Multivariate Longitudinal Analysis with Bivariate Correlation Test

International audienceIn the context of multivariate multilevel data analysis, this paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the dimensional residual terms are assumed uncorrelated. Using the EM algorithm, we suggest more general expressions of the model's parameters estimators. These estimators can be used in the framework of the multivariate longitudinal data analysis as well as in the more general context of the analysis of multivariate multilevel data. By using a likelihood ratio test, we test the significance of the correlations between the random effects of two dependent variables of the model, in order to investigate whether or not it is useful to model these dependent variables jointly. Simulation studies are done to assess both the parameter recovery performance of the EM estimators and the power of the test. Using two empirical data sets which are of longitudinal multivariate type and multivariate multilevel type, respectively, the usefulness of the test is illustrated

Acquisition of natural humoral immunity to <i>P. falciparum</i> in early life in Benin:impact of clinical, environmental and host factors

To our knowledge, effects of age, placental malaria infection, infections during follow-up, nutritional habits, sickle-cell trait and individual exposure to Anopheles bites were never explored together in a study focusing on the acquisition of malaria antibody responses among infants living in endemic areas. Five hundred and sixty-seven Beninese infants were weekly followed-up from birth to 18 months of age. Immunoglobulin G (IgG), IgG1 and IgG3 specific for 5 malaria antigens were measured every 3 months. A linear mixed model was used to analyze the effect of each variable on the acquisition of antimalarial antibodies in 6- to 18-month old infants in univariate and multivariate analyses. Placental malaria, nutrition intakes and sickle-cell trait did not influence the infant antibody levels to P. falciparum antigens. In contrary, age, malaria antibody levels at birth, previous and present malaria infections as well as exposure to Anopheles bites were significantly associated with the natural acquisition of malaria antibodies in 6- to 18-month old Beninese infants. This study highlighted inescapable factors to consider simultaneously in an immuno-epidemiological study or a vaccine trial in early life

Evolution of the levels of human leukocyte antigen G (HLA-G) in Beninese infant during the first year of life in a malaria endemic area: using latent class analysis

Abstract Background: HLA-G, a non-classical HLA class I antigen, is of crucial interest during pregnancy by inhibiting maternal immune response. Its role during infections is discussed, and it has been described that high levels of soluble HLA-G during childhood increase the risk of malaria. To explore more precisely interactions between soluble HLA-G and malaria, latent class analysis was used to test whether distinct sub-populations of children, each with distinctive soluble HLA-G evolutions may suggest the existence of groups presenting variable malaria susceptibility. Method: A study was conducted in Benin from 2010 to 2013 and 165 children were followed from birth to 12 months. Evolution of soluble HLA-G was studied by the latent class method. Results: Three groups of children were identified: one with consistently low levels of soluble HLA-G during follow-up, a second with very high levels and a last intermediate group. In all groups, low birth weight, high number of malaria infections and high exposure to malaria transmission were associated with high level of soluble HLA-G. Placental malaria was not. Presence of soluble HLA-G in cord blood increased the probability of belonging to the highest trajectory. Conclusion: These results, together with previous ones, confirm the important role of HLA-G in the individual susceptibility to malaria. Assaying soluble HLA-G at birth could be a good indicator of newborns more fragile and at risk of infections during childhood

Human leukocyte antigen (HLA-G) influence on malaria susceptibility in pregnant women and infants

L’objectif général de cette thèse était d’étudier le rôle de la protéine soluble HLA-G (sHLA- G) dans la variabilité des réponses à l’infection par P. falciparum chez la femme enceinte et son nouveau-né pendant ses deux premières années de vie. Précisément, nous avons étudié, chez les mères pendant la grossesse et leurs nourrissons de la naissance à 2 ans, les relations entre les niveaux de sHLA-G et l’infection palustre au niveau périphérique et placentaire. Nous avons également étudié les polymorphismes génétiques situés dans la région 3’UTR du gène HLA- G chez les mères et leurs nourrissons par la détermination des fréquences alléliques, génotypiques et haplotypiques afin évaluer l’impact de ces polymorphismes sur la cinétique d’expression de sHLA-G dans un contexte d’infection palustre. Nos résultats ont montré une association entre le niveau élevé de sHLA-G chez les nourrissons et l’augmentation du risque d’infection palustre au cours du trimestre suivant. Ces niveaux élevés de sHLA-G dans le sang de cordon ont été également associés au faible poids de naissance du nouveau-né. De même, nous avons trouvé une forte corrélation entre les niveaux de sHLA-G maternels dans le sang périphérique à l’accouchement et ceux de l’enfant dans le sang du cordon à la naissance. Nous avons aussi montré l’existence de trois profils d’expression de sHLA-G chez les individus inclus dans l'étude. Certains individus expriment la protéine à chaque prélèvement (HLA-G ++) alors que d’autres l’expriment par intermittence (HLA-G +-) ou ne l’expriment pas (HLA-G --). Le risque de développer un accès palustre chez les mères était respectivement trois fois plus élevé (p=0,001, OR=3,47;p=0,008, OR=3,14) chez celles appartenant au groupe HLA-G (++) et HLA-G (+-) que le groupe HLA-G (--). L’analyse génétique de la région 3’UTR du gène nous a permis de mettre en évidence huit sites polymorphes dans cette région et de construire six haplotypes correspondant (UTR 1, 2, 3, 4, 5, 6). Nous avons aussi montré chez les mères une association entre l’allèle T en position +3001 (C/T) et une expression plus fréquente de sHLA-G tandis que l’allèle C en position +3003 (T/C) et l’haplotype UTR-4 ont été associés à une expression moins fréquente de la protéine. Ces associations n’ont pas été mises en évidence chez les enfants. L’ensemble de ces résultats suggère l'implication de sHLA-G dans la sensibilité à l'infection palustre. Cette sensibilité serait, en partie, corrélée à l’inhibition des réponses anticorps spécifiquement dirigées contre P. falciparum. sHLA-G pourrait donc à terme devenir un bio-marqueur de susceptibilité au paludisme chez la femme enceinte et chez le nouveau-né au cours des premières années de vie.The general objective of this thesis was to study the role of soluble HLA-G protein (sHLA-G) in the variability of individual response to malaria during pregnancy and during the first 2 years of infant life. Actually, we assessed the relationships between sHLA-G and malaria infection in peripheral and placental blood. We also investigated the effect of polymorphisms in the 3’UTR region of HLA-G gene in 400 mothers and their infants on the kinetic of sHLA-G expression three times during pregnancy and at 6, 9, 12, 18, 24 months of life in a context of malaria infection. Our results showed that high levels of sHLA-G increased the risk of malaria at the subsequent trimester in infants and were associated with low birth weight. We also showed a strong correlation between the plasmatic sHLA-G level of the mothers at delivery and those of newborns in cord blood. We found that the risk of developing malaria in mothers was respectively three fold higher in the HLA-G (++) (OR=3.47; p=0.001) and HLA-G(+-)(OR=3.14, p=0.008) groups compared to HLA-G (--) group. Besides, we described eight polymorphic sites in the 3’UTR corresponding to six haplotypes (UTR 1, 2, 3, 4, 5, 6) and showed in mothers, an association between the allele T at position +3001 (C/T) and a higher frequency of sHLA-G expression. However, the allele C at position +3003 (T/C) and UTR-4 were associated to a lower frequency of sHLA-G expression. In infants, no association was observed between alleles or haplotypes and expression of the soluble protein. Overall, these results suggest that sHLA-G is implicated in malaria susceptibility. This could be partly, related to the inhibition of P. falciparum-specific antibody responses. Therefore, sHLA-G might be useful as a bio- marker of malaria susceptibility during pregnancy and during the first years of infancy

Posterior distributions of random intercepts conditional on the data related to School 47 in the education dataset.

<p>Left panels assume independence across the two dimensions while right panels assume dependence. Top panels for the joint distribution of the random intercepts, middle panels for the joint distribution of random intercept in first dimension and random slope in the second dimension, bottom panels for the joint distribution of the random slopes.</p

Hierarchical cluster tree on malaria-related proteins.

<p>Hierarchical cluster tree on malaria-related proteins.</p

Coefficients of variation of entries of Γ.

<p><i>N</i> = 5000 observations and <i>n</i> = 300 subjects.</p

Modeling of covariates on post-test achievement in language and arithmetic from [79].

<p>Modeling of covariates on post-test achievement in language and arithmetic from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159649#pone.0159649.ref079" target="_blank">79</a>].</p

Variables present in the analyzed dataset.

<p>Variables present in the analyzed dataset.</p

Empirical analysis of the asymptotic distribution of the LR statistic <i>S</i> under <i>H</i>₀, using longitudinal data sets (200 replications) with size <i>N</i> ∈ {50, 100, 150, 200, …, 2000} coming from <i>n</i> ∈ {10, 20, 30, …, 400} subjects.

<p>An asymptotic distribution of <i>χ</i>²(4) is assumed and the type I error (at log10 scale) is ploted against the total number of observations of the data set that has served to compute the LR statistic <i>S</i>. The blue curve is obtained by applying the empirical Bartlett correction to <i>S</i> and the red curve is obtained without correction. The horizontal dashed lines represent the significance levels of 5% and 10%, respectively.</p