### Study site

The study was conducted in the town of Nouna and the villages of Cissé and Goni. These three sites are part of the Nouna Demographic Surveillance Systems (DSS) area [19], which is located in Kossi province in the north-western part of Burkina Faso (Figure 1).

### Study population

Children were selected at each site by cluster sampling of households, using a sampling frame produced from the DSS database. The sample size was set to detect inter-site differences in clinical malaria incidence of at least 10%, with 80% power and 95% confidence, and accounting for 15% loss to follow up. Children were involved after getting informed consent from their parents. In total, 676 children (Cissé: 171, Goni: 240 and Nouna: 265), aged 6 to 59 months, took part in the study. The Nouna ethical committee approved the study.

### Clinical malaria detection

Three trained interviewers, one based at each site, visited each child at home every week. At each visit, they measured the child's axillary temperature and collected a blood film (by finger prick) from any child who was febrile (axillary temperature > = 37.5 C). In addition, interviewers collected information on bed net use and housing conditions. Blood films were read in the Laboratory of the Nouna Health Research Centre. Details on the clinical malaria detection procedure are provided elsewhere [20]. The outcome measure was clinical malaria episode, defined as being febrile with parasiteamia.

For purposes of this study, incidence was defined as the number of clinical malaria episodes detected per 1000 units of person time bearing in mind that some illness episodes which occurred between visits may have been missed.

For ethical reasons, children with fever were treated presumptively with cholorquine (CQ) according to the then national treatment guidelines for malaria. When fever persisted for two days or other symptoms surfaced, the interviewers immediately referred the child to the nearest health centre. The project covered all related costs.

### Meteorological data

Rainfall, temperature, and humidity were measured on the ground using meteorological units installed at each of the three sites. Each meteorological unit consisted of a Digital Datalogger (THIES Datalogger, MeteoLOG TDL 14), to which three sensors (temperature, humidity, and rainfall) were connected (Figure 2). Following standard meteorological conventions, the temperature and humidity sensors were set at a height of 2.5 metres and the rainfall sensor 1.5 metres above the ground. The Dataloggers were set for 10-second measurement cycles and 10-minute recording cycles. Every month, a meteorological supervisor visited each site, downloaded the data from the Datalogger into a memory card, and transferred them into a meteorological database. Daily minimum, mean, and maximum temperatures, relative humidity, and total rainfall were then calculated.

### Statistical Analysis

A conventional binary outcome logistic regression model was used to assess the effects of mean, minimum, and maximum temperatures (T°C), relative humidity (RH), and amount of rainfall (Pmm) of the previous month on clinical malaria rates among study participants. The interaction terms (T°C*RH', 'T°C* Pmm' and 'RH*Pmm') were included in the model to control for the high correlation of the three individual variables. Other covariates included in the model were site of the study; sex; age; use of bed net; type of house; presence of a well; presence of a farm (presence of any farming; which included cereal and vegetable farms); presence of animals; and presence of a mosquito breeding site within a 30-metre radius of a participant's house. As the temperature, rainfall and relative humidity are continuous variables and their relationships with clinical malaria might not be linear, multivariate FP procedures [21, 22] were used to determine the best-fitting relationship they had with clinical malaria. The fitting procedure involves transforming a continuous variable, using a class of eight possible functions to identify the one that provides the best fit. These functions are *H*
_{1}(*X*) = *X*
^{p}, where *p* takes eight possible values: -2, -1, -0.5, 0, 0.5, 1, 2, 3. The linear model is represented by *X*
^{1}, and *X*
^{0} represents the logarithm of *X*. The transformation can be either first or second-degree [21, 22].

For the simplest model, the one with one continuous variable (e.g. temperature) and one binary variable (e.g. bed net use, Yes or No), the logistic regression model using the first-degree FP is

log*it*(*π*
_{
ib
}) = *α* + *β*
_{1}H_{1}(*X*
_{
i
}) + *γW*
_{
b
}

... Where π_{
ib
}is the predicted probability of a child testing positive for clinical malaria at a temperature *i*, and for bed net use *b* (yes or no); *H*
_{1} (X) is the functional form to which the co-variable X is transformed; *β*
_{1} its coefficient; and γ is the coefficient of the co-variable; *W*
_{
b
}, the use of a bed net. The rate ratio for the first-degree PF transformation is given by the formula:

*RR* = exp (*β* * (H_{1}(*X*
_{1}) - *H*
_{1}(*X* _{0})))

Second-degree transformation uses a combination of two powers from the list of eight. In total, 36 combinations are possible. This is calculated as follows:{C}_{k}^{n}=\frac{n!}{k!(n-k)!}, where *n* is the number of possible powers (8), and *k* the number of powers in each combination (2); then{C}_{2}^{8}=\frac{8!}{2!(8-2)!}=28. In addition, the eight combinations with the same power are added. The eight powers and the 36 combinations are tested consecutively. For the first-degree FP, the differences in deviance of each model from the linear one are calculated and compared with the chi-square distribution, with one degree of freedom at α = 0.05. For the second-degree FP, the differences in deviance of each model from the best fitting first-degree FP are calculated and compared with the chi-square distribution with two degrees of freedom. The model with the largest significant deviance difference compared to the best first-degree FP is selected as the best second-degree FP. The second-degree FP is therefore implicitly a better fit than either the linear model or the first-degree FP. Using the same example as in the first-degree FP; the second-degree FP model is defined mathematically as follows:

log*it*(*π*
_{
ib
}) = *α* + *β*
_{1}H_{1}(*X*
_{
i
}) + *β*
_{1}H_{1}(*X*
_{
i
}) + *γW*
_{
b
}

..where, H_{1}(X) and H_{2}(X) are the respective functions to which co-variable X is transformed.

The rate ratio for the second-degree FP is given by the formula:

*RR* = exp (*β*
_{1} * (H_{1}(*X*
_{1}) - *H*
_{1}(*X*
_{0})) + *β*
_{2} * (H_{2}(*X*
_{1}) - *H*
_{2}(*X*
_{0})))

All the models were run and fit using STATA ^{®} software [23]. The output of each model (coefficients and transformed variables) was used to calculate rate ratios (RR), only including variables with a significant effect on the risk of clinical malaria. These are mean temperature, rainfall, and relative humidity. Other variables, including minimum and maximum temperature, were removed from the final model by an in-built backward elimination procedure in the FP algorithm. For each variable, reference points **(** *x*
_{0}
**)** were defined. These are mean temperature = 27°C, the value at which clinical malaria risk peaked; rainfall = 164 mm, the highest value observed; and relative humidity = 60%, the minimum value required for malaria vector survival.