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# Association between climatic variables and the incidence of pulmonary tuberculosis in Brunei Darussalam

### Data gathering

The weekly case count of all diagnosed PTB cases who resided in Brunei-Muara District, Brunei between January 2001 and December 2018 (18 years, 939 weeks) was compiled from the National Tuberculosis Coordination Center ( NTCC). Brunei-Muara district is the most populous district in the country where 69.7% of the population resides21, and where the capital is located. The NTCC was established as part of the National Tuberculosis Control Program in Brunei and has operated tuberculosis surveillance, treatment and control programs since 2000. All patients suspected of having any form of tuberculosis throughout the country are often referred directly to the NTCC or any respective district. observed, short-stay treatment (DOTS) center for diagnosis, treatment and follow-up25. All modes of diagnosis for PTB cases were included (such as smear positive, smear negative and by chest x-ray and/or clinician decision). These case numbers were summarized by epidemiological week and year, according to the date of treatment initiation. In cases where the treatment start date is missing, the NTCC registration date was used.

Daily data on climate variables for the same period were obtained from a local weather station, located in Brunei-Muara district. Variables provided include total sunshine hours, total precipitation (in millimeters), average wind speed (in knots), relative humidity (RH) in percentage (minimum, average and maximum) and the temperature in degrees Celsius (minimum, average and maximum) . These daily data were averaged by epidemiological week and by year. Any missing daily values ​​(n=5) were replaced with the mean value for that particular month and year. Vapor pressure (a measure of absolute humidity) was calculated using the Clausius-Clapeyron equation26by entering average relative humidity values ​​and standard temperature and pressure conditions.

### statistical analyzes

Spearman’s rank correlation test was used to explore the correlation between each climatic variable and with the number of PTB cases. The stationarity of the time series for the weekly number of PT cases and each climatic variable was checked using the augmented Dickey-Fuller test.

We used the Distributed Lag Nonlinear Model (DLNM) framework to investigate the association between climatic variables and the incidence of PTB. In this model framework, the negative binomial distribution was assumed to account for overdispersion, and cross terms were constructed for each climate variable. These terms include 2 dimensions: one specifying the conventional exposure-response relationship, and the other specifying the delay-response relationship.27. Natural cubic splines with 7 degrees of freedom (df) per calendar year were used to account for long-term trends and seasonality. This adjustment was included based on previous similar studies for TB5.17, and the number of df was determined using Akaike’s Information Criterion (AIC) value. Natural cubic splines with 3 df were used to describe both lagged and nonlinear effects of each climate variable.

The median incubation period for PTB ranges from a few months to 2 years14and there is often a delay in the diagnosis of tuberculosis, of about 5 to 6 months25.28. Given these factors, we decided to specify lags of up to 12 months (52 weeks) to capture the delayed effects of climate variables. The goal is to cover as much of the incubation period without sacrificing any loss of statistical precision and efficiency that might be caused by adding more delays4.17. The general structure of the model formula used is as follows:

$$log Eleft( {Y_{t} } right) = alpha + sum CB left( {M,lag} right) + nsleft( {t,df = 7/an times no . of years} right)$$

where E(Yyou) is the expected number of PTB cases at week t, (alpha) is the y-intercept, CB is the cross function used for each climatic variable to be evaluated (M), and ns is the natural cubic spline function applied to account for the long-term trend and seasonality. The presence of any residual autocorrelation was assessed using partial autocorrelation function plots (PACF). Any remaining autocorrelation detected was taken into account by adding lags of the model deviance residuals in the final model.

Although not all variables yield significant results in univariate analysis, we decided to include 5 cross terms that represent different aspects of climatic variables and are also previously known to be associated with TB incidence . The rationale here is to include these variables to control for potential confounders. The AIC value was used to assess the variables to be included in the final model. This resulted in the choice of the following 5 variables in the final model: average wind speed, hours of total sunshine, total precipitation, average RH and minimum temperature. To guarantee a minimum of multi-collinearity and/or correlation problems (due to the use of several crossed terms in a single model), the consistency of the results obtained between univariate and multivariate was checked using visual analysis and referring to the AIC value.

We reported the relative risk (RR) of weekly PTB cases at the 5th and 95th percentiles of each climatic variable, relative to their median, with corresponding 95% confidence intervals (95% CI). For climate variables with significant results observed at either percentile, we further determined and reported the starting lag week at which that significant result can be found. Global relationship patterns were also described using three-dimensional (3D) plots and contours. Lag plots were used to show trend differences at lags of 0, 13, 26, 39, and 52 weeks (corresponding to 0, 3, 6, 9, and 12 months), with a higher number of lags indicating an effect shifted longer by the corresponding climatic variable. For further sub-analysis, we repeated the same analysis described above to report the RR of weekly smear-positive PTB cases. Sensitivity analyzes were performed by repeating the analysis using 5 and 9 df natural cubic splines for the long-term trend. All analyzes were performed and all figures were generated in R (ver. 4.1), using tseries, splines and dlnm packages29.30.

This study was approved by the Medical and Health Research and Ethics Committee (MHREC), Ministry of Health, Brunei (Ref: MHREC/UBD/2019/2). All methods were performed in accordance with current guidelines and regulations. Informed consent was waived because all analyzes were based on aggregated data that does not contain any identifying or sensitive information.