A goodness-of-fit test for logistic regression models based on case-control data

Qin, Jing; Zhang, Biao

doi:10.1093/biomet/84.3.609

Cited by 228 publications

(364 citation statements)

References 17 publications

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“…Equations (22), (24) and (26) defined expressions for the components of the asymptotic variance of √ n(P EV − P EV ), σ 2 9 . We only need to substitute l(θ) in the definition of P 1 P 2 and Q 1 Q 2 (equation (23) and (25)) with the likelihood function based on case-control data, which are defined by Prentice and Pyke (1979), Qin andZhang (1997) andZhang (2000).…”

Section: Proof Of Theorem Item (Ix)mentioning

confidence: 99%

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Measures to Summarize and Compare the Predictive Capacity of Markers

Gu¹,

Pepe²

2009

The International Journal of Biostatistics

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The predictive capacity of a marker in a population can be described using the population distribution of risk (Huang et al. 2007;Pepe et al. 2008a;Stern 2008). Virtually all standard statistical summaries of predictability and discrimination can be derived from it (Gail and Pfeiffer 2005). The goal of this paper is to develop methods for making inference about risk prediction markers using summary measures derived from the risk distribution. We describe some new clinically motivated summary measures and give new interpretations to some existing statistical measures. Methods for estimating these summary measures are described along with distribution theory that facilitates construction of confidence intervals from data. We show how markers and, more generally, how risk prediction models, can be compared using clinically relevant measures of predictability. The methods are illustrated by application to markers of lung function and nutritional status for predicting subsequent onset of major pulmonary infection in children suffering from cystic fibrosis. Simulation studies show that methods for inference are valid for use in practice. KEYWORDS: discrimination, risk, classification, decision makingAuthor Notes: This work is supported in part by grants from the National Institutes of Health (R01 GM054438 and U01 CA086368).Unauthenticated Download Date | 5/11/18 6:02 AMThe predictive capacity of a marker in a population can be described using the population distribution of risk (Huang et al. 2007;Pepe et al. 2008a;Stern 2008). Virtually all standard statistical summaries of predictability and discrimination can be derived from it (Gail and Pfeiffer 2005). The goal of this paper is to develop methods for making inference about risk prediction markers using summary measures derived from the risk distribution. We describe some new clinically motivated summary measures and give new interpretations to some existing statistical measures. Methods for estimating these summary measures are described along with distribution theory that facilitates construction of confidence intervals from data. We show how markers and, more generally, how risk prediction models, can be compared using clinically relevant measures of predictability. The methods are illustrated by application to markers of lung function and nutritional status for predicting subsequent onset of major pulmonary infection in children suffering from cystic fibrosis. Simulation studies show that methods for inference are valid for use in practice. BackgroundLet D denote a binary outcome variable, such as presence of disease or occurrence of an event within a specified time period and let Y denote a set of predictive markers used to predict a bad outcome, D = 1, or a good outcome, D = 0. For example, elements of the Framingham risk score (age, gender, total and high-density lipoprotein cholesterol, systolic blood pressure, treatment for hypertension and smoking) are used to predict occurrence of a cardiovascular event within 10 years (http://hp2010.nhlbihin.net/...

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Section: Proof Of Theorem Item (Ix)mentioning

confidence: 99%

“…1, Art. 27 DOI: 10.2202/1557-4679.1188 Result 3 A proof can be found in Prentice and Pyke (1979), Qin and Zhang (1997) and Zhang (2000).…”

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confidence: 91%

Measures to Summarize and Compare the Predictive Capacity of Markers

Gu¹,

Pepe²

2009

The International Journal of Biostatistics

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“…A test was constructed based on the hypothesis that the additional parameters are equal to zero to shrink the class of models to the desired logistic model. In the context of case-control studies, Qin and Zhang (1997) pointed out that model (1) is equivalent to a two-sample semiparametric model and proposed a goodnessof-fit test by comparing the observed distribution of covariates and the expected counterpart under the assumed model.…”

Section: Introductionmentioning

confidence: 99%

A New Method for Logistic Model Assessment

Shu¹,

He²

2017

IJSP

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It is well known that the logistic model plays an important role for the analysis of binary outcomes. Most of the existing methods for the assessment of logistic models are constructed based on the distance between the observed and the predicted outcomes. We consider a new method from a different perspective by assessing the distance between two consistent estimators developed under the same logistic model form. The proposed tests are easy to implement and are applicable to both prospective and case-control studies.

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“…Various density-ratio models for some conventional density functions were discussed in Kay and Little [8]. It has been shown recently that the density-ratio model provides a good fit to the observed data in some medical applications (Qin and Zhang [9]; Qin et al [10]; Zhang [11]), genetic quantitative trait loci analysis (Zou et al [12]), and clinical trials with skewed outcomes (White and Thompson [13]). Liu, Jiang and Zhou [14] considered estimation and inference for the two-sample varying-coefficient density-ratio model (1) by constructing the local empirical likelihood function.…”

Section: Introductionmentioning

confidence: 99%

Local Empirical Likelihood Diagnosis of Varying Coefficient Density-Ratio Models Based on Case-Control Data

Wang¹,

Lin²,

Dai³

2014

OJS

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In this paper, a varying-coefficient density-ratio model for case-control studies is developed. We investigate the local empirical likelihood diagnosis of varying coefficient density-ratio model for case-control data. The local empirical log-likelihood ratios for the nonparametric coefficient functions are introduced. First, the estimation equations based on empirical likelihood method are established. Then, a few of diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation studies.

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A goodness-of-fit test for logistic regression models based on case-control data

Cited by 228 publications

References 17 publications

Measures to Summarize and Compare the Predictive Capacity of Markers

Measures to Summarize and Compare the Predictive Capacity of Markers

A New Method for Logistic Model Assessment

Local Empirical Likelihood Diagnosis of Varying Coefficient Density-Ratio Models Based on Case-Control Data

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