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The authors have declared that no competing interests exist.

Conceived and designed the experiments: N Zaitlen, N Patterson, AL Price, P Kraft, E Tchetgen Tchetgen. Performed the experiments: N Zaitlen, AL Price, S Pollack. Analyzed the data: N Zaitlen, AL Price, B Pasaniuc, P Kraft. Contributed reagents/materials/analysis tools: M Cornelis, G Genovese, A Barton, H Bickeböller, DW Bowden, S Eyre, BI Freedman, DJ Friedman, JK Field, L Groop, A Haugen, J Heinrich, BE Henderson, PJ Hicks, LJ Hocking, LN Kolonel, MT Landi, CD Langefeld, L Le Marchand, M Meister, AW Morgan, OY Raji, A Rosenberger, A Risch, D Scherf, S Steer, M Walshaw, KM Waters, AG Wilson, P Wordsworth, S Zienolddiny, C Haiman, DJ Hunter, RM Plenge, J Worthington, DC Christiani, DA Schaumberg, DI Chasman, D Altshuler, B Voight. Wrote the paper: N Zaitlen, S Lindström, AL Price.

Genetic case-control association studies often include data on clinical covariates, such as body mass index (BMI), smoking status, or age, that may modify the underlying genetic risk of case or control samples. For example, in type 2 diabetes, odds ratios for established variants estimated from low–BMI cases are larger than those estimated from high–BMI cases. An unanswered question is how to use this information to maximize statistical power in case-control studies that ascertain individuals on the basis of phenotype (case-control ascertainment) or phenotype and clinical covariates (case-control-covariate ascertainment). While current approaches improve power in studies with random ascertainment, they often lose power under case-control ascertainment and fail to capture available power increases under case-control-covariate ascertainment. We show that an informed conditioning approach, based on the liability threshold model with parameters informed by external epidemiological information, fully accounts for disease prevalence and non-random ascertainment of phenotype as well as covariates and provides a substantial increase in power while maintaining a properly controlled false-positive rate. Our method outperforms standard case-control association tests with or without covariates, tests of gene x covariate interaction, and previously proposed tests for dealing with covariates in ascertained data, with especially large improvements in the case of case-control-covariate ascertainment. We investigate empirical case-control studies of type 2 diabetes, prostate cancer, lung cancer, breast cancer, rheumatoid arthritis, age-related macular degeneration, and end-stage kidney disease over a total of 89,726 samples. In these datasets, informed conditioning outperforms logistic regression for 115 of the 157 known associated variants investigated (P-value = 1^{−9}). The improvement varied across diseases with a 16% median increase in χ^{2} test statistics and a commensurate increase in power. This suggests that applying our method to existing and future association studies of these diseases may identify novel disease loci.

This work describes a new methodology for analyzing genome-wide case-control association studies of diseases with strong correlations to clinical covariates, such as age in prostate cancer and body mass index in type 2 diabetes. Currently, researchers either ignore these clinical covariates or apply approaches that ignore the disease's prevalence and the study's ascertainment strategy. We take an alternative approach, leveraging external prevalence information from the epidemiological literature and constructing a statistic based on the classic liability threshold model of disease. Our approach not only improves the power of studies that ascertain individuals randomly or based on the disease phenotype, but also improves the power of studies that ascertain individuals based on both the disease phenotype and clinical covariates. We apply our statistic to seven datasets over six different diseases and a variety of clinical covariates. We found that there was a substantial improvement in test statistics relative to current approaches at known associated variants. This suggests that novel loci may be identified by applying our method to existing and future association studies of these diseases.

Genetic risk in case-control studies often varies as a function of body mass index (BMI), age or other clinical covariates. For example, in a recent type 2 diabetes study, 23 of 29 established associated SNPs had higher odds ratios when estimated from low-BMI cases than from high-BMI cases (average odds ratios 1.182 versus 1.128)

The question of how to optimally incorporate these covariates in case-control association studies is a function of the study design. We divide the set of possible study designs into three classes, random ascertainment (cohort or cross-section designs), case-control ascertainment that ascertains individuals based on phenotype, and case-control-covariate ascertainment that ascertains on both phenotype and clinical covariate (as in age-matched studies). When individuals are randomly ascertained, conditioning on covariates associated with phenotype can increase study power by reducing phenotypic variance

Here, we investigate a new approach to estimating the parameters of the liability threshold (LT) model

We apply the method to empirical case-control ascertained and case-control-covariate ascertained studies for seven different diseases: type 2 diabetes, prostate cancer, lung cancer, post-menopausal breast cancer, rheumatoid arthritis, age-related macular degeneration, and end-stage kidney disease over a total of 89,726 samples. Our method uses published prevalence data (as a function of clinical covariates) for each disease to estimate the LT parameters. The published prevalence data are an external source of information not utilized by the other statistical tests.

In these datasets, which include case-control and case-control-covariate designs, informed conditioning outperforms marginal logistic regression for 115 of the 157 known associated variants investigated (P-value = 1×10^{−9}) with a 16% median increase in χ^{2} test statistic and a commensurate increase in power, attaining a substantial and highly statistically significant improvement in association statistics. We conclude that application of informed conditioning to future case-control-covariate ascertained and case-control ascertained association studies of these diseases, or other diseases with analogous effects of age, BMI, or other covariates on genetic risk, has the potential to substantially increase the power of disease gene discovery.

The model is defined by

Our method employs a three-step procedure. First, we fit the parameters

The approach is best illustrated by an example. We consider a simulated BMI-matched case-control-covariate type 2 diabetes (T2D) dataset. In T2D, prevalence is greater in the population of individuals with high BMI. Our toy example contains 3,000 cases and 3,000 controls, half with BMI = 24 and half with BMI = 35. (This gives a mean BMI of 29.5 and standard deviation of 5.5, similar to the real T2D studies analyzed below.) We first fit the parameters of the liability threshold model using published information on prevalence as a function of BMI. This procedure is described in detail below and gives a liability model

We next compute the posterior mean value of the residual quantitative trait adjusted for BMI according to

The posterior mean of

Posterior mean E( |
Allele frequency | |

Cases, BMI = 24 | 2.09 | 0.55 |

Cases, BMI = 35 | 1.37 | 0.53 |

Controls, BMI = 24 | −0.10 | 0.50 |

Controls, BMI = 35 | −0.36 | 0.49 |

We test a causal variant with minor allele frequency (maf) 0.5 in the population and an effect size on the liability scale of

In these simulations, the likelihood ratio test has an expected χ^{2}(1 dof) = 30.3 (P = 3.7×10−8), which is genome-wide significant. It is notable that applying logistic regression (LogR) directly to case-control phenotypes produces a less significant statistic—either with or without conditioning on BMI, which has virtually no effect since cases and controls are BMI-matched. Logistic Regression of case-control status against genotype has an expected χ^{2}(1 dof) = 27.9 (P = 1.3×10−7), and an expected χ^{2}(1 dof) = 27.9 (P = 1.3×10−7) when using BMI as a covariate. Neither of these statistics is genome-wide significant. Studies with case-control-covariate ascertainment often attempt to match on a covariate, such as BMI in this example in order to prevent a loss of power that can come from stratified testing

We begin with published prevalence information over a range of values of clinical covariates. One means of finding the liability threshold parameters to minimize the normalized least-squares error_{i}

When there are multiple covariates we treat them as independent but infer the parameters jointly. For example, in T2D we fit the parameters

The main idea is that instead of conducting an association test using case-control phenotype

We show below that this is equivalent to the Score test, which is also commonly used in genetic association studies

We generalized the simulations from the toy case-control-covariate example for T2D above. These simulations used a BMI-matched design, which is a special case of case-control-covariate ascertainment. For each effect size _{case,24}, _{control,24}, _{case,35}, _{control,35} based on the liability threshold model. Using these simulations, we evaluated power and false-positive rate. We also considered non-additive models, as well as the effect of mis-specifying the parameters of the LT model.

We considered five different statistical tests: logistic regression (LogR) using case-control phenotype, LogR using case-control phenotype with BMI as covariate (LogR+Cov), a χ^{2}(2 dof) test for main genetic effect and gene x BMI interaction (G+GxE) ^{2}(2 dof) statistic (G+GxE) is a likelihood ratio test comparing the null model of no main genetic effect and no gene x BMI interaction to the causal model with main genetic effect and gene x BMI interaction.

For each test, the average χ^{2} statistic is displayed in ^{2} statistics compared to LogR. The improvement is a function of BMI distribution, effect size, disease prevalence, minor allele frequency, and study design. The G+GxE test loses power due to the extra degree of freedom. The LogRSub test performs nearly as well as the LogR test, showing that low-BMI cases contribute more power than high-BMI cases.

γ | LogR | LogR+Cov | G+GxE | LogRSub | LT | ORLBMI | ORHBMI |

0.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |

0.06 | 11.27 | 11.27 | 9.69 | 10.60 | 12.11 | 1.15 | 1.10 |

0.07 | 14.61 | 14.61 | 12.86 | 13.72 | 15.77 | 1.17 | 1.12 |

0.08 | 18.43 | 18.43 | 16.52 | 17.32 | 19.97 | 1.20 | 1.13 |

0.09 | 23.11 | 23.12 | 21.04 | 21.66 | 25.03 | 1.23 | 1.15 |

0.10 | 27.88 | 27.89 | 25.73 | 26.21 | 30.34 | 1.25 | 1.17 |

0.11 | 33.45 | 33.47 | 31.15 | 31.38 | 36.48 | 1.28 | 1.19 |

0.12 | 39.77 | 39.80 | 37.51 | 37.24 | 43.46 | 1.31 | 1.20 |

0.13 | 45.92 | 45.95 | 43.64 | 42.89 | 50.29 | 1.34 | 1.22 |

0.14 | 52.74 | 52.78 | 50.55 | 49.11 | 57.79 | 1.37 | 1.24 |

0.15 | 59.63 | 59.68 | 57.89 | 55.60 | 65.55 | 1.39 | 1.26 |

In addition to these five main tests we considered two additional tests: A χ^{2}(1 dof) statistic, which compares the null model of main genetic effect only to the causal model with main genetic effect and gene x BMI interaction, and is equal to the difference between G+GxE and LogR statistics; a case-only logistic regression comparing BMI = 24 to BMI = 35 ^{2}(1 dof) statistics less than 5.0 for all effect sizes and are not considered further. Another approach, probit regression

Average χ^{2} statistics are useful for comparison purposes, but do not provide a formal assessment of power. We also performed power calculations, computing the proportion of 1,000,000 simulations achieving the conventional GWAS cutoff for significance at 5% level following correction for multiple testing of P<5×10^{−8}. Results for a subset of methods are displayed in ^{2} statistic. We caution that these results will vary as a function of the ascertainment of BMI in the study. Furthermore, for any choice of ascertainment strategy, these results may overstate the prospects for improvement in real data, since simulated data and association statistics were based on the same model and model parameters.

For each statistic we display power to attain P<5^{−8} based on 1,000,000 simulations of 3000 cases and 3000 controls, for various effect sizes

We repeated the above experiments under a range of ascertainment schemes (random, case-control, case-control-covariate) and effect sizes (see Text S1 and Table S2 in

To investigate the properties of the LT statistic under the null we computed the mean value in the simulations above when ^{2} (1 dof) distribution. The two-tailed K-S test of the full distribution was not significant (P-value = 0.34), nor was the K-S test restricted to the tail where the LT statistic had χ^{2}>3.84 (P-value = 0.21). In order to further investigate the extreme tail of the distribution we ran 10^{8} tests under the null and verified that 98 of the 10^{8} tests (10^{−6}) had a P-value<10^{−6}. The LT statistic is a score test when the parameters are estimated correctly and will therefore have the correct null distribution. We investigated the properties of the LT statistic when the parameters were severely mis-estimated and found no inflation (see Text S1 in

The LT statistic assumes the same model used to generate the data in the above experiments, and its increase in performance over other methods may be driven by this fact. To examine this possibility we conducted case-control study simulations under a logit model as opposed to liability threshold model of disease used above. We also performed simulations in which the LT parameters were estimated from simulated epidemiological summary statistics. In all cases, the LT statistic continued to outperform the other methods by a similar margin (see Text S1 and Table S6 in

Our above simulations examine a range of alternatives consistent with additivity on the liability scale. While data and theory suggest that additivity explains most of the genetic variance for a range of phenotypes

Adjustment for informative covariates is not unique to genetics and the problem of estimation from case-control data has received considerable attention ^{2} than the LT statistic in the simulations from

To investigate the sensitivity of the LT statistic to mis-specification of model parameters, we performed additional simulations in which we assumed model parameters that were different from those used to simulate the data. We concluded that the LT statistic is robust to deviations in model parameters (see Table S1 in

We estimated parameters for each of the diseases using published prevalence data as a function of the relevant covariates. For example, for T2D we used prevalences 2%, 3%, 5%, 8%, 13%, and 24% for BMIs 18, 21.5, 24.5, 27.5, 30.5, 35 respectively. Using these data we fit the liability threshold model parameters so as to minimize the squared error between the expected thresholds and those specified by the model(see

Disease | %VarianceExplained | LT Model for φ |

T2D (Metabo) | BMI = 14%, age = 6% | 0.08*(BMI-26.5)+0.029*(age-50)-1.38 |

BMI = 15% | 0.08*(BMI-26.5)-1.44 | |

age = 9% | 0.029*(age-50)-1.28 | |

T2D (MEC) | BMI = 14%, age = 4% | 0.08*(BMI-26.5)+0.029*(age-50)-1.38 |

BMI = 15% | 0.08*(BMI-26.5)-1.44 | |

age = 5% | 0.029*(age-50)-1.28 | |

PC | age = 14% | 0.049*(age-50)-2.49 |

LC | age = 2%,smoking = 76% | 0.03*(age-50)+2.6*(smoking-0.25)-3.06 |

age = 17% | 0.04*(age-50)-3.30 | |

smoking = 51% | 2.04*(smoking-0.25)-2.37 | |

BC | age = 8% | 0.032*(age-50)-2.26 |

RA | age = 6%, sex = 2% | 0.022*(age-50)+0.32*(sex-0.5)-2.46 |

age = 6% | 0.022*(age-50)-2.46 | |

sex = 2% | 0.32*(sex-0.5)-2.34 | |

ESKD | age = 15% | 0.02*(age-50)-2.08 |

AMD | age = 17%, BMI30 = 5% | 0.03*(age-50)+0.61*(BMI30-0.30)-2.00 |

age = 11% | 0.04*(age-50)-2.10 | |

BMI30 = 6% | 0.35*(BMI30-0.30)-1.72 |

Disease | Ascertainment | Cases | Controls | SNPs | ORL>ORH | LTPub>LogR |

T2D (Metabo) | Case-Control-Covariate | 5051 | 3529 | 47 | 37 | 37 |

T2D (MEC) | Case-Control-Covariate | 6142 | 7403 | 19 | 15 | 16 |

PC | Case-Control-Covariate | 10501 | 10831 | 39 | 32 | 30 |

LC | Case-Control-Covariate | 6952 | 6661 | 16 | 13 | 12 |

BC | Case-Control-Covariate | 9619 | 12244 | 20 | 12 | 11 |

RA | Case-Control | 5024 | 4281 | 21 | 16 | 15 |

ESKD | Case-Control | 1030 | 1025 | 1 | 1 | 1 |

AMD | Case-Control-Covariate | 473 | 1103 | 2 | 2 | 2 |

SUM | n/a | 37840 | 40416 | 165 | 128 | 128 |

We applied informed conditioning to a case-control-covariate ascertained dataset of 5,051 T2D cases and 3,529 controls from three Swedish cohorts (the Malmo Preventive Project, Scania Diabetes Registry, and Botnia Study)

We compared association statistics over these T2D data using four approaches: LogR, LogR+Cov, logistic regression with an interaction term (G+GxE), and LT. Logistic regression without high-BMI cases (LogRSub) was not included since it contains strictly fewer individuals and its performance is not expected to exceed LogR. The G+GxE test underperformed relative to other methods in all datasets due to its extra degree of freedom. This is expected since the SNPs were discovered with a marginal test, and are therefore less likely to have gene x covariate interactions on the liability scale. Results are displayed in ^{2} statistics across all loci is 51% higher for LT than LogR. As expected under an LT model, the odds ratios computed from individuals with low BMI are greater than those computed from individuals with high BMI. The T2D LT models also use age as a covariate and in the LTPub estimation method age and BMI were fit jointly (see

Disease | LTPub | LogR | LogR+Cov | LTPub vs LogR |

T2D (Metabo) | 369.7 | 244.05 | 252.23 | +51% |

T2D (MEC) | 402.86 | 320.08 | 400.89 | +26% |

PC | 1912.88 | 1787.61 | 1844.40 | +7% |

LC | 416.95 | 359.64 | 331.28 | +16% |

BC | 395.16 | 390.86 | 386.83 | +1% |

RA | 511.31 | 470.91 | 466.11 | +9% |

ESKD | 188.38 | 137.80 | 134.70 | +37% |

AMD | 185.6 | 159.38 | 110.33 | +16% |

It is of interest to include non-European ancestries in studies of T2D, because non-Europeans have higher T2D risk ^{2} statistics than LogR. We reran the LTPub estimation fitting BMI and age separately and found the improvements over LogR to be 20% and 3% respectively.

The Metabochip study included a large number of low-BMI cases as part of their ascertainment strategy whereas the MEC study ascertained randomly with respect to BMI. Including low-BMI cases increases the power of the Metabochip study since odds ratios estimated from the population of low-BMI individuals will be larger

For each T2D dataset, we simulated 100,000 datasets with the same sample sizes, covariates, and case-control status as the real datasets. We simulated a causal variant with effect size 0.1 and minor allele frequency 0.1 under the LT model for T2D and computed statistics for LT and LogR. The percent improvements were 40%

We applied informed conditioning to a case-control-covariate ascertained dataset of 10,501 prostate cancer cases and 10,831 controls (with 7 of 8 cohorts age-matched) from the NCI Breast and Prostate Cancer Cohort Consortium (BPC3) that were genotyped at 39 SNPs identified by previous prostate cancer GWAS

We compared association statistics using four approaches: LogR, LogR with age as covariate, logistic regression with an interaction term (G+GxE), and LT. As was the case for T2D, G+GxE underperformed relative to the other methods due to its extra degree for freedom. Results are displayed in ^{2} statistics than LogR and that the odds ratios computed from early-onset cases are greater than those computed from late-onset cases. Including study cohort as a covariate had no significant effect on these tests. The age information in this study is age at onset and we therefore repeated the analysis using ^{2} statistics from 1912.88 to 1925.65.

We repeated the analysis computing association statistics separately for each of the eight BPC3 cohorts and performing a meta-analysis across cohorts using inverse variance weighting to combine test statistics ^{2} statistics of LT compared to LogR. However, one difference is that LogR with age as covariate produced a 1.3% increase in χ^{2} statistics in the combined analysis (both with and without study as a covariate) but a 2.3% decrease in χ^{2} statistics in the meta-analysis. We sought to understand this difference by comparing performance separately for each cohort. We determined that LogR with age as covariate performs similarly to LogR if cases and controls are age-matched, performs worse than LogR if controls are much younger, slightly older or much older than cases, but performs better if controls are slightly younger than cases—as in the HPFS cohort and in the combined analysis. LogR with age as covariate performs better in the latter case because age-adjusted case-control phenotype has a more extreme value in younger cases than in older cases, mimicking the posterior mean quantitative trait phenotype used in the LT statistic. The effect of conditioning covariate in LogR is a complex function of ascertainment strategy, effect size, and the distribution in the cohort, and should not be viewed as a method that improves power in the general case

For the prostate cancer dataset, we simulated 100,000 datasets with the same sample size, covariates, and case-control status as the real dataset. We simulated a causal variant with effect size 0.07 and minor allele frequency 0.05 under the LT model and computed statistics for LT and LogR. The percent improvement was 6%

In addition to T2D and prostate cancer, we examined lung cancer ^{2} statistics from 395.16 to 393.39.

Averaging across the eight datasets analyzed, the LT approach we propose attained a median improvement of 16% and mean improvement of 20% as compared to the commonly used LogR method, with an improvement for 115 of 157 SNPs (P-value = 1×10^{−9}). To show that relative improvement of LT is not solely due to SNPs with large values of LogR, we computed the sum of LT and LogR for the SNPs in the lower 50% of LogR for each disease excluding the single SNP of ESKD. The LT statistic had a 15% median improvement and an 18% mean improvement over LogR for these lower 50% SNPs. We also ran permutations to show that the gains of the LT relative to LogR require the correct covariate information and that genotype and covariate are correlated for known loci, as predicted by the liability threshold model (see Text S1 in

T2D and lung cancer are both affected by clinical covariates (BMI and smoking status) that are partly genetically driven. In such instances, LT modeling of the covariate will generally increase power to detect SNPs whose primary association is to the disease, and reduce power to detect SNPs whose primary association is to the covariate with secondary association to the disease. In light of this, LT modeling of the covariate is our recommended strategy, since SNPs whose primary association is to the covariate are best discovered via separate studies of association to the covariate trait. Following this strategy, we used both BMI and age as covariates for T2D. We note that the T2D SNPs tested include one locus (FTO) which has a primary association to BMI with induced secondary association to T2D

In the case of lung cancer, if the goal is to identify lung cancer SNPs (rather than smoking SNPs) we recommend including both age and smoking as covariates. However, our task of evaluating the LT model for lung cancer was complicated by the fact that many known lung cancer loci have a primary association to smoking with a secondary (less statistically significant) association to lung cancer

For each disease we permuted the genotypes of the individuals, keeping the case-control and covariates fixed 100,000 times. We reran the LT statistic on each permutation using the same LTPub parameters for each disease as above, and verified that LT had the appropriate 5% type 1 error rate at each SNP and ^{2}(1 dof) distribution was not significant (P-value = 0.26), nor was the K-S test restricted to the tail with LT χ^{2}>3.84 (P-value = 0.15).

We have shown that informed conditioning on clinical covariates in association studies with case-control-covariate or case-control ascertainment yields a substantial increase in power in the simulations and empirical datasets analyzed here. The gain in power varies across diseases and is a function of the proportion of variance on the liability scale explained by the covariate(s), the disease prevalence, and the ascertainment strategy. We note that the increase in power will often exceed the increase in χ^{2} statistics. For example, a GWAS with 5000 cases and 5000 controls has 43.7% power at P-value threshold 5×10^{−8} to detect a SNP with a minor allele frequency of 20% and an odds ratio of 1.2. The power increases to 59.8% (a>36% increase in power, in the sense that >36% more variants will be discovered) when increasing χ^{2} statistics by 16%, which is similar to the median increase in χ^{2} statistics that we observed in our empirical studies. Additional significant gains in power, particularly under the LT approach, are possible by collecting cases at phenotypic extremes

Thus, there is a very strong motivation for applying the approach we have described to type 2 diabetes, prostate cancer, lung cancer, age-related macular degeneration, and end-stage kidney disease (for which the LTPub parameters in

We caution against the use of standard conditioning approaches (LogR+Cov) in case-control ascertained studies, which can increase or decrease power as a function of covariate effect size and disease prevalence

We designed the LT method for effects that are additive on the liability scale, which are hypothesized to account for the majority of genetic variation across a range of complex phenotypes

Meta-analysis is easily handled in the context of the liability threshold framework. Summary statistics are typically combined using odds ratios and standard errors. The LT statistics returns effect sizes on the liability scale and standard errors. Since these are easily converted to odds ratios (see Text S1 in

The LT statistic uses covariates to increase power. We assume that the LT model parameters estimated from epidemiological data, as well as the values of the covariates measured in the study, are reasonably accurate. Under inaccurate estimation of model parameters our method will have reduced power relative to its power with accurate model parameters, but it will still have the correct null distribution. In simulations, mis-specifying the parameters by a moderate amount produced almost no change in power and mis-specifying the parameters by a large amount (up to 100%) still performed at least as well as logistic regression with no conditioning in all cases examined (see Text S1 in

When conducting an association study where known clinical factors alter disease risk, the gain in power of the LT statistic is function of the number of individuals with available covariate information. For example, in the DIAGRAM dataset all 31 cohorts had BMI information and 20 had age at diagnosis information, thus the gain in power possible from the LT method will be nearly maximal ^{2} is 16%, then an individual with a covariate provides the same power as 1.16 individuals with no covariate. Researchers should therefore carefully weigh the cost of collecting covariates when designing studies since it may provide a more cost effective way to substantially increase power than genotyping more individuals.

In cross-sectional studies when data are randomly ascertained with respect to both case-control status and clinical covariate, the LT statistic and LogR+Cov are expected to perform similarly and our recommendation is to use LogR+Cov. In case-control studies of high prevalence diseases when clinical covariates are randomly ascertained, but cases are oversampled relative to their prevalence in the population, the LT statistic will slightly outperform LogR+Cov and our recommendation is to use the LT statistic. In case-control diseases of low prevalence, or in case-control-covariate studies when clinical covariates are non-randomly ascertained the LT statistic will substantially outperform LogR+Cov (which may often lose power relative to LogR) and our recommendation is to use the LT statistic. As described above, the LT statistic also outperforms other methods. In summary, informed conditioning on clinical covariates has a large potential to increase the power of case-control association studies and identify new risk variants.

LTSOFT software:

Supporting information.

(DOC)

The authors thank R. Do, S. Kathiresan, D. Reich, D. Spiegelman, N. Chatterjee, E. Stahl, and P. Visscher for helpful discussions and the BPC3 breast and prostate cancer consortium for assistance with the breast and prostate cancer data.