Revisiting the Wald Test in Small Case-Control Studies With a Skewed Covariate.

The Wald test is routinely used in case-control studies to test for association between a covariate and disease. However, when the evidence for association is high, the Wald test tends to inflate small P values as a result of the Hauck-Donner effect (HDE). Here, we investigate the HDE in the context of genetic burden, both with and without additional covariates. First, we examine the burden-based P values in the absence of association using whole-exome sequence data from 1000 Genomes Project reference samples (n = 54) and selected preterm infants with neonatal complications (n = 74). Our careful analysis of the burden-based P values shows that the HDE is present and that the cause of the HDE in this setting is likely a natural extension of the well-known cause of the HDE in 2 × 2 contingency tables. Second, in a reanalysis of real data, we find that the permutation test provides increased power over the Wald, Firth, and likelihood ratio tests, which agrees with our intuition since the permutation test is valid for any sample size and since it does not suffer from the HDE. Therefore, we propose a powerful and computationally efficient permutation-based approach for the analysis and reanalysis of small case-control association studies.

FREQMAX provides an alternative approach for determining high-resolution allele frequency thresholds in carrier screening.

As whole-genome data become available for increasing numbers of individuals across diverse populations, the list of genomic variants of unknown significance (VOUS) continues to grow. One powerful tool in VOUS interpretation is determining whether an allele is too common to be considered pathogenic. As genetic and epidemiological parameters vary across disease models, so too does the pathogenic allele frequency threshold for each disease gene. One threshold-setting approach is the maximum credible allele frequency (MCAF) method. However, estimating some of the input values MCAF requires, especially those involving heterogeneity, can present nontrivial statistical challenges. Here, we introduce FREQMAX, our alternative approach for determining allele frequency thresholds in carrier screening. FREQMAX makes efficient use of the data available for well-studied traits and exhibits flexibility for traits where information may be less complete. For cystic fibrosis, more alleles are excluded as benign by FREQMAX than by MCAF. For less-comprehensively characterized traits like ciliary dyskinesia and Smith-Lemli-Opitz syndrome, FREQMAX is able to set the allele frequency threshold without requiring a priori estimates of maximum genetic and allelic contributions. Furthermore, though we describe FREQMAX in the context of carrier screening, its classical population genetics framework also provides context for adaptation to other trait models.

Prediction of short-term neonatal complications in preterm infants using exome-wide genetic variation and gestational age: a pilot study.

BACKGROUND: Preterm birth is the leading cause of mortality and morbidity in young children, with over a million deaths per year worldwide arising from neonatal complications (NCs). NCs are moderately heritable although the genetic causes are largely unknown. Therefore, we investigated the impact of accumulated genetic variation (burden) on NCs in non-Hispanic White (NHW) and non-Hispanic Black (NHB) preterm infants. METHODS: We sequenced 182 exomes from infants with gestational ages from 26 to 31 weeks. These infants were cared for in the same time period and hospital environment. Eighty-one preterm infants did not develop NCs, whereas 101 developed at least one severe complication. We measured the effect of burden at the single-gene and exome-wide levels and derived a polygenic risk score (PRS) from the top 10 genes to predict NCs. RESULTS: Burden across the exome was associated with NCs in NHW (p = 0.05) preterm infants suggesting that multiple genes influence susceptibility. In a post hoc analysis, we find that PRS alone predicts NCs (AUC = 0.67) and that PRS is uncorrelated with GA ([Formula: see text] = 0.05; p = 0.53). When PRS and GA at birth are combined, the AUC is 0.87. CONCLUSIONS: Our results support the hypothesis that genetic burden influences NCs in NHW preterm infants.

Replication, reanalysis, and gene expression: ME2 and genetic generalized epilepsy.

OBJECTIVE: Genetic generalized epilepsy (GGE) consists of epileptic syndromes with overlapping symptoms and is considered to be largely genetic. Previous cosegregation and association studies have pointed to malic enzyme 2 (ME2) as a candidate susceptibility gene for adolescent-onset GGE. In this article, we present new evidence supporting ME2's involvement in GGE. METHODS: To definitively test ME2's influence on GGE, we used 3 different approaches. First, we compared a newly recruited GGE cohort with an ethnically matched reference sample from 1000 Genomes Project, using an efficient test of association (POPFAM+). Second, we used POPFAM+ to reanalyze a previously collected data set, wherein the original controls were replaced with ethnically matched reference samples to minimize the confounding effect of population stratification. Third, in a post hoc analysis of expression data from healthy human prefrontal cortex, we identified single nucleotide polymorphisms (SNPs) influencing ME2 messenger RNA (mRNA) expression; and then we tested those same SNPs for association with GGE in a large case-control cohort. RESULTS: First, in the analysis of our newly recruited GGE Cohort, we found a strong association between an ME2 SNP and GGE (P = 0.0006 at rs608781). Second, in the reanalysis of previously collected data, we confirmed the Greenberg et al (2005) finding of a GGE-associated ME2 risk haplotype. Third, in the post hoc ME2 expression analysis, we found evidence for a possible link between GGE and ME2 gene expression in human brain. SIGNIFICANCE: Overall, our research, and the research of others, provides compelling evidence that ME2 influences susceptibility to adolescent-onset GGE.

DNA methylation of the BRD2 promoter is associated with juvenile myoclonic epilepsy in Caucasians.

OBJECTIVE: Juvenile myoclonic epilepsy (JME) is a common adolescent-onset genetic generalized epilepsy (GGE) syndrome. Multiple linkage and association studies have found that BRD2 influences the expression of JME. The BRD2-JME connection is further corroborated by our murine model; Brd2 haploinsufficiency produces characteristics that typify the clinical hallmarks of JME. Neither we, nor several large-scale studies of JME, found JME-related BRD2 coding mutations. Therefore, we investigated noncoding BRD2 regions, seeking the origin of BRD2's JME influence. BRD2's promoter harbors a JME-associated single nucleotide polymorphism (rs3918149) and a CpG (C-phosphate-G dinucleotides) island (CpG76), making it a potential "hotspot" for JME-associated epigenetic variants. Methylating promoter CpG sites causes gene silencing, often resulting in reduced gene expression. We tested for differences in DNA methylation at CpG76 in 3 different subgroups: (1) JME patients versus their unaffected family members, (2) JME versus patients with other forms of GGE, and (3) Caucasian versus non-Caucasian JME patients. METHODS: We used DNA pyrosequencing to analyze the methylation status of 10 BRD2 promoter CpG sites in lymphoblastoid cells from JME patients of Caucasian and non-Caucasian origin, unaffected family members, and also non-JME GGE patients. We also measured global methylation levels and DNA methyl transferase 1 (DNMT1) transcript expression in JME families by standard methods. RESULTS: CpG76 is highly methylated in JME patients compared to unaffected family members. In families with non-JME GGE, we found no relationship between promoter methylation and epilepsy. In non-Caucasian JME families, promoter methylation was mostly not associated with epilepsy. This makes the BRD2 promoter a JME-specific, ethnicity-specific, differentially methylated region. Global methylation was constant across groups. SIGNIFICANCE: BRD2 promoter methylation in JME, and the lack of methylation in unaffected relatives, in non-JME GGE patients, and in non-Caucasian JME, demonstrate that methylation specificity is a possible seizure susceptibility motif in JME risk and suggests JME therapeutics targeting BRD2.

Comparison of the Lund and Browder table to computed tomography scan three-dimensional surface area measurement for a pediatric cohort.

BACKGROUND: Treating burns effectively requires accurately assessing the percentage of the total body surface area (%TBSA) affected by burns. Current methods for estimating %TBSA, such as Lund and Browder (L&B) tables, rely on historic body statistics. An increasingly obese population has been blamed for increasing errors in %TBSA estimates. However, this assumption has not been experimentally validated. We hypothesized that errors in %TBSA estimates using L&B were due to differences in the physical proportions of today's children compared with children in the early 1940s when the chart was developed and that these differences would appear as body mass index (BMI)-associated systematic errors in the L&B values versus actual body surface areas. MATERIALS AND METHODS: We measured the TBSA of human pediatric cadavers using computed tomography scans. Subjects ranged from 9 mo to 15 y in age. We chose outliers of the BMI distribution (from the 31st percentile at the low through the 99th percentile at the high). We examined surface area proportions corresponding to L&B regions. RESULTS: Measured regional proportions based on computed tomography scans were in reasonable agreement with L&B, even with subjects in the tails of the BMI range. The largest deviation was 3.4%, significantly less than the error seen in real-world %TBSA estimates. CONCLUSIONS: While today's population is more obese than those studied by L&B, their body region proportions scale surprisingly well. The primary error in %TBSA estimation is not due to changing physical proportions of today's children and may instead lie in the application of the L&B table.

Pathogenic EFHC1 mutations are tolerated in healthy individuals dependent on reported ancestry.

OBJECTIVE: Screening for specific coding mutations in the EFHC1 gene has been proposed as a means of assessing susceptibility to juvenile myoclonic epilepsy (JME). To clarify the role of these mutations, especially those reported to be highly penetrant, we sought to measure the frequency of exonic EFHC1 mutations across multiple population samples. METHODS: To find and test variants of large effect, we sequenced all EFHC1 exons in 23 JME and 23 non-JME idiopathic generalized epilepsy (IGE) Hispanic patients, and 60 matched controls. We also genotyped specific EFHC1 variants in IGE cases and controls from multiple ethnic backgrounds, including 17 African American IGE patients, with 24 matched controls, and 92 Caucasian JME patients with 103 matched controls. These variants are reported to be pathogenic, but are also found among unphenotyped individuals in public databases. All subjects were from the New York City metro area and all controls were required to have no family history of seizures. RESULTS: We found the reportedly pathogenic EFHC1 P77T-R221H (rs149055334-rs79761183) JME haplotype in one Hispanic control and in two African American controls. Public databases also show that the EFHC1 P77T-R221H JME haplotype is present in unphenotyped West African ancestry populations, and we show that it can be found at appreciable frequency in healthy individuals with no family history of epilepsy. We also found a novel splice-site mutation in a single Hispanic JME patient, the effect of which is unknown. SIGNIFICANCE: Our findings raise questions about the effect of reportedly pathogenic EFHC1 mutations on JME. One intriguing possibility is that some EFHC1 mutations may be pathogenic only when introduced into specific genetic backgrounds. By focusing on data from multiple populations, including the understudied Hispanic and Black/African American populations, our study highlights that for complex traits like JME, the body of evidence necessary to infer causality is high.

PedMIDAS-based scoring underestimates migraine disability on non-school days.

OBJECTIVE: The aim of this study is to compare daily Pediatric Migraine Disability Assessment (PedMIDAS)-based scores for headaches occurring on school days vs non-school days and during the school year vs the summer holiday. BACKGROUND: The PedMIDAS is the only instrument validated to assess migraine disability among school-aged children. However, the PedMIDAS may underestimate disability during prolonged school holidays. METHODS: In a prospective cohort study, migraine patients aged 10-18 years completed a 90-day Internet-based headache diary. For each headache day, they answered PedMIDAS-based questions and rated their headache intensity (scale 1-10). PedMIDAS-based scores, headache intensity ratings, and relative headache frequencies were compared for school days vs non-school days and for the school year vs the summer holiday. RESULTS: Fifty-two patients completed 4680 diary entries comprising 984 headache days. The headache frequencies and intensity ratings did not differ between time periods. However, the mean headache disability scores (as measured from PedMIDAS-based questions) were significantly different for school days (0.85) compared to non-school days (0.45), P < .001, and for the school year (0.73) compared to the summer holiday (0.46), P < .016. CONCLUSION: Given similar headache intensities and frequencies, daily PedMIDAS-based scores significantly underestimate headache disability on non-school days. Accordingly, PedMIDAS scoring during the school year may not be comparable to assessments done during the summer holiday. These potential differences must be considered when using the instrument as an outcome measure for clinical trials.

Obtaining accurate p values from a dense SNP linkage scan.

A major concern of resequencing studies is that the pathogenicity of most mutations is difficult to predict. To address this concern, linkage (i.e. co-segregation) analysis is often used to exclude neutral mutations and to better predict pathogenicity among the candidate mutations that remain. However, when linkage disequilibrium (LD) is present in the population but ignored in the analysis, unlinked regions with high LD can inflate the type 1 error and thousands of neutral mutations may be mistakenly included in a follow-up resequencing study, which could dramatically reduce the power to identify causal variants. To illustrate the need for concern, we simulated data on a sparsely spaced panel of single nucleotide polymorphisms (average spacing 1.27 cM) using an LD pattern estimated from real data. In our simulations, we find that the type 1 error of the maximum LOD can be as high as 14%. Therefore, to control the type 1 error of linkage tests we created Haplodrop - a fast and flexible simulation program that generates the haplotypes of founders with LD and then 'drops' these haplotypes with recombination to all non-founders in the pedigree. Haplodrop can be used to control the type 1 error of any linkage test, agrees well with existing software, accommodates arbitrary pedigree structures, and scales easily to the whole genome. Moreover, by correctly excluding mutations that lie in unlinked regions with high LD, Haplodrop should aid significantly in reducing the multiple testing burden of follow-up resequencing studies.

BioNetGMMFit: estimating parameters of a BioNetGen model from time-stamped snapshots of single cells.

Mechanistic models are commonly employed to describe signaling and gene regulatory kinetics in single cells and cell populations. Recent advances in single-cell technologies have produced multidimensional datasets where snapshots of copy numbers (or abundances) of a large number of proteins and mRNA are measured across time in single cells. The availability of such datasets presents an attractive scenario where mechanistic models are validated against experiments, and estimated model parameters enable quantitative predictions of signaling or gene regulatory kinetics. To empower the systems biology community to easily estimate parameters accurately from multidimensional single-cell data, we have merged a widely used rule-based modeling software package BioNetGen, which provides a user-friendly way to code for mechanistic models describing biochemical reactions, and the recently introduced CyGMM, that uses cell-to-cell differences to improve parameter estimation for such networks, into a single software package: BioNetGMMFit. BioNetGMMFit provides parameter estimates of the model, supplied by the user in the BioNetGen markup language (BNGL), which yield the best fit for the observed single-cell, time-stamped data of cellular components. Furthermore, for more precise estimates, our software generates confidence intervals around each model parameter. BioNetGMMFit is capable of fitting datasets of increasing cell population sizes for any mechanistic model specified in the BioNetGen markup language. By streamlining the process of developing mechanistic models for large single-cell datasets, BioNetGMMFit provides an easily-accessible modeling framework designed for scale and the broader biochemical signaling community.

How should we be searching for genes for common epilepsy? A critique and a prescription.

Despite enormous data collection and analysis efforts, the genetic influences on common epilepsies remain mostly unknown. We propose that reasons for the lack of progress can be traced to three factors: (1) A reluctance to consider fine-grained phenotype definitions based on extensive and carefully collected clinical data; (2) the pursuit of genetic analysis methods that are popular but poorly conceived and are inadequate to the task of resolving the problems inherent in common disease studies; (3) preconceived ideas about the genetic mechanisms that cause epilepsy (which we have discussed elsewhere). We propose a paradigm for finding epilepsy-related loci and alleles that has proven successful in other common diseases.

Multiple subsampling of dense SNP data localizes disease genes with increased precision.

BACKGROUND/AIMS: Current linkage studies detect and localize trait loci using genotypes sampled at hundreds of thousands of single nucleotide polymorphisms (SNPs). Such data should provide precise estimates of trait location once linkage has been established. However, correlations between nearby SNPs can distort the information about trait location. Traditionally, when faced with this dilemma, three approaches have been used: (1) ignore the correlation; (2) approximate the correlation; or, (3) analyze a single, approximately uncorrelated subset of the original dense data. METHODS: Here, we examine and test a simple and efficient estimator of trait location that averages location estimates across random subsamples of the original dense data. Based on pairwise estimates of correlation, we ensure that the SNPs within each subsample are approximately uncorrelated. In addition, we use the nonparametric bootstrap procedure to compute narrow, high-resolution candidate gene regions (i.e. confidence intervals for the true trait location). RESULTS: Using simulated data, we show that the three existing approaches to dense SNP linkage analysis (described above) can yield biased and/or inefficient estimation depending on the underlying correlation structure. With respect to mean squared error, our estimator outperforms the third approach, and is as good as, but usually better than the first and second approaches. Relative to the third approach, our estimator led to a 47.5% reduction in the candidate gene region length based on the analysis of 15 hypertension families genotyped at approximately 500,000 SNPs. CONCLUSION: The method we developed will be an important tool for constructing high-resolution candidate gene regions that could ultimately aid in targeting regions for sequencing projects.

Bayesian EM algorithm for scoring polymorphic deletions from SNP data and application to a common CNV on 8q24.

Copy number variations (CNVs) in the human genome provide exciting candidates for functional polymorphisms. Hence, we now assess association between CNV carrier status and diseases status by evaluating the signal intensity of SNP genotyping assays. Here, we present a novel statistical method designed to perform such inference and apply this method to a known CNV in a bipolar disorder linkage region. Using Bayesian computations we calculate the posterior probability for carrier status of a CNV in each individual of a sample by jointly analyzing genotype information and hybridization intensity. We model the signal intensity as a mixture of normal distributions, allowing for locus-specific and allele-specific distributions. Using an expectation maximization algorithm we estimate the parameters of these distributions and use these estimates for inferring carrier status of each individual and for the boundaries of the CNV. We applied the method to a sample of 3,512 individuals to a previously described common deletion on 8q24, a region consistently showing linkage to bipolar disorder, and unambiguously inferred 172 heterozygous and 1 homozygous deletion carrier. We observed no significant association between bipolar disorder and carrier status. We carefully assessed the validity of the inferred carrier status and observed no indication of errors. Furthermore, the algorithm precisely identifies the boundaries of the CNV. Finally, we assessed the power of this algorithm to detect shorter CNVs by sub-sampling from the SNPs covered by this deletion, demonstrating that our EM algorithm produces precise estimates of carrier status.

A new linear regression-like residual for survival analysis, with application to genome wide association studies of time-to-event data.

In linear regression, a residual measures how far a subject's observation is from expectation; in survival analysis, a subject's Martingale or deviance residual is sometimes interpreted similarly. Here we consider ways in which a linear regression-like interpretation is not appropriate for Martingale and deviance residuals, and we develop a novel time-to-event residual which does have a linear regression-like interpretation. We illustrate the utility of this new residual via simulation of a time-to-event genome-wide association study, motivated by a real study seeking genetic modifiers of Duchenne Muscular Dystrophy. By virtue of its linear regression-like characteristics, our new residual may prove useful in other contexts as well.

Brd2 haploinsufficiency extends lifespan and healthspan in C57B6/J mice.

Aging in mammals is the gradual decline of an organism's physical, mental, and physiological capacity. Aging leads to increased risk for disease and eventually to death. Here, we show that Brd2 haploinsufficiency (Brd2+/-) extends lifespan and increases healthspan in C57B6/J mice. In Brd2+/- mice, longevity is increased by 23% (p<0.0001), and, relative to wildtype animals (Brd2+/+), cancer incidence is reduced by 43% (p<0.001). In addition, relative to age-matched wildtype mice, Brd2 heterozygotes show healthier aging including: improved grooming, extended period of fertility, and lack of age-related decline in kidney function and morphology. Our data support a role for haploinsufficiency of Brd2 in promoting healthy aging. We hypothesize that Brd2 affects aging by protecting against the accumulation of molecular and cellular damage. Given the recent advances in the development of BET inhibitors, our research provides impetus to test drugs that target BRD2 as a way to understand and treat/prevent age-related diseases.

Lung Allocation Score Thresholds Prioritize Survival After Lung Transplantation.

BACKGROUND: The lung allocation score (LAS) prioritizes lung transplant (LTx) candidates with poor transplant-free survival and expected survival benefit from LTx. Although patients with the highest LAS have the shortest waiting time, mortality benefit is unclear in this group, raising criticism that the LAS inappropriately prioritizes critically ill candidates. We aim to identify a threshold above which increasing LAS values do not predict increasing survival benefit. METHODS: The United Network for Organ Sharing Registry was queried for first-time adult LTx candidates with LAS ≥ 30 between May 2005 and December 2016. Survival was tracked from the time of listing through the posttransplant period and compared with survival while remaining on the waitlist, using proportional hazards regression. The survival benefit of LTx was modeled as a piecewise-constant time-dependent covariate, moderated by candidate LAS. RESULTS: Of the overall cohort (N = 21,157), LTx was particularly protective for 365 patients with an initial LAS of 70 to 79 (hazard ratio of death after undergoing LTx relative to remaining on the waitlist, 0.2; 95% CI, 0.1-0.3). However, the survival benefit of LTx did not meaningfully increase for 1,042 patients listed with even higher LAS. Among patients with cystic fibrosis, the survival benefit of LTx was constant above an LAS of approximately 50. CONCLUSIONS: Consistent survival benefit of LTx was observed among patients with an initial LAS of 70 and greater. This result supports equalizing priority for donor lung allocation for patients with LAS ≥ 70. A lower LAS threshold for maximum priority is indicated in patients with cystic fibrosis.

Mathematical modelling identifies the role of adaptive immunity as a key controller of respiratory syncytial virus in cotton rats.

Respiratory syncytial virus (RSV) is a common virus that can have varying effects ranging from mild cold-like symptoms to mortality depending on the age and immune status of the individual. We combined mathematical modelling using ordinary differential equations (ODEs) with measurement of RSV infection kinetics in primary well-differentiated human bronchial epithelial cultures in vitro and in immunocompetent and immunosuppressed cotton rats to glean mechanistic details that underlie RSV infection kinetics in the lung. Quantitative analysis of viral titre kinetics in our mathematical model showed that the elimination of infected cells by the adaptive immune response generates unique RSV titre kinetic features including a faster timescale of viral titre clearance than viral production, and a monotonic decrease in the peak RSV titre with decreasing inoculum dose. Parameter estimation in the ODE model using a nonlinear mixed effects approach revealed a very low rate (average single-cell lifetime > 10 days) of cell lysis by RSV before the adaptive immune response is initiated. Our model predicted negligible changes in the RSV titre kinetics at early times post-infection (less than 5 dpi) but a slower decay in RSV titre in immunosuppressed cotton rats compared to that in non-suppressed cotton rats at later times (greater than 5 dpi) in silico. These predictions were in excellent agreement with the experimental results. Our combined approach quantified the importance of the adaptive immune response in suppressing RSV infection in cotton rats, which could be useful in testing RSV vaccine candidates.

Logistic Bayesian LASSO for detecting association combining family and case-control data.

Because of the limited information from the GAW20 samples when only case-control or trio data are considered, we propose eLBL, an extension of the Logistic Bayesian LASSO (least absolute shrinkage and selection operator) methodology so that both types of data can be analyzed jointly in the hope of obtaining an increased statistical power, especially for detecting association between rare haplotypes and complex diseases. The methodology is further extended to account for familial correlation among the case-control individuals and the trios. A 2-step analysis strategy was taken to first perform a genome-wise single single-nucleotide polymorphism (SNP) search using the Monte Carlo pedigree disequilibrium test (MCPDT) to determine interesting regions for the Adult Treatment Panel (ATP) binary trait. Then eLBL was applied to haplotype blocks covering the flagged SNPs in Step 1. Several significantly associated haplotypes were identified; most are in blocks contained in protein coding genes that appear to be relevant for metabolic syndrome. The results are further substantiated with a Type I error study and by an additional analysis using the triglyceride measurements directly as a quantitative trait.

Predictive Utility of Lung Allocation Score for Retransplantation Outcomes.

BACKGROUND: Treatment of primary graft failure after lung transplantation (LTx) may include retransplantation (rLTx). The number of rLTx cases has doubled since implementation of the Lung Allocation Score in 2005. The Lung Allocation Score was intended to predict LTx outcomes, but its predictive utility has not been assessed in rLTx. We investigated whether 1-year outcomes of LTx and rLTX were equally well predicted by the Lung Allocation Score. METHODS: Recipients of LTx and rLTx aged 18 years or more were identified in 2005 to 2015 United Network for Organ Sharing data. The Lung Allocation Score was entered in multivariable logistic regression models of 1-year retransplant-free survival. Areas under the receiver-operating characteristics curve summarized model predictive value. We examined whether the Lung Allocation Score and its components were differentially associated with outcomes of LTx and rLTx. RESULTS: There were 16,837 LTx and 765 rLTx cases meeting inclusion criteria. Crude 1-year retransplant-free survival rates were 86% after LTx compared with 74% after rLTx. On univariate analysis, both LTx and rLTx cohorts showed poor predictive utility of the Lung Allocation Score (area under the curve 0.55 and 0.57, respectively; difference by transplant type, p = 0.307). Neither the Lung Allocation Score nor its components was differentially associated with LTx compared with rLTx outcomes. CONCLUSIONS: The Lung Allocation Score achieved comparable, but poor, predictive utility for 1-year outcomes of primary LTx and rLTx. We found no evidence that Lung Allocation Score components should be weighted differently for rLTx candidates.