scholarly journals The Weighting is the Hardest Part: On the Behavior of the Likelihood Ratio Test and the Score Test Under a Data-Driven Weighting Scheme in Sequenced Samples

2017 ◽  
Vol 20 (2) ◽  
pp. 108-118 ◽  
Author(s):  
Camelia C. Minică ◽  
Giulio Genovese ◽  
Christina M. Hultman ◽  
René Pool ◽  
Jacqueline M. Vink ◽  
...  
Keyword(s):  
Exome Sequencing ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Association Studies ◽  
Score Test ◽  
Weighting Scheme ◽  
Data Driven ◽  
Ratio Test ◽  
Sequencing Data ◽  
Exome Sequencing Data

Sequence-based association studies are at a critical inflexion point with the increasing availability of exome-sequencing data. A popular test of association is the sequence kernel association test (SKAT). Weights are embedded within SKAT to reflect the hypothesized contribution of the variants to the trait variance. Because the true weights are generally unknown, and so are subject to misspecification, we examined the efficiency of a data-driven weighting scheme. We propose the use of a set of theoretically defensible weighting schemes, of which, we assume, the one that gives the largest test statistic is likely to capture best the allele frequency–functional effect relationship. We show that the use of alternative weights obviates the need to impose arbitrary frequency thresholds. As both the score test and the likelihood ratio test (LRT) may be used in this context, and may differ in power, we characterize the behavior of both tests. The two tests have equal power, if the weights in the set included weights resembling the correct ones. However, if the weights are badly specified, the LRT shows superior power (due to its robustness to misspecification). With this data-driven weighting procedure the LRT detected significant signal in genes located in regions already confirmed as associated with schizophrenia — the PRRC2A (p = 1.020e-06) and the VARS2 (p = 2.383e-06) — in the Swedish schizophrenia case-control cohort of 11,040 individuals with exome-sequencing data. The score test is currently preferred for its computational efficiency and power. Indeed, assuming correct specification, in some circumstances, the score test is the most powerful test. However, LRT has the advantageous properties of being generally more robust and more powerful under weight misspecification. This is an important result given that, arguably, misspecified models are likely to be the rule rather than the exception in weighting-based approaches.

scholarly journals The weighting is the hardest part: on the behavior of the likelihood ratio test and score test under weight misspecification in rare variant association studies

2015 ◽  
Author(s):  
Camelia C. Minica ◽  
Giulio Genovese ◽  
Christina M. Hultman ◽  
René Pool ◽  
Jacqueline M. Vink ◽  
...  
Keyword(s):  
Exome Sequencing ◽  
Likelihood Ratio ◽  
Rare Variant ◽  
Association Studies ◽  
Score Test ◽  
P Value ◽  
Ratio Test ◽  
Sequencing Data ◽  
Rare Variant Association ◽  
Exome Sequencing Data

Rare variant association studies are at a critical inflexion point with the increasing availability of exome-sequencing data. A popular test of association is the sequence kernel association test (SKAT). Weights are embedded within SKAT to reflect the hypothesized contribution of the variants to the trait variance. Correct weighting is expected to boost power, and yet the correct weights are generally unknown. It is therefore important to assess the effect of weight misspecification in SKAT. We evaluated the behavior of the score and likelihood ratio tests (LRT) under weight misspecification. Simulation and empirical results revealed that LRT is generally more robust and more powerful than score test in such a circumstance. For instance, when the simulated betas were larger for rarer than for more common variants, (incorrectly) assigning equal weights reduced the power of the LRT by ~5%, while the power of the score test dropped by ~30%. To optimize weighting we proposed a data-driven weighting scheme. With this scheme and LRT we detected significant enrichment of rare case mutations (MAF<5%; P-value=7E-04) of a set of constrained genes in the Swedish schizophrenia case-control cohort with exome-sequencing data. The score test is currently preferred for its computational efficiency and power. Indeed, assuming correct specification, in some circumstances the score test is the most powerful test. However, LRT has the compelling qualities of being generally more powerful and more robust to misspecification. This is an important result given that, arguably, misspecified models are likely to be the rule rather than the exception in weighting-based approaches.

Homogeneity testing for binomial proportions under stratified double-sampling scheme with two fallible classifiers

2020 ◽  
Vol 29 (12) ◽  
pp. 3547-3568
Author(s):  
Shi-Fang Qiu ◽  
Qi-Xiang Fu
Keyword(s):  
Least Squares ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Weighted Least Squares ◽  
Score Test ◽  
Double Sampling ◽  
Ratio Test ◽  
Sample Sizes ◽  
Log Transformation ◽  
Binomial Proportions

This article investigates the homogeneity testing problem of binomial proportions for stratified partially validated data obtained by double-sampling method with two fallible classifiers. Several test procedures, including the weighted-least-squares test with/without log-transformation, logit-transformation and double log-transformation, and likelihood ratio test and score test, are developed to test the homogeneity under two models, distinguished by conditional independence assumption of two classifiers. Simulation results show that score test performs better than other tests in the sense that the empirical size is generally controlled around the nominal level, and hence be recommended to practical applications. Other tests also perform well when both binomial proportions and sample sizes are not small. Approximate sample sizes based on score test, likelihood ratio test and the weighted-least-squares test with double log-transformation are generally accurate in terms of the empirical power and type I error rate with the estimated sample sizes, and hence be recommended. An example from the malaria study is illustrated by the proposed methodologies.

scholarly journals Power comparison of Rao′s score test, the Wald test and the likelihood ratio test in (2xc) contingency tables

2015 ◽  
Vol 52 (2) ◽  
pp. 95-104
Author(s):  
Anita Dobek ◽  
Krzysztof Moliński ◽  
Ewa Skotarczak
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Contingency Tables ◽  
Score Test ◽  
Wald Test ◽  
Likelihood Ratio Tests ◽  
Ratio Test ◽  
Power Comparison ◽  
Testing Hypotheses

Abstract There are several statistics for testing hypotheses concerning the independence of the distributions represented by two rows in contingency tables. The most famous are Rao′s score, the Wald and the likelihood ratio tests. A comparison of the power of these tests indicates the Wald test as the most powerful.

A likelihood ratio test for detecting patterns of disease-marker association

1997 ◽  
Vol 61 (4) ◽  
pp. 335-350 ◽  
Author(s):  
A. P. MORRIS ◽  
J. C. WHITTAKER ◽  
R. N. CURNOW
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Ratio Test ◽  
Disease Marker
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