Conditional Score Test Research Articles

A comparison of hypothesis tests for homogeneity in meta-analysis with focus on rare binary events.

Analysis of rare binary events is an important problem for biomedical researchers. Due to the sparsity of events in such problems, meta-analysis that integrates information across multiple studies can be applied to increase the efficiency of statistical inference. Although it is critical to examine whether the effect sizes are homogeneous across all studies, a comprehensive review of homogeneity tests has been lacking, and in particular, no attention has been paid to infrequent dichotomous outcomes. We systematically review statistical methods for homogeneity testing. By conducting an extensive simulation analysis and two case studies, we examine the performance of 30 tests in meta-analysis of rare binary outcomes. When using log-odds ratio as the association measure, our simulation results suggest that there is no uniform winner. However, we recommend the test proposed by Kulinskaya and Dollinger (BMC Med Res Methodol, 2015, 15), which uses a gamma distribution to approximate the null distribution, for its generally good performance; for very rare events coupled with small within-study sample sizes, in addition to the Kulinskaya-Dollinger test, we further recommend the conditional score test based on the random-effects hypergeometric model proposed by Liang and Self (Biometrika, 1985, 72:353-358). One should be cautious about the use of the Wald tests, the Lipsitz tests (Biometrics, 1998, 54:148-160), and tests proposed by Bhaumik et al (J Am Stat Assoc, 2012, 107:555-567).

An efficient and flexible test for rare variant effects.

Since it has been claimed that rare variants with extremely small allele frequency play a crucial role in complex traits, there is great demand for the development of a powerful test for detecting these variants. However, due to the extremely low frequencies of rare variants, common statistical testing methods do not work well, which has motivated recent extensive research on developing an efficient testing procedure for rare variant effects. Many studies have suggested effective testing procedures with reasonably high power under some presumed assumptions of parametric statistical models. However, if the parametric assumptions are violated, these tests are possibly under-powered. In this paper, we develop an optimal, powerful statistical test called the aggregated conditional score test (ACST) for simultaneously testing M rare variant effects without restrictive parametric assumptions. The proposed test uses a test statistic aggregating the conditional score statistics of effect sizes of M rare variants. In simulation studies, ACST generally performed well compared with the two most commonly used tests, the optimal sequence kernel association test (SKAT-O) and Kullback-Leibler distance test. Finally, we demonstrate the performance and practical utility of ACST using the Dallas Heart Study data.

Recurrent Stroke in the Warfarin versus Aspirin in Reduced Cardiac Ejection Fraction (WARCEF) Trial

Background and Purpose: WARCEF randomized 2,305 patients in sinus rhythm with ejection fraction (EF) ≤35% to warfarin (INR 2.0-3.5) or aspirin 325 mg. Warfarin reduced the incident ischemic stroke (IIS) hazard rate by 48% over aspirin in a secondary analysis. The IIS rate in heart failure (HF) is too low to warrant routine anticoagulation but epidemiologic studies show that prior stroke increases the stroke risk in HF. In this study, we explore IIS rates in WARCEF patients with and without baseline stroke to look for risk factors for IIS and determine if a subgroup with an IIS rate high enough to give a clinically relevant stroke risk reduction can be identified. Methods: We compared potential stroke risk factors between patients with baseline stroke and those without using the exact conditional score test for Poisson variables. We looked for risk factors for IIS, by comparing IIS rates between different risk factors. For EF we tried cut-off points of 10, 15 and 20%. The cut-off point 15% was used as it was the highest EF that was associated with a significant increase in IIS rate. IIS and EF strata were balanced as to warfarin/aspirin assignment by the stratified randomized design. A multiple Poisson regression examined the simultaneous effects of all risk factors on IIS rate. IIS rates per hundred patient years (/100PY) were calculated in patient groups with significant risk factors. Missing values were assigned the modal value. Results: Twenty of 248 (8.1%) patients with baseline stroke and 64 of 2,048 (3.1%) without had IIS. IIS rate in patients with baseline stroke (2.37/100PY) was greater than patients without (0.89/100PY) (rate ratio 2.68, p < 0.001). Fourteen of 219 (6.4%) patients with ejection fraction (EF) <15% and 70 of 2,079 (3.4%) with EF ≥15% had IIS. In the multiple regression analysis stroke at baseline (p < 0.001) and EF <15% vs. ≥15% (p = 0.005) remained significant predictors of IIS. IIS rate was 2.04/100PY in patients with EF <15% and 0.95/100PY in patients with EF ≥15% (p = 0.009). IIS rate in patients with baseline stroke and reduced EF was 5.88/100PY with EF <15% decreasing to 2.62/100PY with EF <30%. Conclusions: In a WARCEF exploratory analysis, prior stroke and EF <15% were risk factors for IIS. Further research is needed to determine if a clinically relevant stroke risk reduction is obtainable with warfarin in HF patients with prior stroke and reduced EF.

Abstract 53: Recurrent Stroke in the Warfarin versus Aspirin in Reduced Ejection Fraction (WARCEF) Trial

Background: WARCEF randomized 2305 patients in sinus rhythm with ejection fraction (EF) ≤35% to warfarin (INR 2.0-3.5) or aspirin 325 mg. Warfarin reduced the incident ischemic stroke (IIS) hazard rate by 48% over aspirin in a secondary analysis. The IIS rate in heart failure (HF) is too low to warrant routine anticoagulation but epidemiologic studies show that prior stroke increases the stroke risk in HF. We here explore IIS rates in WARCEF patients with and without baseline stroke to determine if a subgroup with an IIS rate high enough (3-5 per 100 patient-years [PY]) to give a clinically relevant warfarin effect can be identified. Methods: We compared the IIS rate between patients with baseline stroke and those without using the exact conditional score test for Poisson variables. We looked for risk factors for IIS , by comparing IIS rates between different levels of each potential risk factor. For EF we tried cut-off points of 10%, 15% and 20%. 15% was used as it was the highest EF that was associated with a significant increase in IIS rate. IIS and EF strata were balanced as to warfarin/aspirin assignment by the stratified randomized design. A multiple Poisson regression examined the simultaneous effects of all risk factors on IIS rate. Missing values were assigned the modal value. Results: Twenty of 248 (8.1%) patients with baseline stroke and 64 of 2048 (3.1%) without had IIS. IIS rates in patients with baseline stroke were significantly greater compared to patients without (rate ratio 2.67; 2.37 per 100PY and 0.89 per 100PY, respectively, p=0.0004). Fourteen of 219 (6.4%) patients with EF&lt;15% and 70 of 2079 (3.4%) with EF ≥15% had IIS. IIS rates in patients with EF&lt;15% and patients with EF ≥15% were 2.04 per 100PY and 0.95 per 100PY, respectively (p=0.012). IIS rate in patients with baseline stroke and EF&lt;15% was 5.88 per 100PY. In the multiple Poisson regression analysis only stroke at baseline (p=0.0001) and EF&lt;15% vs. ≥15% (p=.005) remained significant predictors of IIS. Conclusions: In a WARCEF exploratory analysis, prior stroke and EF&lt;15% were risk factors for IIS. A clinically relevant stroke risk reduction might be obtainable with warfarin in HF patients with prior stroke and EF&lt;15%.

Testing the Non‐Unity of Rate Ratio under Inverse Sampling

Inverse sampling is considered to be a more appropriate sampling scheme than the usual binomial sampling scheme when subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic indices are undefined. In this article, we study various statistics for testing non-unity rate ratios in case-control studies under inverse sampling. These include the Wald, unconditional score, likelihood ratio and conditional score statistics. Three methods (the asymptotic, conditional exact, and Mid-P methods) are adopted for P-value calculation. We evaluate the performance of different combinations of test statistics and P-value calculation methods in terms of their empirical sizes and powers via Monte Carlo simulation. In general, asymptotic score and conditional score tests are preferable for their actual type I error rates are well controlled around the pre-chosen nominal level, and their powers are comparatively the largest. The exact version of Wald test is recommended if one wants to control the actual type I error rate at or below the pre-chosen nominal level. If larger power is expected and fluctuation of sizes around the pre-chosen nominal level are allowed, then the Mid-P version of Wald test is a desirable alternative. We illustrate the methodologies with a real example from a heart disease study.

Testing the New Keynesian Phillips Curve Without Assuming Identification

We re-examine the evidence on the new Phillips curve model of Gali and Gertler (Journal of Monetary Economics 1999) using the conditional score test of Kleibergen (Econometrica 2005),which is robust to weak identification. In contrast to earlier studies, we find that US postwar data are consistent both with the view that inflation dynamics are forward-looking, and with the opposite view that they are predominantly backward-looking. Moreover, the labor share does not appear to be a relevant determinant of inflation. We show that this is an important factor contributing to the weak identification of the Phillips curve.

A Likelihood Ratio Approach to Family‐based Association Studies with Covariates

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.

Adjusted homogeneity tests of odds ratios when data are clustered

AbstractThree modified tests for homogeneity of the odds ratio for a series of 2 × 2 tables are studied when the data are clustered. In the case of clustered data, the standard tests for homogeneity of odds ratios ignore the variance inflation caused by positive correlation among responses of subjects within the same cluster, and therefore have inflated Type I error. The modified tests adjust for the variance inflation in the three existing standard tests: Breslow–Day, Tarone and the conditional score test. The degree of clustering effect is measured by the intracluster correlation coefficient, ρ. A variance correction factor derived from ρ is then applied to the variance estimator in the standard tests of homogeneity of the odds ratio. The proposed tests are an application of the variance adjustment method commonly used in correlated data analysis and are shown to maintain the nominal significance level in a simulation study. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Conditional score tests in the exponential family

The similar test for an affine hypothesis in the exponential family is approximated by a score statistic, derived from the Edgeworth expansion of the conditional distribution given the minimal sufficient statistic under the null hypothesis.

Exact and Asymptotic Power Determination For Dose-Response Studies With Ordinal Response

In this article, we describe a conditional score test for detecting a monotone dose-response relationship with ordinal response data. We consider three different versions of this test: asymptotic, conditional exact, and mid-P conditional score test. Exact and asymptotic power formulae based on these tests will be studied. Asymptotic sample size formulae based on the asymptotic conditional score test will be derived. The proposed formulae are applied to a vaccination study and a developmental toxicity study for illustrative purposes. Actual significance level and exact power properties of these tests are compared in a small empirical study. The mid-P conditional score test is observed to be the most powerful test with actual significance level close to the pre-specified nominal level.

Sample Sizes for Survival Analysis Based on the Conditional Score Test for Person-time Observations.

In the design of clinical trials in which the primary endpoint is time to occurrence of a clinical event, sample size calculation should be based on the subsequent survival analysis. This paper gives sample size formulas based on the conditional score test for the hazard ratio, which is equivalent to the normal approximation of the Cox F test. The proposed method is adopted to uniform patient entry, loss to follow-up, and treatment switching. In cancer clinical trials, it is sometimes required to show that the two treatments have equivalent survival benefit when the new treatment has apparent advantages on toxicity. Application of the proposed sample size formula to the equivalence test of two treatments is also given.

A unified framework for transmission-disequilibrium test analysis of discrete and continuous traits.

This paper presents a unified framework for transmission-disequilibrium tests for discrete and continuous traits. A conditional score test is derived that maximizes power to detect small effects for any exponential family distribution, which includes binary and normal distributions, and distributions that are skewed or have non-normal kurtosis. The specific distributional form need not be specified, and the method applies to sibships of arbitrary size. Formulas for the distribution of the test statistic are given for models including complex genetic effects (additive, dominant, and recessive gene action), covariates, multiple gene models including gene-gene interactions or heterogeneity, and gene-environment interactions. We develop refinements of our method for trait-based sampling designs and multiple siblings that can have dramatic effects on power.

Joint and separate score tests for state dependence and unobserved heterogeneity

The paper compares separate, conditional, and joint score tests of duration dependence and unobserved heterogeneity when the null is the exponential model and the alternative is the heterogeneous Weibull model. The score tests based on the conditional score function include the Neyman C(α) test as a special case. An examination of the non-null distribution of the joint test explains when all score tests have low power in the presence of multiple misspecifications. Monte Carlo experiments show that the conditional score tests are superior to the standard separate tests which confound unobserved heterogeneity and duration dependence.

The asymptotic efficiency of conditional likelihood methods

SUMMARY This paper concerns the efficiency of the conditional likelihood method for inference in models which include nuisance parameters. A new concept of ancillarity, asymptotic weak ancillarity, is introduced. It is shown that the conditional maximum likelihood estimator and the conditional score test of 0, the parameter of interest, are asymptotically equivalent to their unconditional counterparts, and hence are asymptotically efficient, provided that the conditioning statistic is asymptotically weakly ancillary. The key assumption that the conditioning statistic is asymptotically weakly ancillary is verified when the underlying distribution is from exponential families. Some illustrative examples are given.