Pauliina Ilmonen

Semiparametrically efficient inference based on signed ranks in symmetric independent component models

We consider semiparametric location-scatter models for which the p-variate observation is obtained as X=Lambda Z+mu, where mu is a p-vector, Lambda is a full-rank p*p matrix, and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Lambda. On the basis of n i.i.d. copies of X, we develop, under a symmetry assumption on Z, signed-rank one-sample testing and estimation procedures for Lambda. We exploit the uniform local and asymptotic normality (ULAN) of the model to define signed-rank procedures that are semiparametrically efficient under correctly specified densities. Yet, as usual in rank-based inference, the proposed procedures remain valid (correct asymptotic size under the null, for hypothesis testing, and root-n consistency, for point estimation) under a very broad range of densities. We derive the asymptotic properties of the proposed procedures and investigate their finite-sample behavior through simulations.

A new performance index for ICA: properties, computation and asymptotic analysis

In the independent component (IC) model it is assumed that the components of the observed p-variate random vector x are linear combinations of the components of a latent p-vector z such that the p components of z are independent. Then x = Ωz where Ω is a full-rank p × p mixing matrix. In the independent component analysis (ICA) the aim is to estimate an unmixing matrix Γ such that Γx has independent components. The comparison of the performances of different unmixing matrix estimates Γ in the simulations is then difficult as the estimates are for different population quantities Γ. In this paper we suggest a new natural performance index which finds the shortest distance (using Frobenius norm) between the identity matrix and the set of matrices equivalent to the gain matrix ΓΩ. The index is shown to possess several nice properties, and it is easy and fast to compute. Also, the limiting behavior of the index as the sample size approaches infinity can be easily derived if the limiting behavior of the estimate Γ is known.

Dynamic logistic regression model and population attributable fraction to investigate the association between adherence, missed visits and mortality: a study of HIV-infected adults surviving the first year of ART

BackgroundAdherence is one of the most important determinants of viral suppression and drug resistance in HIV-infected people receiving antiretroviral therapy (ART).MethodsWe examined the association between long-term mortality and poor adherence to ART in DART trial participants in Uganda and Zimbabwe randomly assigned to receive laboratory and clinical monitoring (LCM), or clinically driven monitoring (CDM). Since over 50% of all deaths in the DART trial occurred during the first year on ART, we focussed on participants continuing ART for 12 months to investigate the implications of longer-term adherence to treatment on mortality. Participants’ ART adherence was assessed by pill counts and structured questionnaires at 4-weekly clinic visits. We studied the effect of recent adherence history on the risk of death at the individual level (odds ratios from dynamic logistic regression model), and on mortality at the population level (population attributable fraction based on this model). Analyses were conducted separately for both randomization groups, adjusted for relevant confounding factors. Adherence behaviour was also confounded by a partial factorial randomization comparing structured treatment interruptions (STI) with continuous ART (CT).ResultsIn the CDM arm a significant association was found between poor adherence to ART in the previous 3-9 months with increased mortality risk. In the LCM arm the association was not significant. The odds ratios for mortality in participants with poor adherence against those with optimal adherence was 1.30 (95% CI 0.78,2.10) in the LCM arm and 2.18 (1.47,3.22) in the CDM arm. The estimated proportions of deaths that could have been avoided with optimal adherence (population attributable fraction) in the LCM and CDM groups during the 5 years follow-up period were 16.0% (95% CI 0.7%,31.6%) and 33.1% (20.5%,44.8%), correspondingly.ConclusionsRecurrent poor adherence determined even through simple measures is associated with high mortality both at individual level as well as at the ART programme level. The number of lives saved through effective interventions to improve adherence could be considerable particularly for individuals monitored without using CD4 cell counts. The findings have important implications for clinical practice and for developing interventions to enhance adherence.

On unitary analogs of GCD reciprocal LCM matrices

A divisor d ∈ ℤ+ of n ∈ ℤ+ is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.

On meet hypermatrices and their eigenvalues

Let be a locally finite meet semilattice. Let be a finite subset of , and let be a complex-valued function on . The -dimensional hypermatrix of order , , given by is called the order meet hypermatrix on with respect to . We consider -dimensional meet hypermatrices of order . As an example, we consider GCD hypermatrices. We examine the structure of order meet hypermatrices with respect to , and provide a structure theoretical result that is a generalization of a known result for meet matrices. We also give a region in which all the eigenvalues of an -dimensional order meet hypermatrix with respect to a real-valued lie, and using that we obtain results concerning positive definiteness and E-eigenvalues of meet hypermatrices. Characteristics of meet matrices and the eigenvalues of supersymmetric hypermatrices are under active research, but the eigenvalues of GCD and related hypermatrices have not hitherto been considered in the literature.

An Affine Equivariant Robust Second-Order BSS Method

The interest in robust methods for blind source separation has increased recently. In this paper we shortly review what has been suggested so far for robustifying ICA and second order blind source separation. Furthermore do we suggest a new algorithm, eSAM-SOBI, which is an affine equivariant improvement of already robust SAM-SOBI. In a simulation study we illustrate the benefits of using eSAM-SOBI when compared to SOBI and SAM-SOBI. For uncontaminated time series SOBI and eSAM-SOBI perform equally well. However, SOBI suffers a lot when the data is contaminated by outliers, whereas robust eSAM-SOBI does not. Due to the lack of affine equivariance of SAM-SOBI, eSAM-SOBI performs clearly better than it for both, contaminated and uncontaminated data.

HIV-1 superinfection can occur in the presence of broadly neutralizing antibodies

BACKGROUND Superinfection of individuals already infected with HIV-1 suggests that pre-existing immune responses may not adequately protect against re-infection. We assessed high-risk female sex workers initially infected with HIV-1 clades A, D or A/D recombinants, to determine if HIV-1 broadly neutralizing antibodies were lacking prior to superinfection. METHODS Six superinfected female sex workers previously stratified by HIV-1 high-risk behavior, infecting virus clade and volunteer CD4 counts were evaluated at baseline (n = 5) and at 350 days post-superinfection (n = 6); one superinfected volunteer lacked pre-superinfection plasma. Retrospective plasmas were assessed for neutralization of a multi-clade panel of 12 HIV-1 viruses before superinfection, and then at quarterly intervals thereafter. Similarly stratified singly infected female sex workers were correspondingly assessed at baseline (n = 19) and 350 days after superinfection (n = 24). Neutralization of at least 50% of the 12 viruses (broad neutralization), and geometric means of the neutralization titers (IC50) were compared before and after superinfection; and were correlated with the volunteer HIV-1 superinfection status, CD4 counts, and pseudovirus clade. RESULTS Preexisting broad neutralization occurred in 80% (4/5) of the superinfected subjects with no further broadening by 350 days after superinfection. In one of the five subjects, HIV-1 superinfection occurred when broad neutralization was lacking; with subsequent broadening of neutralizing antibodies occuring within 9 months and plateauing by 30 months after detection of superinfection. Clade B and C pseudoviruses were more sensitive to neutralization (13; [87%]); and (12; [80%]) than the locally circulating clades A (10; [67%]) and D (6; [40%]), respectively (p = 0.025). Low antibody titers correlated with clade D viruses and with >500 CD4 T cell counts, but not with the superinfection status. CONCLUSION These data demonstrate that HIV-1 superinfection can occur both in the presence, and in the absence of broadly neutralizing antibodies.

Generalized eigenvalue problems for meet and join matrices on semilattices

Abstract We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general assumptions. The applied methodology is flexible, and it is shown in the case of GCD and LCM matrices that even sharper bounds can be obtained by applying the known properties of the divisor lattice. These results can also be easily modified for the dual problem of eigenvalues of join matrices with respect to meet matrices, which we briefly consider as well. We investigate the effectiveness of the obtained bounds for select examples involving number-theoretical lattices.

HIV-1 transmission networks in high risk fishing communities on the shores of Lake Victoria in Uganda: A phylogenetic and epidemiological approach

Background Fishing communities around Lake Victoria in sub-Saharan Africa have been characterised as a population at high risk of HIV-infection. Methods Using data from a cohort of HIV-positive individuals aged 13–49 years, enrolled from 5 fishing communities on Lake Victoria between 2009–2011, we sought to identify factors contributing to the epidemic and to understand the underlying structure of HIV transmission networks. Clinical and socio-demographic data were combined with HIV-1 phylogenetic analyses. HIV-1 gag-p24 and env-gp-41 sub-genomic fragments were amplified and sequenced from 283 HIV-1-infected participants. Phylogenetic clusters with ≥2 highly related sequences were defined as transmission clusters. Logistic regression models were used to determine factors associated with clustering. Results Altogether, 24% (n = 67/283) of HIV positive individuals with sequences fell within 34 phylogenetically distinct clusters in at least one gene region (either gag or env). Of these, 83% occurred either within households or within community; 8/34 (24%) occurred within household partnerships, and 20/34 (59%) within community. 7/12 couples (58%) within households clustered together. Individuals in clusters with potential recent transmission (11/34) were more likely to be younger 71% (15/21) versus 46% (21/46) in un-clustered individuals and had recently become resident in the community 67% (14/21) vs 48% (22/46). Four of 11 (36%) potential transmission clusters included incident-incident transmissions. Independently, clustering was less likely in HIV subtype D (adjusted Odds Ratio, aOR = 0.51 [95% CI 0.26–1.00]) than A and more likely in those living with an HIV-infected individual in the household (aOR = 6.30 [95% CI 3.40–11.68]). Conclusions A large proportion of HIV sexual transmissions occur within house-holds and within communities even in this key mobile population. The findings suggest localized HIV transmissions and hence a potential benefit for the test and treat approach even at a community level, coupled with intensified HIV counselling to identify early infections.

Smith meets Smith: Smith normal form of Smith matrix

In 1861, Henry John Stephen Smith [H.J.S. Smith, On systems of linear indeterminate equations and congruences, Philos. Trans. Royal Soc. London. 151 (1861), pp. 293–326] published famous results concerning solving systems of linear equations. The research on Smith normal form and its applications started and continues. In 1876, Smith [H.J.S. Smith, On the value of a certain arithmetical determinant, Proc. London Math. Soc. 7 (1875/76), pp. 208–212] calculated the determinant of the n × n matrix ((i, j)), having the greatest common divisor (GCD) of i and j as its ij entry. Since that, many results concerning the determinants and related topics of GCD matrices, LCM matrices, meet matrices and join matrices have been published in the literature. In this article these two important research branches developed by Smith, in 1861 and in 1876, meet for the first time. The main purpose of this article is to determine the Smith normal form of the Smith matrix ((i, j)). We do this: we determine the Smith normal form of GCD matrices defined on factor closed sets.