]. For example, while [16‐18] found that rainfall was closely related to malaria incidence, [19‐21] failed to identify such an association. Similar inconsistent results were also reported in sub-Saharan Africa [22].

Biologically speaking, climate is fundamentally associated to the malaria incidence through its effects on both the mosquito vector and the development of the malaria parasite inside the mosquito vector. Two aspects of the meteorological effects require special attention, the lag and non-linear characteristics. On the one hand, most time series studies have provided evidence of an association between meteorological variables and malaria, typically at a single lag of 0, 1 or 2 months [23‐27]. However, the single fixed lag assumption was not plausible for describing population level associations. From the perspective of biological mechanism, there are several periods need to be considered for the lag effect, such as the time for mosquito to develop, the development period of parasites within the mosquito, and the incubation period of parasites within human body. Every stage shall show a variation in terms of the time lag, resulting in a smoothly varied lag distribution at population level between climatic factors and malaria cases. On the other hand, the non-linear effect was recognized in temperature, and substantial existing studies validated the nonlinear correlation between temperature and malaria in terms of laboratory and epidemiological studies [13, 18, 28‐30]. Similar potential non-linear correlations were also proposed to rainfall [30‐32].

The association between malaria and meteorological factors is complex due to the above two characteristics. Existing inconsistent findings may be due to two reasons. On the one hand, regional variations makes distinct regions have different association patterns. On the other hand, invalid statistical assumptions result either from the misspecification of the single fixed lag or from the invalid assumption of the linear relationship.

At present, there are few studies regarding the pattern of delayed effect for meteorological factors after accounting for the nonlinearity. Besides, the comprehensive lag pattern for meteorological factors have not been examined in China. [33] investigated the lag pattern for rainfall in Anhui Province in China using monthly data. However, it is not satisfying, since monthly data was relatively coarse for the lag pattern, and other crucial meteorological variables were not included in the analysis.

The purpose of this work is to explore the lag association between meteorological variables and malaria in south-west China. Specifically, a Multilevel Distributed Lag Non-linear Model (MDLNM) was used to study the temporal lagged correlation between weekly malaria cases and weekly meteorological factors using the data from 2004 to 2009 in 30 counties in south-east China. Using these more reasonable models a better understanding can be obtained for the association between climatic variables and malaria transmission, testing the biological hypothesis in terms of epidemiological level. Also, the result may have the potential to improve forecasting of changes in malaria incidence, which would shed light to public health authorities on how to effectively distribute resources for malaria control programmes.

Like all mosquitoes, anophelines go through four stages in their life cycle: egg, larva, pupa, and adult [50]. The first three stages are aquatic and also depend on the temperature. The adult stage is when the female Anopheles mosquito acts as malaria vector [51]. Once adult mosquitoes have emerged, the temperature, humidity, and rains will determine their chances of survival. To transmit malaria successfully, female Anopheles must survive long enough after they have become infected to allow the parasites they harbour to complete their growth cycle [52]. Furthermore, a better climatic environment will also shorten the time required for the parasite development in the mosquito (the extrinsic incubation period) [53]. In summary, the meteorological variables can affect the malaria cases through the effect both on every stage of mosquitoes and the parasite within mosquitoes.

The results find that different meteorological factors have distinct patterns and magnitudes for the lagged correlation. Rainfall is associated with malaria cases in both hot and cold weather counties with a delayed correlation and a relatively long lag range, suggesting that rainfall may create collections of water to promote the whole process for the mosquitoes’ development. Furthermore, the lag is longer in hot weather counties compared to cold weather counties, which is biologically plausible, as temperature must be warm enough to support the developments of mosquito and parasites. Besides, although greater rainfall leads to a higher relative risks for malaria cases in both hot and cold weather counties, the increase is greatest when the rainfall is low, while the increase is weaker when the rainfall is high. The saturation effect may be used to explain this phenomenon, in the sense that when rainfall is sufficient, additional rainfall contributes little to the developments of mosquito and parasites.

While relative humidity is not statistically significant in the cold weather counties, the association is statistically significant at early and late lags in the hot weather counties. This could be explained as follows. When the temperature is not low, the relative humidity primarily contributes to the mature of parasites and early development of mosquitoes, respectively.

Minimum temperature has a longer lag range and larger correlation coefficients for the hot weather counties compared to cold weather counties. This is contradictory with some existing studies [44, 54], in which they found that small increases in temperature will have a greater effect on malaria transmission in areas with lower average temperatures. This may result from the large difference regarding prevalence rate between the hot and cold weather counties, which can be inferred from the incidence. Hot weather counties have significantly larger incidences than cold weather counties according to Table 1 and the six years incidences for the two kinds of counties, with 407/10,000 and 66/10,000 for the hot and cold weather counties, respectively. Therefore, more infected persons can lead the mosquitoes to a greater exposure chance, which could compensate the less increase effect from minimum temperatures in warmer counties. Maximum temperature is only statistically associated with malaria cases at early lags, implying that maximum temperature may contribute to the mature of the parasite.

The lag functional form is relatively stable for all four meteorological variables within a climatic condition. On the other hand, in terms of the magnitude, the rainfall presents a variation among different values while the other three climatic factors do not show such variation. This indicates the lag pattern is crucial and greatly determines the variation of the effect. Also, it reflects the non-linearity.

Spearman correlation between meteorological variables shows strong correlation between maximum and minimum temperatures on the one hand, and between rainfall and relative humidity on the other hand. This highlights the importance of including a comprehensive set of climatic variables in the model to avoid invalid association.

Existing studies concluded different lags for meteorological factors, and our work gives two possible reasons. On the one hand, existing studies usually assume a fixed lag, and use statistical methods to select the statistically best lag. This approach omits the variation for the lag time, leading to imprecise estimates for the lag. On the other hand, distinct temperature conditions lead to different lag patterns, and therefore existing conclusions are limited to generalize to similar climatic conditions.

The goal of this study is for scientific understanding, not predicting, but the results may provide suggestions for future predicting model. China is implementing a National Malaria Elimination Programme, and the southern border areas will be the one of most hard issue to elimination the disease, particularly in Yunnan [55]. One measure is to predict the malaria cases and release early warning signal when necessary. The results imply that the traditional moving average or fixed lag methods should be modified to weight different time intervals to take account of the biological mechanism.

The nonlinearity was not extensively examined, since the focus is on the lag pattern. Furthermore, it turned out that the lag pattern did not vary significantly with the change of meteorological variables, indicating that the lag pattern is relatively stable within a climatic condition.

This study still has several limitations. First, as with all observational studies for malaria and meteorological factors, it is likely that some confounders influence the result [56]. 30 counties might have different preventive measures (with different magnitudes) to combat malaria, and they may also have different behaviours, such as the use of nets. Including city-specific random effect could not eliminate the potential bias. Second, the quality and completeness of the data may change over the six year period [57‐59]. The change mainly occurs in the time dimension, with best quality in 2009 [59]. Third, the finite and pre-defined lag ranges for meteorological variables were used. The lag lengths were chosen mainly according to [44], which gave both the biological reasoning and the empirical study. Finally, the lag pattern of P. vivax and P. falciparum malaria could be different. As with some existing studies [5], separate analyses by different parasites were not made owing to a lack of detailed information on P. vivax and P. falciparum in this study. The difference may come from the incubation period, the time between the initial malaria infection and symptoms. However, the incubation period generally ranges from 9 to 14 days for P. falciparum and 12 to 18 days for P. vivax[60], and therefore the general lag pattern should not differentiate greatly. Nonetheless, further epidemiological researches are warranted to explore the possible different lag patterns.

Using weekly malaria cases and meteorological information, this work studied the temporal lagged association pattern between malaria cases and meteorological information over six years (2004–2009) in 30 counties in south-west China. The results can be viewed as supplementary information for the existing inconsistent findings on the lag pattern, especially for China, where no similar study was reported before. Different meteorological factors show distinct patterns and magnitudes for the lagged correlation, and the patterns will depend on the climatic condition. Therefore, existing inconsistent findings for climatic factors’ lags could be due to either the invalid assumption of a single fixed lag or the distinct temperature conditions from different study sites. The lag pattern for meteorological factors should be considered in the development of malaria early warning system, and how to incorporate the lag pattern into predicting model is an open question.