Detecting the undetected: estimating the total number of loci underlying a quantitative trait

Recent studies have begun to reveal the genes underlying quantitative trait differences between closely related populations. Not all quantitative trait loci (QTL) are, however, equally likely to be detected. QTL studies involve a limited number of crosses, individuals, and genetic markers and, as a result, often have little power to detect genetic factors of small to moderate effects. In this article, we develop an estimator for the total number of fixed genetic differences between two parental lines. Like the Castle-Wright estimator, which is based on the observed segregation variance in classical crossbreeding experiments, our QTL-based estimator requires that a distribution be specified for the expected effect sizes of the underlying loci. We use this expected distribution and the observed mean and minimum effect size of the detected QTL in a likelihood model to estimate the total number of loci underlying the trait difference. We then test the QTL-based estimator and the Castle-Wright estimator in Monte Carlo simulations. When the assumptions of the simulations match those of the model, both estimators perform well on average. The 95% confidence limits of the Castle-Wright estimator, however, often excluded the true number of underlying loci, while the confidence limits for the QTL-based estimator typically included the true value approximately 95% of the time. Furthermore, we found that the QTL-based estimator was less sensitive to dominance and to allelic effects of opposite sign than the Castle-Wright estimator. We therefore suggest that the QTL-based estimator be used to assess how many loci may have been missed in QTL studies.     

Time-related mapping of quantitative trait loci underlying tiller number in rice.

Using time-related phenotypic data, methods of composite interval mapping and multiple-trait composite interval mapping based on least squares were applied to map quantitative trait loci (QTL) underlying the development of tiller number in rice. A recombinant inbred population and a corresponding saturated molecular marker linkage map were constructed for the study. Tiller number was recorded every 4 or 5 days for a total of seven times starting at 20 days after sowing. Five QTL were detected on chromosomes 1, 3, and 5. These QTL explained more than half of the genetic variance at the final observation. All the QTL displayed an S-shaped expression curve. Three QTL reached their highest expression rates during active tillering stage, while the other two QTL achieved this either before or after the active tillering stage.     

Quasi-likelihood estimation for relative risk regression models

For a prospective randomized clinical trial with two groups, the relative risk can be used as a measure of treatment effect and is directly interpretable as the ratio of success probabilities in the new treatment group versus the placebo group. For a prospective study with many covariates and a binary outcome (success or failure), relative risk regression may be of interest. If we model the log of the success probability as a linear function of covariates, the regression coefficients are log-relative risks. However, using such a log-linear model with a Bernoulli likelihood can lead to convergence problems in the Newton-Raphson algorithm. This is likely to occur when the success probabilities are close to one. A constrained likelihood method proposed by Wacholder (1986, American Journal of Epidemiology 123, 174-184), also has convergence problems. We propose a quasi-likelihood method of moments technique in which we naively assume the Bernoulli outcome is Poisson, with the mean (success probability) following a log-linear model. We use the Poisson maximum likelihood equations to estimate the regression coefficients without constraints. Using method of moment ideas, one can show that the estimates using the Poisson likelihood will be consistent and asymptotically normal. We apply these methods to a double-blinded randomized trial in primary biliary cirrhosis of the liver (Markus et al., 1989, New England Journal of Medicine 320, 1709-1713).     

Thermolabile methylenetetrahydrofolate reductase: an inherited risk factor for coronary artery disease.

Severe methylenetetrahydrofolate reductase (MTHFR) deficiency with less than 2% of normal enzyme activity is characterized by neurological abnormalities, atherosclerotic changes, and thromboembolism. We have discovered a "new" variant of MTHFR deficiency which is characterized by the absence of neurological abnormalities, an enzyme activity of about 50% of the normal value, and distinctive thermolability under specific conditions of heat inactivation. In this study, lymphocyte MTHFR specific activities in the thermolabile variant and control groups were 5.58 +/- 0.91 and 10.33 +/- 2.89 nmol formaldehyde formed/mg protein/h, respectively. The difference was significant (P less than .01). However, there was overlap among the individual values from the two groups. On the other hand, residual MTHFR activity after heat inactivation was 11.2 +/- 1.43% in the thermolabile variant and 36.3 +/- 5.18% in the controls. There was no overlap. Enzyme studies in 10 subjects with thermolabile MTHFR and their family members support the hypothesis that thermolabile MTHFR is inherited as an autosomal recessive trait. To elucidate the association of thermolabile MTHFR with the development of coronary artery disease, we determined the thermostability of lymphocyte MTHFR in 212 patients with proven coronary artery disease and in 202 controls without clinical evidence of atherosclerotic vascular disease. Thermolabile MTHFR was found in 36 (17.0%) cardiac patients and 10 (5.0%) controls. The difference in incidence between the two groups was statistically significant (P less than .01). The average age at onset of clinical coronary artery disease in 36 patients with thermolabile MTHFR was 57.3 +/- 7.6 years (35-72 years). The mean total plasma homocysteine concentration in patients with thermolabile MTHFR was 13.19 +/- 5.32 nmol/ml and was significantly different from the normal mean of 8.50 +/- 2.80 nmol/ml (P less than .05). There was no association between thermolabile MTHFR and other major risk factors. We conclude that thermolabile MTHFR is a variant(s) of MTHFR deficiency which is inherited as an autosomal recessive trait. In addition, it is positively associated with the development of coronary artery disease. Determination of in vitro thermostability of lymphocyte MTHFR is a reliable method for identifying subjects with this abnormality.     

The number of trait loci in late-onset Alzheimer disease

Although it is clear that apoE plays an important role in the genetics of late-onset Alzheimer disease (AD), evidence exists that additional genes may play a role in AD, and estimates of the total contribution of apoE to the variance in onset of AD vary widely. Unfortunately, little information is available on the number and contribution of additional genes. We estimated the number of additional quantitative-trait loci and their contribution to the variance in age at onset of AD, as well as the contribution of apoE and sex, in an oligogenic segregation analysis of 75 families (742 individuals) ascertained for members with late-onset AD. We found evidence that four additional loci make a contribution to the variance in age at onset of late-onset AD that is similar to or greater in magnitude than that made by apoE, with one locus making a contribution several times greater than that of apoE. Additionally, we confirmed previous findings of a dose effect for the apoE varepsilon4 allele, a protective effect for the varepsilon2 allele, evidence for allelic interactions at the apoE locus, and a small protective effect for males. Furthermore, although we estimate that the apoE genotype can make a difference of 相似文献   

Pulsed-field gel electrophoresis-fingerprinting, genome size estimation and rrn loci number of Rhizobium galegae

I. HUBER AND S. SELENSKA-POBELL. 1994. The genomes of several Rhizobium galegae (of.) strains, which effectively nodulate Galega officinalis host, were analysed by pulsed-field gel electrophoresis (PFGE). Individual PFGE-fingerprints were obtained for every particular strain when the rarely cutting restriction endonucleases Spe I and Asn I were applied. In hybridization experiments, where a DNA fragment carrying the rrnB ribosomal RNA operon of Escherichia coli was used as a probe, the number of the resulting strain-specific Spe I and Asn I bands was reduced to three for all of the strains studied. This suggests that in Rh. galegae (of.) there are at least three rrn loci. On the basis of the lengths of the Spe I fragments, separated by PFGE, the genome size of five Rh. galegae (of.) strains was estimated to be 5852 ± 198 kbp.     

Interval estimation of disease loci: development and applications of new linkage methods

Three variants of the confidence set inference (CSI) procedure were proposed and applied to both the simulated and the Collaborative Study on the Genetics of Alcoholism (COGA) data. For each of the two applications, we first performed a preliminary genome scan study based on the microsatellite markers using the GENEHUNTER+ software to identify regions that potentially harbor disease loci. For each such region, we estimated the sibling identity-by-descent sharing probability distribution at the putative disease locus. Based on these estimated probabilities, the CSI procedures were employed to further localize the disease loci using the single-nucleotide polymorphism markers, leading to confidence intervals/regions for their locations. For our analysis with the simulated data, we had knowledge of the simulating models at the time we performed the analysis.     

A genetic risk score combining ten psoriasis risk loci improves disease prediction

Psoriasis is a chronic, immune-mediated skin disease affecting 2–3% of Caucasians. Recent genetic association studies have identified multiple psoriasis risk loci; however, most of these loci contribute only modestly to disease risk. In this study, we investigated whether a genetic risk score (GRS) combining multiple loci could improve psoriasis prediction. Two approaches were used: a simple risk alleles count (cGRS) and a weighted (wGRS) approach. Ten psoriasis risk SNPs were genotyped in 2815 case-control samples and 858 family samples. We found that the total number of risk alleles in the cases was significantly higher than in controls, mean 13.16 (SD 1.7) versus 12.09 (SD 1.8), p = 4.577×10⁻⁴⁰. The wGRS captured considerably more risk than any SNP considered alone, with a psoriasis OR for high-low wGRS quartiles of 10.55 (95% CI 7.63–14.57), p = 2.010×10⁻⁶⁵. To compare the discriminatory ability of the GRS models, receiver operating characteristic curves were used to calculate the area under the curve (AUC). The AUC for wGRS was significantly greater than for cGRS (72.0% versus 66.5%, p = 2.13×10⁻⁸). Additionally, the AUC for HLA-C alone (rs10484554) was equivalent to the AUC for all nine other risk loci combined (66.2% versus 63.8%, p = 0.18), highlighting the dominance of HLA-C as a risk locus. Logistic regression revealed that the wGRS was significantly associated with two subphenotypes of psoriasis, age of onset (p = 4.91×10⁻⁶) and family history (p = 0.020). Using a liability threshold model, we estimated that the 10 risk loci account for only11.6% of the genetic variance in psoriasis. In summary, we found that a GRS combining 10 psoriasis risk loci captured significantly more risk than any individual SNP and was associated with early onset of disease and a positive family history. Notably, only a small fraction of psoriasis heritability is captured by the common risk variants identified to date.     

Segregation of marker loci in families with an inherited paracentric insertion of chromosome 9.

Cytogenetic, enzyme dosage, serological, and electrophoretic analyses of blood samples from members of three Newfoundland kindreds in which one specific paracentric insertion chromosome inv ins(9)(q22.1q34.3q34.1) is segregating provide data indicating that ABO lies in 9q22.1-q34.3, AK1 in 9q34.1-q34.3, and ORM in 9q34.3-qter.     

Correcting for variable age of onset in the estimation of familial relative risk when there is a secular trend in incidence of disease

We discuss the effects that a secular trend in incidence would have on estimation of familial relative risk (ratio of observed to expected cumulative incidence among relatives of index cases). For example, when age-specific incidence rates of a condition have increased during the lifetimes of relatives among whom relative risk is to be estimated, familial relative risk will be biased downward if cross-sectional, age-specific incidence data are used to estimate expected cumulative incidence among relatives. The stronger the trend and the older the ages of unaffected relatives, the greater the bias will be. Incorporating different age-specific incidence curves for different birth cohorts into the analysis is an approach we suggest for correcting the bias.     

Improving the estimation of celiac disease sibling risk by non-HLA genes

Celiac Disease (CD) is a polygenic trait, and HLA genes explain less than half of the genetic variation. Through large GWAs more than 40 associated non-HLA genes were identified, but they give a small contribution to the heritability of the disease. The aim of this study is to improve the estimate of the CD risk in siblings, by adding to HLA a small set of non-HLA genes. One-hundred fifty-seven Italian families with a confirmed CD case and at least one other sib and both parents were recruited. Among 249 sibs, 29 developed CD in a 6 year follow-up period. All individuals were typed for HLA and 10 SNPs in non-HLA genes: CCR1/CCR3 (rs6441961), IL12A/SCHIP1 and IL12A (rs17810546 and rs9811792), TAGAP (rs1738074), RGS1 (rs2816316), LPP (rs1464510), OLIG3 (rs2327832), REL (rs842647), IL2/IL21 (rs6822844), SH2B3 (rs3184504). Three associated SNPs (in LPP, REL, and RGS1 genes) were identified through the Transmission Disequilibrium Test and a Bayesian approach was used to assign a score (BS) to each detected HLA+SNPs genotype combination. We then classified CD sibs as at low or at high risk if their BS was respectively < or ≥ median BS value within each HLA risk group. A larger number (72%) of CD sibs showed a BS ≥ the median value and had a more than two fold higher OR than CD sibs with a BS value < the median (O.R = 2.53, p = 0.047). Our HLA+SNPs genotype classification, showed both a higher predictive negative value (95% vs 91%) and diagnostic sensitivity (79% vs 45%) than the HLA only. In conclusion, the estimate of the CD risk by HLA+SNPs approach, even if not applicable to prevention, could be a precious tool to improve the prediction of the disease in a cohort of first degree relatives, particularly in the low HLA risk groups.     

Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection

We investigate the merit of deriving an estimate of the basic reproduction number early in an outbreak of an (emerging) infection from estimates of the incidence and generation interval only. We compare such estimates of with estimates incorporating additional model assumptions, and determine the circumstances under which the different estimates are consistent. We show that one has to be careful when using observed exponential growth rates to derive an estimate of , and we quantify the discrepancies that arise.