In the present paper we introduce SDR, an algorithm specifically conceived to detect non-linear gene-gene interactions in presence of right-censored data. The need for such a bioinformatics tool comes from the observation that several studies in the medical field deal with the loss of data during the period of study, and that methods that do not take into account censored data give upwardly biased estimates of failure and/or suffer from information loss due to reduced sample size. Cox regression , the most popular statistical technique used to analyse time-to-event multivariate model, is not adequate to detect non-linearities either. Indeed, to properly model interaction in Cox regression, the user should have a priori knowledge of the variable relationships and may need to enter nonlinear transforms of the predictors, but this is often a trial and error approach. Also, the number of polynomial terms needed to model complex interactions is inflated as the number of predictors grows, increasing standard errors and, thus, type I error [6, 7].
Using simulated epistatic lifetime datasets, we demonstrated that the SDR algorithm retains a fully satisfactory power to sort out a set of causative genes with mild-to-moderate epistatic effect size from a pool of candidate genes. These results have been accomplished by the intrinsic properties of the SDR methodology. Firstly, SDR is non-parametric, in the sense that it is not necessary to make a priori assumptions about the underlying interaction model. Also, SDR requires no assumptions concerning the nature or shape of the underlying survival distribution. Secondly, SDR performs well even in datasets where the right-censorship rate is high (up to 70% of cases in our simulation). Notably, when we run MDR ignoring censorship on the same simulated datasets we observed a dramatic reduction in the power to detect the causative pair of genes, that ranged from 5% to more than 90% (results not shown). Beside power, an additional advantage of SDR is that, combining cross-validation with permutation testing, the chance of false-positive findings is minimized . Yet, to generate the simulated datasets we required the hazards among multilocus cells to be proportional along the lifetime distribution. Hence, further simulations are needed to ascertain whether SDR is suitable for situations where this assumption does not hold, as for instance in case of additive hazard models. Similarly, further simulations are needed to establish SDR performance in larger datasets, in presence of genetic heterogeneity, linkage disequilibrium, or different ranges of MAF.
SDR is, de facto, an extension of the MDR algorithm optimized to analyse lifetime distributions, hence it suffers from similar limitations  and it shares some peculiarities with the latter. Namely, the power of SDR is influenced by the epistatic effect size, which is strictly related to the (cumulative) heritability of the model . Moreover, as with MDR, the biological significance of SDR models may be difficult to interpret due to the non-linear distribution of high-risk and low-risk cells across the multidimensional space . Finally, SDR cannot make predictions when multilocus cells contain no data and GM estimates may be upwardly or downwardly inflated when multilocus cells contain few data.
Having demonstrated the capability of SDR to detect gene-gene interactions in lifetime datasets, we applied the algorithm to a population of patients with active RA to identify epistatic interactions that may affect time-related responses to anti-TNF biological agents. We did show that among a set of 39 candidate-gene loci, none of which had a detectable marginal effect on the outcome variable, the non-linear interaction between the rs1801274 (FcγRIIa) and the rs10954213 (IRF5) SNPs significantly predicted the responses to anti-TNF therapy.
Whilst it is difficult to dissect the biological meaning of statistical epistatic models , it should be noted that several lines of evidence support a role for Fcγ receptors and IRF5 in rheumatoid arthritis and TNF driven processes. Associations between IRF5 polymorphisms and RA have been described in different populations  and a recent genome-wide association study (GWAS) showed that the rs4728142 variant in the IRF5 gene, in tight linkage disequilibrium with rs10954213, is strongly associated with RA susceptibility . Of interest, functional experiments demonstrated that the rs10954213 SNP significantly alters IRF5 mRNA expression . The association between IRF5 gene and RA may be linked, at least in part, to the ability of IRF5 to regulate the secretion of pro-inflammatory cytokines. Indeed, Takaoka et al  using mouse models deficient in the IRF5 gene, showed that IRF5 is generally involved downstream of the toll-like receptor (TLR)-MyD88 signalling pathway for gene induction of TNFα and other cytokines relevant to the pathogenesis of RA. Of interest, the use of anti-TNF agents was shown to decrease TLRs expression on different cellular types [44, 45]. Similarly to IRF5, the FcγRIIa is involved in TNFα production in the rheumatoid synovia, as observed by Clavel and co-workers . The interaction between the genetic variants of IRF5 and Fcγ receptors could thus influence TNFα production and/or availability, affecting the clinical response to anti-TNF agents. Additionally, as postulated by Cañete at al , polymorphisms of the FcγRIIa may alter the clearance rate of anti-TNF antibodies modulating plasma concentrations and consequently their biological effect in subjects with active RA. Theoretically, this effect should not restricted only to anti-TNF antibodies, as also anti-TNFα receptors (e.g. etanercept) contain a Fc portion of IgG1 capable of binding to FCγ receptors to produce biological effects, such as antibody-dependent cell-mediated cytotoxicity .