Pierre-Emmanuel Poulet
email: pierre-emmanuel.poulet@inria.fr

Stanley Durrleman
email: stanley.durrleman@inria.fr

Mixture modeling for identifying subtypes in disease course mapping

Keywords: Mixture model, Non-linear mixed-effect model, Disease course mapping, Alzheimer's disease subtypes

Disease modeling techniques summarize the possible trajectories of progression from multimodal and longitudinal data. These techniques often assume that individuals form a homogeneous cluster, thus ignoring possible disease subtypes within the population. We extend a non-linear mixed-effect model used for disease course mapping with a mixture framework. We jointly estimate model parameters and subtypes with a tempered version of a stochastic approximation of the Expectation Maximisation algorithm. We show that our model recovers the ground truth parameters from synthetic data, in contrast to the naive solution consisting in post hoc clustering of individual parameters from a one-class model. Applications to Alzheimer's disease data allows the unsupervised identification of disease subtypes associated with distinct relationship between cognitive decline and progression of imaging and biological biomarkers.

Introduction

In the wake of medical progress and general increase of life expectancy, neurodegenerative diseases have seen a dramatic surge in the population. In order to better understand these diseases, our goal is to build digital models of their progression, which may span decades in the life of the patients. Such models may be estimated from longitudinal data sets of several patients at different disease stages. Data may include cognitive or behavioral assessments, biological biomarkers or image-based biomarkers such as regional brain volumes.

The statistical analysis of longitudinal data is often done in the framework of mixed-effects models [START_REF] Laird | Random-effects models for longitudinal data[END_REF]. Linear mixed-effects models (LMEM) are widely used, yet their application to medical observations is not adapted because of the non-linearity of the disease progression over large periods of time [START_REF] Jack | Update on hypothetical model of Alzheimer's disease biomarkers[END_REF]. Nonlinear mixed-effects models (NLMEM) have been proposed in recent years [START_REF] Taddé | Dynamic modeling of multivariate dimensions and their temporal relationships using latent processes: Application to Alzheimer's disease[END_REF][START_REF] Marinescu | DIVE: A spatiotemporal progression model of brain pathology in neurodegenerative disorders[END_REF]. Mixed-effects models separate fixed effects, assumed to be common to the population, and individual effects, which are random variables describing how the model should change to accommodate for inter-individual differences. They are often assumed to follow a unimodal distribution, thus assuming the homogeneity of the population. However, this is often not the case as neurodegenerative diseases are known to be heterogeneous, with various subtypes that are difficult to characterize. Uncovering the underlying clusters of population is a complex task to perform in addition to an already complex NLMEM.

Our work contribution is a framework allowing for both unsupervised clustering and estimation of an NLMEM for each cluster. We propose a mixture model based on a nonlinear Riemannian mixed-effect model which we will refer to as a disease course mapping model [START_REF] Schiratti | A Bayesian Mixed-Effects Model to Learn Trajectories of Changes from Repeated Manifold-Valued Observations[END_REF]. The joint estimation of clusters and model parameters is performed using a mixture Monte-Carlo Markov chain stochastic approximation Expectation Maximisation (M-MCMC SAEM) algorithm [START_REF] Lavielle | An improved SAEM algorithm for maximum likelihood estimation in mixtures of non linear mixed effects models[END_REF]. This end-to-end approach differs from a more naive approach based on a posteriori clustering the parameters of the individual effects after the estimation of an NLMEM. We applied the proposed mixture model to the Alzheimer's disease neuroimaging initiative (ADNI) cohort. Our main focus is the separation of two obvious clusters: controls and patients diagnosed with Alzheimer. We then included the mild cognitive impaired (MCI) patients to understand their position relatively to the two previously found clusters.

Related work

Analysis of longitudinal data can be performed with various types of models. Discrete models include event-based models which estimate the temporal ordering of sequence of pathological events [START_REF] Fonteijn | An event-based model for disease progression and its application in familial Alzheimer's disease and Huntington's disease[END_REF][START_REF] Archetti | Multi-study validation of data-driven disease progression models to characterize evolution of biomarkers in Alzheimer's disease[END_REF][START_REF] Bilgel | Predicting time to dementia using a quantitative template of disease progression[END_REF]. This approach has been extended with the SuStaIn model [START_REF] Young | Uncovering the heterogeneity and temporal complexity of neurodegenerative diseases with Subtype and Stage Inference[END_REF] to identify clusters in the population.

Continuous models include the linear mixed-effects model [START_REF] Laird | Random-effects models for longitudinal data[END_REF]. Several NLMEM have been proposed, one being the generalized linear framework [START_REF] Mccullagh | Generalized Linear Models[END_REF] where the observations result of simple non-linear transformation of an LMEM. Typically the link function can be the logit, allowing for a sigmoid-shaped model. NLMEM include univariate models with time-reparameterizing functions [START_REF] Jedynak | A Computational Neurodegenerative Disease Progression Score: Method and Results with the Alzheimer's Disease Neuroimaging Initiative Cohort[END_REF]. Multivariate approaches include DIVE [START_REF] Marinescu | DIVE: A spatiotemporal progression model of brain pathology in neurodegenerative disorders[END_REF], a voxel-based model which also clusters disease trajectories, and disease course mapping which combines variations in progression dynamics with phenotypic differences [START_REF] Schiratti | A Bayesian Mixed-Effects Model to Learn Trajectories of Changes from Repeated Manifold-Valued Observations[END_REF][START_REF] Couronné | Learning disease progression models with longitudinal data and missing values[END_REF][START_REF] Louis | Riemannian Geometry Learning for Disease Progression Modelling[END_REF][START_REF] Koval | Statistical Learning of Spatiotemporal Patterns from Longitudinal Manifold-Valued Networks[END_REF]. In this approach, the observations belong to a Riemannian manifold and each individual trajectory in time is a parallel to a geodesic curve representing the population trajectory. Other models are also based on differential equation models [START_REF] Taddé | Dynamic modeling of multivariate dimensions and their temporal relationships using latent processes: Application to Alzheimer's disease[END_REF]. Non parametric models using deep learning were also explored [START_REF] Mehdipour Ghazi | Training recurrent neural networks robust to incomplete data: Application to Alzheimer's disease progression modeling[END_REF].

Estimation of complex parametric models such as NLMEM corresponds to the maximization of the likelihood. Such optimization can be performed with the Expectation Maximization (EM) and more especially its stochastic approxima-tion variant with Monte-Carlo Markov chain (MCMC SAEM) which has been proven to have good theoretical properties [START_REF] Delyon | Convergence of a Stochastic Approximation Version of the EM Algorithm[END_REF][START_REF] Kuhn | Coupling a stochastic approximation version of EM with an MCMC procedure[END_REF][START_REF] Allassonnière | Construction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study[END_REF]. Moreover the EM algorithm is also a staple for mixture model estimation. Combining the estimation of the mixture model and the NLMEM has already been studied [START_REF] Lavielle | An improved SAEM algorithm for maximum likelihood estimation in mixtures of non linear mixed effects models[END_REF]. However the theoretical properties are often not enough as the MCMC SAEM tends, in practice, to suffer from local maxima attraction. In particular, changing cluster assignments is known to be challenging in such methods; it is a problem referred to as trapping states. Adding a tempering scheme has been shown to alleviate this issue by flattening the target distribution and thus easing the exploration of the parameter space [START_REF] Allassonniere | Learning spatiotemporal piecewisegeodesic trajectories from longitudinal manifold-valued data[END_REF]. A mixture model on top of a disease progression model was also proposed in [START_REF] Debavelaere | Learning the Clustering of Longitudinal Shape Data Sets into a Mixture of Independent or Branching Trajectories[END_REF], the clustering during estimation was handled with hard labels and a probability for individuals to switch from one cluster to another.

Method

Disease course mapping model

We present here the disease course mapping model first mentioned in [START_REF] Schiratti | A Bayesian Mixed-Effects Model to Learn Trajectories of Changes from Repeated Manifold-Valued Observations[END_REF] and improved in [START_REF] Couronné | Learning disease progression models with longitudinal data and missing values[END_REF][START_REF] Koval | Statistical Learning of Spatiotemporal Patterns from Longitudinal Manifold-Valued Networks[END_REF]. We introduce the notations and essential equations for the rest of the article. In this work we focus on the particular case where the model takes the form of a series of logistic curves for each biomarker.

We assume a longitudinal dataset (y ijk ) 1≤i≤n,1≤j≤Ni,1≤k≤d where each patient i has N i visits, at time t ij , and d features observed at each visit. The number of visits N i may vary from one patient to another. Data y ijk are assumed to be points on a Riemannian manifold M. This model is a mixed effect model in the following sense: we define the population parameters or fixed effects as a set of parameters describing an average population trajectory as a geodesic γ 0 in the Riemannian manifold, with γ 0 (t 0 ) = p and γ0 (t 0 ) = v. The individual effects take into account a temporal effect with an individual reparametrization of time and space-shifts, also called inter-marker spacing parameters. Following the hypothesis of sigmoids for neurodegenerative disease biomarkers [START_REF] Jack | Update on hypothetical model of Alzheimer's disease biomarkers[END_REF], we use the logistic variant of the disease course mapping model:

y ijk = 1 + ( 1 p k -1)exp(- v k (e ξi (t ij -t 0 -τ i ) + t 0 ) + w ik p k (1 -p k ) ) -1 + ijk (1)
with the noise ij ∼ N (0 d , σ 2 I d ). The individual time reparametrization takes the following form:

ψ i (t) = α i (t -t 0 -τ i ) + t 0
, where τ i is called the timeshift and models a straight delay or advance one individual can have on the average trajectory, and α i = e ξi is called the acceleration factor. This time reparametrization captures two phenomena: the fact that a patient can have an early or late disease onset, and the fact that a patient can be a slow or fast progressor. The space-shifts (w i ) i have the same dimension as the observations, but for more interpretability the model uses an ICA decomposition with N s independent sources (s i ) 1≤i≤Ns . This leads to a formulation w i = As i such that the columns A l = d-1 k=1 β lk B k are a linear combination of an orthonormal basis (B k ) 1≤k≤d-1 of the orthogonal hyperplane to Span(v).

The hierarchical statistical model assumes that the population and individual parameters are latent, and follow Gaussian distributions directly or after transformation:

ξ i ∼ N (0, σ 2 ξ ), τ i ∼ N (0, σ 2 τ ) and s i ∼ N (0 Ns , I Ns ); g k = 1 p k -1 and g ∼ N (ḡ, σ 2 g I d ), v k = e ṽk and ṽ ∼ N (v, σ 2 v I d ), t 0 ∼ N ( t0 , σ 2 t ), β lk ∼ N ( βlk , σ 2 β
). The individual parameters are noted z i = (ξ i , τ i , w i ). The population parameters, i.e. the fixed effects, are noted z pop = (g, v, t 0 , A). All the latent variables are noted z = (z pop , (z i ) 1≤i≤n ). Finally the statistical model parameters are θ = (σ ξ , σ τ , ḡ, v, t0 , βlk ), while σ g , σ t , σ v , σ β are fixed.

MCMC-SAEM

The estimation of the parameters in the disease course mapping model is performed with the Monte Carlo Markov chain stochastic approximation variant of the Expectation Maximization algorithm. The convergence of the MCMC-SAEM has been proven [START_REF] Kuhn | Coupling a stochastic approximation version of EM with an MCMC procedure[END_REF] for the curved exponential family, which is the family of distributions for which the log-likelihood can be written as: ∀θ ∈ Θ, log q(y, z, θ) = -Φ(θ) + S(y, z), g(θ) where Φ and g are smooth functions, S are called the sufficient statistics. The sufficient statistics are to be understood as a summary of the required information from the latent variables z and the observations y. The algorithm alternates between two steps:

-Expectation: latent parameters are estimated by a Metropolis-Hastings within Gibbs sampler algorithm. First new values z * are sampled from a proposal law. Proposal value z * is accepted over current value z K with probability 1∧ q(y,z * |θ) q(y,z K |θ) . This Metropolis-Hastings scheme guarantees that the new value z K+1 is asymptotically sampled from the target distribution q(y, •|θ K ). The Gibbs sampler is used to sequentially estimate the population parameters z pop and the individual parameters z i . Based on the latent variables z K+1 , the sufficient statistics are computed, giving an approximation of log q -Maximization: the model parameters θ K are updated by maximizing the expectation of the log-likelihood θ K+1 = argmax θ∈Θ log(q(y, z K+1 , θ)), which is computed in closed form as a function of the sufficient statistics only

Mixture of disease course mapping models

The improvement we brought to the disease course mapping model is a new layer atop of the hierarchical structure already built. If we write q(y, z, θ) the likelihood of the model parametrized by θ, with latent variables z and observations y, then the likelihood of a mixture model with L clusters is:

Q θ1,...,θ L (y, z) = L c=1 π c q(y, z, θ c
) where π c denotes the probability of cluster c. Then each cluster c has its own set of parameters θ c . We assume that each individual has a true latent class π i and a set of individual parameters z πi i corresponding to the model attached to the cluster π i . The estimation algorithm is described in Algorithm 1. It is a mixture version of the MCMC-SAEM, where we add the latent variables π c i for the probability of each individual i to be in each cluster c, and (z c i ) i are the individual parameters for an individual i in cluster c. Contrarily to [START_REF] Debavelaere | Learning the Clustering of Longitudinal Shape Data Sets into a Mixture of Independent or Branching Trajectories[END_REF] where the latent variable is directly π i , forcing individuals to attach to a cluster, our use of soft cluster labelling avoids cluster freeze and trapping states. By conditioning, we rewrite the likelihood of individual i in cluster c q(y i , z c i |θ c , z c pop ) as the product of q(y i |θ c , z c pop , z c i ) the likelihood of the observations and p(z c i |θ c , z c pop ) the likelihood of the individual parameters. These two terms are akin to the classical terms of the L2 loss (resulting from the choice of the Gaussian noise) and the regularization respectively.

Algorithm 1: M-MCMC-SAEM estimation

Initialization: π 0 , (θ c 0 ), (z c 0,i ) for K = 0...N do Compute probability of individual i to belong to cluster c:

π c K+1,i = ∀i, set z c K+1,i = z c * ,i with probability α i else z c K+1,i = z c K,i Compute sufficient statistics (S c (y i , z K+1 )) i • M step Update θ c K+1 = argmax θ∈Θ log q(y, z c K+1,pop , (z c K+1,i ) i , θ) Compute π c K = 1 n i π c K,i end end
The challenging part is the update of model parameters within each cluster. In the case of a single model, the updates of the parameters θ of the model are computed in a closed form and are only a function of the total sufficient statistic, which writes S(y, z K+1 ) = i S(y i , z K+1 ) since the observations (y i ) i are supposed independent. When mixtures are involved, the log-likelihood changes to log q(y, z c , θ c ) = i log ( c π c i q(y i , z c i , z c pop , θ c )). However since the EM computes an expectation of the log-likelihood, we can condition on the true latent class π i of each individual i such that π c i = P(π i = c) :

E z log c π c i q(y i , z c i , z c pop , θ c ) = E π E z log c 1 πi=c q(y i , z c i , z c pop , θ c ) |π i = E π E z c 1 πi=c log q(y i , z c i , z c pop , θ c ) |π i = E z c π c i log (q(y i , z c i , z c pop , θ c ))
Thus we obtain the total sufficient statistics for each cluster S c (y, z K+1 ) = i π c i S(y i , z K+1 ) which can be used to update θ c . This formula is intuitive: each sufficient statistic for each cluster weights the contribution of the individual data by the probability of this individual being in the cluster. This result also proves that the mixture model still belongs to the curved exponential family. Therefore, the convergence of this algorithm is guaranteed by the MCMC-SAEM proof [START_REF] Kuhn | Coupling a stochastic approximation version of EM with an MCMC procedure[END_REF].

Tempered scheme

Even with theoretical guarantees, the convergence might be very slow in practice. The estimation of individual parameters in a non-linear single model may be challenging. Building a mixture on top of it further adds to the difficulty. Practical experiences show a high reliability on initialization. One of the bottleneck is the amount of cluster regularization contained in the term p(z c i |θ c , z c pop ) in the likelihood. Until the cluster population parameters stabilize, we do not want to restrict the exploration of the individual parameters space.

We thus propose to use a tempered scheme for the Gibbs sampler, mimicking simulated annealing. Tempered MCMC-SAEM has been shown to converge [START_REF] Allassonniere | Learning spatiotemporal piecewisegeodesic trajectories from longitudinal manifold-valued data[END_REF]. In a tempered scheme, inverse temperature comes as a multiplier of the log-likelihood of the model. We realized our model had overly constraining regularization, outweighing the data term in the likelihood. Thus we applied temperature only to the regularization term of the log-likelihood in the sample.

In practice, we propose to simply replace p by p = p 1/T in Algorithm 1.

For the temperature scheme, we opted for a sinusoidal pattern with a decreasing hull (sine cardinal) following [START_REF] Allassonniere | Learning spatiotemporal piecewisegeodesic trajectories from longitudinal manifold-valued data[END_REF]:

T (κ) = 1 + b sin(κ) κ , κ = ∆ + 2π K p
, where b can be seen as the amplitude of the oscillations, ∆ as a phase delay, and p as a period, K is the iteration number. The use of this tempered scheme allows for an alternation between exploratory phases (high temperature) and exploitation phases (low temperature). The values of the hyperparameters were empirically set to b = 1, ∆ = 0, p = N iter /100 after several attempts.

Initialization method

With the same practical considerations, we had to find an initialization method which would improve the odds of convergence towards the global optimum. Random or manual initialization of the model parameters (θ c 0 ) c was not satisfying, as we will see in the experiments.

We opted for an initialization as close to the clusters as possible. We first fit a disease course mapping model (without mixture) on the whole data. This yields a set of parameters (θ init , z pop,init , (z i,init )). Then we use a Gaussian mixture model (GMM) on the estimated individual parameters z i,init . The GMM allows us to identify L clusters within the individual data. The parameters of each mode c in the GMM combined with the population parameters θ init produce new population parameters for a disease course mapping model which represent the mode: for instance the new t c 0 is the shift of t 0,init by the mean value of τ i in the mode. This provides initialization parameters for as many disease course mapping models as there are modes in the GMM, and we use these initialization parameters for the clusters of the mixture model.

Please note that the use of a post hoc clustering on the estimated parameters is not equivalent to the joint estimation in the mixture model, so this initialization method does not directly give the right cluster parameters. Indeed, we can only produce clusters such that ∀c, v c ∈ Span(v init ), which is a strong limit to the posterior analysis of a one-class model.

Results and Discussion

Simulated data

Univariate model We first show that the mixture model accurately recovers the ground truth parameters on simulated data. We generated data by creating two unimodal disease course mapping models with chosen population parameters. We fix the first model with t 0 = 70, σ τ = 2, σ ξ = 0.1, log(v 0 ) = -2, log(g 0 ) = 1. For the second model we change the values of t 0 and v 0 . We use the Kullback-Leibler divergence to determine the difference between the two model distributions. We then assume the two clusters have equal prevalence and we create 512 individuals, which consists in randomly attributing the individual to a cluster and sample individual parameters according to the distribution of the cluster. Next we arbitrarily decide the number (7 in average) and time of the "visits" for each individual, and we compute the values associated to these timepoints. Finally we add a small Gaussian noise (σ = 0.01) to the output.

A simplified version of the model consists in assuming that there is no sources in the ICA, leading to an univariate model with no space-shifts. In this case, the only individual parameters left are the time-related ones: (ξ i ) i and (τ i ) i . This special case of the model converges more easily since there are less parameters to estimate, which allows us to initialize the model without having to first fit a single model. We evaluated the class estimation with the area under the ROC curve (ROC AUC) metric. For the evaluation of population and individual parameters, we computed the absolute error between the ground truth parameters of each cluster and the parameters of the closest estimated cluster, this error being normalized by the standard deviation of the parameter. Figure 1 shows the reconstruction metrics on simulated data as a function of the Kullback-Leibler divergence between clusters. With the ROC AUC, we are able to see that the mixture perfectly separates two clusters, once the two clusters are different enough.

The estimation errors for population parameters increases slightly as the clusters get farther from each other, which is understandable since the algorithm needs to do more exploration. The mean error on individual parameters shows a very stable curve. The reconstruction is limited by the noise of the generated data. In all the univariate experiments, the estimated parameters allowed the model to reach a L2 loss close to the noise level. The consistent errors for individual parameters seemingly correspond to the range in which individual parameters differences can be mistaken for noise. Multivariate model In the previous experiment, the results show consistent performance on a simplified univariate model. However when we add multiple sources, the number of parameters increases drastically and convergence might be more challenging in practice. We generated a dataset as in the first experiment but with two sources and three-dimensional observations. We first fitted a single disease course mapping model on the generated dataset, yielding (θ init , z pop,init ). We then fitted several mixture models to compare the different initialization methods, with or without the tempered scheme. Final results are shown in Table 1. Each model estimation takes about 5 minutes for 4,000 iterations which is the number of iterations required in this setup for the log-likelihood to stabilize.

The table shows that the tempered version allows for a better fit at the cost of regularization overall. Random initialization does not work. "Init" shows a better fit but is not able to cluster the individuals. "GMM" initialization is the best method in the absence of better heuristics.

Applications on Alzheimer's disease data

Experiment without MCI We apply the method to the ADNI dataset 1 . We first build a model considering only stable Alzheimer's disease (AD) patients Table 1. Performances of models. Single: single disease course mapping model; Random: random initialization; Init: initialization for both clusters at (θinit, zpop,init); GMM: the initialization method described previously using a GMM on (zi,init)i; True: perfect initialization at the ground truth parameters. Fit: log-likelihood related to the observations. Regularization: log-likelihood related to parameters' distribution.

Model

ROC AUC Fit (log q) Regularization (log p) We select 8 features that are most relevant to the progression of AD based on a medical expert's advice, which included cognitive scores, MRI-derived regional volumes and biomarkers level. We then fit a single disease course mapping model on it. The posterior analysis of individual parameters highlights the need to take heterogeneity into account. The posterior distribution of the couple (τ i , ξ i ) is shown in Fig. 2.

The GMM on the individual parameters provides two initial clusters for our mixture model. Optimal number of clusters was decided based on the Bayesian Information Criterion (BIC). The results of the mixture model are shown in Figure 3. The two clusters have very distinct average trajectories. The most obvious difference is the much earlier and rapid cognitive decline in cluster 2 compared to the cluster 1, while the progression of imaging and CSF biomarkers is only a few years earlier in cluster 2.

Interestingly, the clustering does not correspond to AD and controls classes. Cluster 1 contains 88% of all controls and 65% of AD cases, meaning cluster 2 accounts for a minority of the data and contains mostly AD patients. Since average trajectory takes controls into account, we plotted the average trajectory of AD patients in each cluster in order to compare them. AD patients in both clusters show rapid cognitive degradation, while AD patients in the first cluster show a steeper increase of their imaging and CSF levels.

To understand why the mixture model did not separate AD patients from controls, we estimated one model on AD patients only and one model on controls only. We then computed the log-likelihood of our models. Results are shown in table 2. They confirm that the mixture model explains the variability seen in the data better than prior categorisation based on diagnosis. We further estimated a mixture with the initial clusters being AD and controls, and the algorithm still converged towards a similar version to the one presented in Figure 3.

Several studies report an association between the atrophy rates of particular brain regions and cognitive decline [START_REF] Zhang | Bayesian model reveals latent atrophy factors with dissociable cognitive trajectories in Alzheimer's disease[END_REF][START_REF] Risacher | For the Alzheimer's Disease Neuroimaging Initiative: Alzheimer disease brain atrophy subtypes are associated with cognition and rate of decline[END_REF], which lead to the identification of disease subtypes based on the differences in regional atrophies. Our analysis suggest that such associations are not systematic: similar pathological processes may lead to distinct pattern of cognitive decline, like similar cognitive decline may have distinct pathological processes. Estimating MCI patients We performed individual personalization of MCI in the previous model, i.e. we estimated individual parameters including likelihood to belong to each cluster while keeping population parameters fixed. The distribution of MCI patients in the two clusters confirmed our hypothesis that cluster 2 is a specific subtype of AD: MCI associated to cluster 2 are mostly converters (66%) while 80% of non-converters are in cluster 1.

Conclusion

We proposed a mixture for a disease course mapping model which has been validated on simulated data. We also introduced an heuristic initialization method to ensure convergence without extensive parameter search. The application to an Alzheimer's disease cohort suggests two subtypes of the disease associated with distinct relationship between cognitive decline and progression of imaging and CSF biomarkers.

Fig. 1 .

 1 Fig. 1. Evaluation metrics for the reconstruction of true parameters. Left: ROC AUC for the estimated cluster probabilities of individuals π c i . Right: Absolute error between estimated parameters and ground truth, normalized by parameter standard deviation.

Fig. 2 .

 2 Fig. 2. Scatter plot of individual parameters, with kernel density estimation. Left: KDE on all AD and control patients. Right: KDE estimated separately for AD and controls.

Fig. 3 .

 3 Fig. 3. Average trajectories in time. AD patients in both clusters have a similar cognitive evolution as shown by the cognitive scores (MMSE, RAVLT and ADAS-COG) whereas AD patients of cluster 1 (green) have a faster progression on MRI-based and CSF biomarkers than AD patients of cluster 2 (red).

Table 2 .

 2 Log-likelihood of models

	Model	Fit (log q) Regularization (log p) Total log-likelihood
	Mixture	38100	-10391	27708
	AD + Controls 37226	-9772	27454

http://adni.loni.usc.edu/

This research has received funding from the program "Investissements d'avenir" ANR-10-IAIHU-06. This work was also funded in part by the French government under management of Agence Nationale de la Recherche as part of the "Investissements d'avenir" program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), and under the joint program in neurodegenerative diseases (JPND) ANR-19-JPW2-000 (E-DADS).

)) j π j K q(yi|θ j K ,z j K,i ,z j


Benoit De Coignac

Dr Nicolas Bouscaren
email: nicolas.bouscaren@chu-reunion.fr

Leptospirosis in French Polynesia: 11 years of surveillance data, 2007-2017

Leptospirosis is a worldwide zoonosis with higher incidence in tropical areas and is a neglected disease in the Pacific region. French Polynesia is a French overseas Territory located in the South Pacific. Data on the epidemiology in French Polynesia are scarce. In this study, we described our understanding of leptospirosis epidemiology in French Polynesia and discussed the prospects concerning this disease and its surveillance to better address preventive actions. We reported 11 years of surveillance data between January 1 st 2007 and December 31 st 2017. Over the study period 1,356 confirmed and probable leptospirosis cases were reported, the mean annual incidence rate was 46.0 (95%CI 43.6-48.5) cases per 100,000 inhabitants, we registered 864 (63.7%) hospitalisations, among them, at least 270 (19.9%) were in intensive care unit and 24 (1.8%) patients died. Even if incidence of leptospirosis is lower in French Polynesia compared to most of other Pacific countries and Territories, our data confirms that the disease is highly endemic in our country. Despite all preventive measures, leptospirosis remains a major public health concern in French Polynesia, highlighting the need to maintain intensive leptospirosis surveillance, medical staff training and information of the general population.

Introduction

Leptospirosis is a worldwide bacterial zoonosis, with a significant health burden on economically vulnerable population [START_REF] Haake | Leptospirosis in Humans[END_REF][START_REF] Torgerson | Global Burden of Leptospirosis: Estimated in Terms of Disability Adjusted Life Years[END_REF][START_REF]Global Leptospirosis environmental action network[END_REF]. It is a neglected tropical disease, especially in the Pacific Region [START_REF] Guernier | A systematic review of human and animal leptospirosis in the Pacific Islands reveals pathogen and reservoir diversity[END_REF][START_REF] Kline | Neglected tropical diseases of Oceania: review of their prevalence, distribution, and opportunities for control[END_REF][START_REF] Victoriano | Leptospirosis in the Asia Pacific region[END_REF].

Leptospirosis is caused by spirochetes of the genus Leptospira, bacteria belonging to the Leptospiraceae family [START_REF] Adler | Leptospira and leptospirosis[END_REF][START_REF] Cerqueira | A century of Leptospira strain typing[END_REF]. Many mammals' species, wild or domestic, can carry the pathogen.

Rodents are the main reservoir of Leptospira [START_REF] Haake | Leptospirosis in Humans[END_REF]. Epidemiology of leptospirosis is characterized in the Pacific islands by a potentially important role of livestock farming animals [START_REF] Guernier | A systematic review of human and animal leptospirosis in the Pacific Islands reveals pathogen and reservoir diversity[END_REF].

Human contamination results from contact of abraded skin or mucous membranes with urine or tissues of infected animals, directly or indirectly via contaminated water or wet soil [START_REF] Haake | Leptospirosis in Humans[END_REF][START_REF] Levett | Leptospirosis[END_REF][START_REF]Human leptospirosis : guidance for diagnosis, surveillance and control[END_REF]. Spectrum of the disease range from subclinical infection as flu-like symptoms to severe disease with multi-visceral complications like acute renal failure, pulmonary haemorrhage (Weil's disease), and death [START_REF] Haake | Leptospirosis in Humans[END_REF][START_REF] Levett | Leptospirosis[END_REF][START_REF] Bharti | Leptospirosis: a zoonotic disease of global importance[END_REF].

Treatment is based on early antibiotic therapy. The vaccine only protects against the serovar Icterohaemorrhagiae, the most frequently responsible for severe human infections, and it must be renewed every two years.

Annual worldwide incidence of leptospirosis is estimated at 1 million cases, with 5-15% of severe diseases [START_REF]WHO | Managing epidemics[END_REF] and about 60,000 deaths [START_REF] Costa | Global Morbidity and Mortality of Leptospirosis: A Systematic Review[END_REF]. Leptospirosis is responsible for 2.9 million Disability Adjusted Life Years (DALYs) per annum with a preponderant occurrence among low and middle-income tropical countries and males [START_REF] Torgerson | Global Burden of Leptospirosis: Estimated in Terms of Disability Adjusted Life Years[END_REF]. The burden of leptospirosis is underestimated because of high proportion of sub-clinical and asymptomatic infections, lack of notification systems, and poor access to accurate laboratory diagnosis in low and middle-income countries [START_REF] Haake | Leptospirosis in Humans[END_REF][START_REF] Ahmed | Molecular Approaches in the Detection and Characterization of Leptospira[END_REF][START_REF] Lau | Combating infectious diseases in the Pacific Islands: sentinel surveillance, environmental health, and geospatial tools[END_REF][START_REF] Musso | Laboratory diagnosis of leptospirosis: a challenge[END_REF]. World Health Organisation (WHO) created in 2009 the Leptospirosis Burden Epidemiology Reference Group (LERG), with the goal to conduct research and develop policy targeted towards decreasing the burden of leptospirosis [START_REF]WHO | Leptospirosis Burden Epidemiology Reference Group (LERG)[END_REF].

Pacific Islands have highly favourable environmental conditions for transmission of leptospirosis: hot and humid tropical and subtropical climate with high rainfall, recurrent flooding, poverty, urbanization, local life style (barefoot walking, swimming), and occupational activities [START_REF] Lau | Combating infectious diseases in the Pacific Islands: sentinel surveillance, environmental health, and geospatial tools[END_REF]. Knowledge of the global burden of leptospirosis in the Pacific region remains incomplete, principally due to the lack of laboratory capacities to confirm cases.

French Polynesia (FP) is a French overseas Territory located in the South Pacific, constituted of five archipelagos: Society, Marquesas, Tuamotu-Gambier and Austral Islands. The population is about 280 000 inhabitants (2017 census), spread in 72 inhibited islands with 70% of the population leaving on Tahiti Island [START_REF]authentifiant les résultats du recensement de la population[END_REF]. Few data on the epidemiology of leptospirosis in FP exist [START_REF] Guernier | A systematic review of human and animal leptospirosis in the Pacific Islands reveals pathogen and reservoir diversity[END_REF][START_REF] Guernier | Leptospira diversity in animals and humans in Tahiti, French Polynesia[END_REF] with the first human infections reported only in 1959 [START_REF] Heuls | Leptospirosis caused by Leptospira icterohemorrhagiae in Tahiti][END_REF]. Number of reported cases per year between 2006 and 2012 ranged between 79 and 127 and the annual incidence between 30 and 49 cases per 100,000 inhabitants [START_REF] Berry | Situation épidémiologique de la leptospirose en Pf (2006-2012)[END_REF][START_REF] Daudens | Recrudescence of leptospirosis in French Polynesia in early 2010[END_REF][START_REF] Hirschauer | Épidémiologie de la leptospirose en Polynésie française de 2006 à 2008[END_REF].

In this study, we described our understanding of leptospirosis epidemiology in FP and discussed the prospects concerning this disease and its surveillance to better address preventive actions.

Methods

We reported 11 years of surveillance data between January 1 st 2007 and December 31 st 2017. In FP, all probable and confirmed leptospirosis cases are collected by the local health authority (Bureau de veille sanitaire), based on notification forms filled in by general practitioners, and laboratory results provided by laboratories of the "Institut Louis Malardé" and of the "Centre Hospitalier de la Polynésie française".

Case definition

Confirmed case: leptospirosis symptoms with either isolation of bacteria by culture or of its DNA by polymerase chain reaction (PCR) or seroconversion of specific immunoglobin class M (IgM).

Probable case: leptospirosis symptoms and IgM detection ELISA on a single serum collected more than 1 week post symptoms onset.

Excluded case: leptospirosis symptoms with PCR negative on sera collected within the first week post symptoms onset or ELISA IgM negative on sera collected more than 1 week post symptoms onset. Demographic data were provided by the FP statistic institute [24]. Population estimation along the duration of the study was calculated using an exponential increase during two consecutive censuses.

All confirmed and probable cases were included in statistical analysis. Qualitative variables were described using frequency and percentages. Quantitative variables were described using mean ± standard deviation [minimum-maximum]. Annual Incidence rates (AIRs), meaning number of cases per 100,000 persons year (PY), were presented with 95% confidence intervals (95%CI), based on the Poisson model. We used a Z test for comparing AIRs between genders and between archipelagos.

Relative Risks (RR) with corresponding 95% CI were computed. A p level of <0.05 was considered statistically significant. All statistical analyses were performed using STATA® V13.1 software (StataCorp LP, Lakeway Drive, College Station, Texas 77845 USA) for Windows. Mapping was done using the QGis® v2.18.1 software and Google Earth Pro®.

Results

Between 1 January 2007 and 31 December 2017, 1,356 leptospirosis cases were reported: 851 (62.8%) confirmed and 505 (37.2%) probable. Over the study period the AIR was 46.0 (95%CI 43.6-48.5) cases per 100,000 PY (Figure 1a). Median number of cases on decade was 109 with a peak in 2017 with 199 cases corresponding to an AIR of 72.1 (95%CI 62.5-82.9) cases per 100,000 PY.

A total of 1,032 (76.1%) cases were reported in men cases and 324 (23.9%) in women (sex ratio 3.2) with an overall average age of 33.7±16.2 [2-80] on men and 35.2±17.8 on women. Comparison of AIRs showed a significant excess risk of contamination in men [68.5 (95%CI 64.4-72.8) cases per 100,000 PY] vs women cases per 100,000 PY], RR=3.1 (IC 95% 2.7-3.5), p<0.001. The age group repartition showed the largest number of cases was [START_REF] Heuls | Leptospirosis caused by Leptospira icterohemorrhagiae in Tahiti][END_REF][START_REF] Berry | Situation épidémiologique de la leptospirose en Pf (2006-2012)[END_REF][START_REF] Daudens | Recrudescence of leptospirosis in French Polynesia in early 2010[END_REF][START_REF] Hirschauer | Épidémiologie de la leptospirose en Polynésie française de 2006 à 2008[END_REF][24][START_REF] Massenet | An Unprecedented High Incidence of Leptospirosis in Futuna, South Pacific, 2004 -2014, Evidenced by Retrospective Analysis of Surveillance Data[END_REF][START_REF] Coudert | Human leptospirosis in French Polynesia. Epidemiological, clinical and bacteriological features[END_REF][START_REF] Nhan | Fatal leptospirosis and chikungunya coinfection: Do not forget leptospirosis during chikungunya outbreaks[END_REF][START_REF] Aubry | Zika Virus Seroprevalence, French Polynesia, 2014-2015[END_REF][START_REF] Cao-Lormeau | French polynesia, South pacific, 2013[END_REF] years with 332 (24.5%) cases representing a peak AIR of 66.8 (95%CI 59.8-74.4) cases per 100,000 PY. During the whole period, cases were reported throughout the year, but mostly between January and May with a noticeable decrease from August to December (Figure 1b).

Geographical distribution

Island of residence was available for 1,282 (94.5%) cases. The Society archipelago accounted for 95.5% of cases with an annual average of 114.7±35. 1 [74-192] cases. The AIRs per archipelago were 48.8 (95%CI 46.1-51.6) cases per 100,000 PY for the Society, 53 (95%CI 39.8-69.2) for the Marquesas, 1.3 (95%CI 0.0-7.4) for the Austral, and 2.2 (95%CI 0.6-5.5) for the Tuamotu Gambier.

Map, number of cases, AIRs and RR by island in Society archipelago are presented in Table 1 and Figure2.

Over the study period we recorded 864 (63.7%) hospitalisations; among them, at least 270 (19.9%) were in intensive care unit and 24 (1.8%) died.

Information on risk factors for leptospirosis was obtained from 920 (67.8%) cases for occupational risk, 885 (65.3%) cases for leisure activity, 835 (61.6%) cases for contact with animals, and 324 (23.9%) cases for high risk facilities (Table 2).

Discussion

The worldwide AIR of leptospirosis is about 15 cases per 100,000 PY; the highest incidence is reported in the Oceania region with 150 cases per 100,000 PY and a mortality rate of 9.6 per 100,000 PY. In this region AIR of up to 844 cases per 100,000 PY over an 11-year period from 2004 to 2014 has been reported in Futuna [START_REF] Massenet | An Unprecedented High Incidence of Leptospirosis in Futuna, South Pacific, 2004 -2014, Evidenced by Retrospective Analysis of Surveillance Data[END_REF], with a pic of 1,945 cases per 100,000 PY in 2008 [START_REF] Guernier | A systematic review of human and animal leptospirosis in the Pacific Islands reveals pathogen and reservoir diversity[END_REF]. The AIR of leptospirosis in FP between 2007 and 2017 was 46.0 (95%CI 43.6-48.5) cases per 100,000 PY, in the lower range of AIR reported in the region (40-270) [START_REF] Costa | Global Morbidity and Mortality of Leptospirosis: A Systematic Review[END_REF]. This incidence is low compared with other Pacific Islands, probably because, at the difference of FP, most of them are low and middle income countries. However, AIR of leptospirosis in FP is most probably underestimated, especially in the most remote islands (Marquesas, Tuamotu Gambier and Austral). Main factors responsible for underestimation of leptospirosis in FP are misdiagnosis with other diseases, especially dengue, a high number of cases with few symptoms , and geographic constraint (isolation, multiplicity of islands, lack of medical personnel to carry out sampling, difficulties in accessing health care facilities, lack of transport or communication within and between islands) [START_REF] Coudert | Human leptospirosis in French Polynesia. Epidemiological, clinical and bacteriological features[END_REF]. Similar clinical symptoms between leptospirosis and arboviral infection is a main issue during arboviral outbreaks, leading to undetection of leptospirosis cases and delayed treatment, potentially responsible for fatal cases [START_REF] Nhan | Fatal leptospirosis and chikungunya coinfection: Do not forget leptospirosis during chikungunya outbreaks[END_REF].

Over the period 2007-2012 we noticed low variation of AIR. A peak of incidence was recorded in 2010. At the end of January 2010, cyclonic depressions (OLI hurricane) caused heavy rainfall and mudslides in many FP islands, especially in Tahiti [START_REF] Daudens | Recrudescence of leptospirosis in French Polynesia in early 2010[END_REF]. These exceptional climatic conditions led to an increase in the number of cases in the first quarter of 2010. The population was quickly made aware by the local health authority of the probable increase in the risk of leptospirosis. Health professionals were encouraged to collect blood sample of patients with acute fever and diffuse pain syndrome. From 2013, the AIR increased due to an increase in screening linked to an arbovirus's epidemic context. Dengue and Zika epidemics occurred simultaneously between September 2013 and March 2014, followed by a major Chikungunya epidemic between October 2014 and March 2015 [START_REF] Aubry | Zika Virus Seroprevalence, French Polynesia, 2014-2015[END_REF][START_REF] Cao-Lormeau | French polynesia, South pacific, 2013[END_REF]. These 3 arboviruses are the main differential diagnoses of leptospirosis in endemic areas [START_REF] Bharti | Leptospirosis: a zoonotic disease of global importance[END_REF][START_REF] Nhan | Fatal leptospirosis and chikungunya coinfection: Do not forget leptospirosis during chikungunya outbreaks[END_REF].

Concomitantly, the development of affordable molecular diagnosis in FP increased the number of tests and then the number of diagnosed cases. The significant increase of AIR in 2017 is mainly related to the heavy rains and floods at the beginning of the year [30].

Leptospirosis is known to be seasonal, and strongly associated with rainfall in tropical settings [START_REF] Levett | Leptospirosis[END_REF].

The number of cases increases during the hot and rainy season and decreases during the cold and dry season [START_REF] Mwachui | Environmental and Behavioural Determinants of Leptospirosis Transmission: A Systematic Review[END_REF][START_REF] Lau | Human Leptospirosis Infection in Fiji: An Eco-epidemiological Approach to Identifying Risk Factors and Environmental Drivers for Transmission[END_REF]. Heavy rains and floods are associated with a six-fold increased risk of developing leptospirosis and are a direct cause of epidemics as for the year 2017 in our cohort [START_REF] Mwachui | Environmental and Behavioural Determinants of Leptospirosis Transmission: A Systematic Review[END_REF]. In FP, rainfall usually increases from December with a peak in January and then decreases until April. In our cohort 60% of cases occurred during the first 5 months of the year, cases increased from January with a peak in March and remains high until June. Thus, the recrudescence of reported cases of leptospirosis seems to be delayed by 2 months compared with the peak rainfall. This phenomenon had already been observed in Futuna and Reunion Island [START_REF] Massenet | An Unprecedented High Incidence of Leptospirosis in Futuna, South Pacific, 2004 -2014, Evidenced by Retrospective Analysis of Surveillance Data[END_REF][START_REF] Desvars | Seasonality of human leptospirosis in Reunion Island (Indian Ocean) and its association with meteorological data[END_REF]. In two studies in Mayotte, cases followed the evolution of rainfall with a three-month delay. According to the authors, the importance of seasonal peaks is more related to the number of consecutive months with heavy rains than to the total rainfall [START_REF] Lernout | Epidemiology of human leptospirosis in Mayotte : an emerging public health problem on the island? Arch Inst Pasteur Madag[END_REF][START_REF] Pagès | Leptospirose à Mayotte : apports de la surveillance épidémiologique, 2008-2015[END_REF]. The discrepancy observed between the incidence of leptospirosis and peak rainfall is explained by the soaking of the soil after the peak rainfall, which favour leptospires survival in the environment [START_REF] Desvars | Seasonality of human leptospirosis in Reunion Island (Indian Ocean) and its association with meteorological data[END_REF][START_REF] Pagès | Leptospirose à Mayotte : apports de la surveillance épidémiologique, 2008-2015[END_REF].

We have found a geographical disparity in the incidence of leptospirosis in FP. AIR were higher in high islands: Leeward Islands, Windward Islands and Marquesas. In contrast, lower islands (atolls) of the Tuamotu-Gambier were almost free of cases due to their geomorphology: coral atolls without relief and very little fresh water standing on the surface, no river or sludge because of the very porous soils, and low rainfall. In the high islands, the development of agricultural and industrial operation, and higher population density create waste and activities that may attract rodents and thus increase the risk of contamination [START_REF] Mwachui | Environmental and Behavioural Determinants of Leptospirosis Transmission: A Systematic Review[END_REF][START_REF] Lau | Human Leptospirosis Infection in Fiji: An Eco-epidemiological Approach to Identifying Risk Factors and Environmental Drivers for Transmission[END_REF]. In the Society archipelago, AIRs are higher in some Windward Islands and in the south-east part of Tahiti which are agricultural regions and where the main pig, cattle, horse and poultry farms are located.

Most cases occurred in males, in accordance with what is described elsewhere. It probably only reflects higher exposure of the male population through agricultural, farming and outdoor leisure activities. The highest AIR was in the [START_REF] Heuls | Leptospirosis caused by Leptospira icterohemorrhagiae in Tahiti][END_REF][START_REF] Berry | Situation épidémiologique de la leptospirose en Pf (2006-2012)[END_REF][START_REF] Daudens | Recrudescence of leptospirosis in French Polynesia in early 2010[END_REF][START_REF] Hirschauer | Épidémiologie de la leptospirose en Polynésie française de 2006 à 2008[END_REF][24][START_REF] Massenet | An Unprecedented High Incidence of Leptospirosis in Futuna, South Pacific, 2004 -2014, Evidenced by Retrospective Analysis of Surveillance Data[END_REF][START_REF] Coudert | Human leptospirosis in French Polynesia. Epidemiological, clinical and bacteriological features[END_REF][START_REF] Nhan | Fatal leptospirosis and chikungunya coinfection: Do not forget leptospirosis during chikungunya outbreaks[END_REF][START_REF] Aubry | Zika Virus Seroprevalence, French Polynesia, 2014-2015[END_REF][START_REF] Cao-Lormeau | French polynesia, South pacific, 2013[END_REF] year's old class. Like sex ratio, a high number of cases in young age's classes possibly reflects a frequent exposure of young active men involved in agriculture and farming activities. However, the hypothesis that older classes are relatively protected by the immunity resulting from previous exposures also deserves consideration.

The main risk factor for leptospirosis in FP is professional or private agricultural activity: prevention measures should target this population. Secondary risk factors are mostly recreational with fresh water contact during leisure time (barefoot walking in mud, river bathing, hiking, gardening or fishing).

Other factors such as contact with rats, pigs as well as dogs (large population of stray dogs), leaving in poor sanitary condition or in family farms in semi-urban areas near watercourses, can contribute to the transmission of the disease [START_REF] Guernier | A systematic review of human and animal leptospirosis in the Pacific Islands reveals pathogen and reservoir diversity[END_REF][START_REF] Guernier | Leptospira diversity in animals and humans in Tahiti, French Polynesia[END_REF].

Conclusion

Leptospirosis is a major public health concern in FP where it will become soon a reportable disease.

All laboratories and medical facilities, including intensive care unit, are available to diagnose and care cases. Prevention includes guidelines for healthcare workers, prevention measures for the general population broadcasted by a bi-monthly bulletin, and a reminder of the risk sent to the media after each heavy rainfall or flooding. In addition, following the WHO One Health approach, collaboration between animal and human health has been initiated to struggle against zoonosis as leptospirosis.

Enhancement of rodents control by the improvement of waste management is needed. Despite all preventive measures, leptospirosis remains highly endemic in our country, highlighting the need to maintain leptospirosis surveillance, medical staff training and information of the general population.

Figures and tables

Figure

  Figure 1a: Leptospirosis cases and annual incidence rates in French Polynesia, 2007-2017

Figure 1b :

 1b Figure 1a: Leptospirosis cases and annual incidence rates in French Polynesia, 2007-2017

Figure 2 :

 2 Figure 2: Map of Society archipelago with a focus on Tahiti island, annual incidence rate of leptospirosis by island and municipality, 2007-2017

Figure 1a :Figure 1b :

 1a1b Figure 1a: Leptospirosis cases and annual incidence rates in French Polynesia, 2007-2017

Table 1 :

 1 Leptospirosis cases, annual incidence rates (AIR) and relative risks (RR) by islands of

	Society archipelago, 2007-2017

Table 2 :

 2 Potential risk factors of leptospirosis, French Polynesia, 2007-2017

Figure 2 :

 2 Map of Society archipelago with a focus on Tahiti island, annual incidence rate of leptospirosis by island and municipality, 2007-2017

	Number of cases											Annual incidence rate (cases/100 000 PY)
								2014 2015 2016 2017
						Year
			Confirmed cases	Probable cases	AIR
	Number of cases
	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
						Month
				Confirmed cases	Probable cases

Table 1 :

 1 Leptospirosis cases, annual incidence rates (AIR) and relative risks (RR) by island of Society AIR : Annual Incidence Rate in number of cases per 100,000 persons year b Comparison of relative risk with the reference group.

	archipelago, 2007-2017
	Islands	n (%)	AIR a (IC95%)	RR (IC95%)	p b
	Tahiti	731 (57.9)	40.0 (37.1-43.0)	1.00 (reference group)
	Moorea -Maiao	121 (9.6)	63.8 (53.0-76.3)	1.6 (1.3-1.9)	<0.001
	Raiatea	191 (15.1)	141.9 (132.3-163.5)	3.6 (3.0-4.2)	<0.001
	Tahaa	94 (7.5)	163.7 (132.3-200.4)	4.1 (3.3-5.1)	<0.001
	Huahine	87 (6.9)	125.5 (100.5-154.8)	3.1 (2.5-3.9)	<0.001
	Bora-Bora	37 (2.9)	35.1 (24.7-48.3)	0.9 (0.6-1.2)	0.437
	Maupiti	1 (0.1)	7.6 (0.2-42.4)	0.2 (0.03-1.4)	0.098

a

Table 2 :

 2 Potential risk factors of leptospirosis, French Polynesia, 2007-2017

				Percentage over
	Category		Number of cases	the total number of cases provided	Missing values for this category
				for this category
		Farmer	383	41.6%
		Sanitation and waste treatment	60	6.5%
	Occupational risk	Animal husbandry	134	14.6%	436	32.2%
		Cattle breeding	23	2.5%
		Horse breeding	17	1.8%
		Pig farming	43	4.7%
		Fishing	131	14.8%
		Hunting	40	4.5%
		Gardening	319	36.0%
	Leisure activity / fresh water contact	Hiking	101	11.4%	471	34.7%
		Walking barefoot	497	56.2%
		Fresh water swimming	277	31.3%
		River mouth surfing	67	7.6%
		Cats	292	35.0%
	Contact with animals	Dogs	466	55.8%	521	38.4%
		Rats	545	65.3%
		Dump in the vicinity	126	38.9%
	High risk facilities				1032	76.1%
		Water abstraction	48	14.8%