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A Bayesian prediction model between a biomarker and the clinical endpoint for dichotomous variables.

Jiang Z, Song Y, Shou Q, Xia J, Wang W - Trials (2014)

Bottom Line: PPV and NPV are employed to describe the patient-level relationship between the biomarker and the clinical outcome.It could be applied in drug development.But the practical problems in applications have to be studied in further research.

View Article: PubMed Central - PubMed

Affiliation: Department of Health Statistics, School of Preventive Medicine, Fourth Military Medical University, No, 169 Changle West Road, Xi'an, Shaanxi, China. jielaixia@yahoo.com.

ABSTRACT

Background: Early biomarkers are helpful for predicting clinical endpoints and for evaluating efficacy in clinical trials even if the biomarker cannot replace clinical outcome as a surrogate. The building and evaluation of an association model between biomarkers and clinical outcomes are two equally important concerns regarding the prediction of clinical outcome. This paper is to address both issues in a Bayesian framework.

Methods: A Bayesian meta-analytic approach is proposed to build a prediction model between the biomarker and clinical endpoint for dichotomous variables. Compared with other Bayesian methods, the proposed model only requires trial-level summary data of historical trials in model building. By using extensive simulations, we evaluate the link function and the application condition of the proposed Bayesian model under scenario (i) equal positive predictive value (PPV) and negative predictive value (NPV) and (ii) higher NPV and lower PPV. In the simulations, the patient-level data is generated to evaluate the meta-analytic model. PPV and NPV are employed to describe the patient-level relationship between the biomarker and the clinical outcome. The minimum number of historical trials to be included in building the model is also considered.

Results: It is seen from the simulations that the logit link function performs better than the odds and cloglog functions under both scenarios. PPV/NPV ≥0.5 for equal PPV and NPV, and PPV + NPV ≥1 for higher NPV and lower PPV are proposed in order to predict clinical outcome accurately and precisely when the proposed model is considered. Twenty historical trials are required to be included in model building when PPV and NPV are equal. For unequal PPV and NPV, the minimum number of historical trials for model building is proposed to be five. A hypothetical example shows an application of the proposed model in global drug development.

Conclusions: The proposed Bayesian model is able to predict well the clinical endpoint from the observed biomarker data for dichotomous variables as long as the conditions are satisfied. It could be applied in drug development. But the practical problems in applications have to be studied in further research.

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The simulation results of Bayesian model for variousNandφBjgiven logit link function (equal positive predictive value and negative predictive value).(PPV: positive predictive value; NPV: negative predictive value)
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Fig4: The simulation results of Bayesian model for variousNandφBjgiven logit link function (equal positive predictive value and negative predictive value).(PPV: positive predictive value; NPV: negative predictive value)

Mentions: Based on the results of the last section, PPV/NPV ≥0.5 is considered here. The values of PPV/NPV are listed in Additional file 1: Table S3. As is seen in Figure 4, the prediction is a little underestimated when φBj = 0.1. The modified bias increases and even deviates from zero positively with the rise of φBj. It varies within (-0.08,0.08) regardless of how φBj changes. The modified RMSE is the smallest when 50 trials are included in model building for φBj = 0.1. But as φBj increases, the larger N does not always bring an accurate prediction. For example, the model built from five trials has the smallest modified RMSE when φBj = 0.5. It is perhaps because there is no treatment effect when φBj = 0.5, and more historical trials include larger variations in the model, which reduces the accuracy of the prediction. Regarding the precision of RR prediction, the average width of the 95% CIs is smaller when N is larger and φBj increases. The detailed simulation results are presented in Additional file 1: Table S3.Figure 4


A Bayesian prediction model between a biomarker and the clinical endpoint for dichotomous variables.

Jiang Z, Song Y, Shou Q, Xia J, Wang W - Trials (2014)

The simulation results of Bayesian model for variousNandφBjgiven logit link function (equal positive predictive value and negative predictive value).(PPV: positive predictive value; NPV: negative predictive value)
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4307375&req=5

Fig4: The simulation results of Bayesian model for variousNandφBjgiven logit link function (equal positive predictive value and negative predictive value).(PPV: positive predictive value; NPV: negative predictive value)
Mentions: Based on the results of the last section, PPV/NPV ≥0.5 is considered here. The values of PPV/NPV are listed in Additional file 1: Table S3. As is seen in Figure 4, the prediction is a little underestimated when φBj = 0.1. The modified bias increases and even deviates from zero positively with the rise of φBj. It varies within (-0.08,0.08) regardless of how φBj changes. The modified RMSE is the smallest when 50 trials are included in model building for φBj = 0.1. But as φBj increases, the larger N does not always bring an accurate prediction. For example, the model built from five trials has the smallest modified RMSE when φBj = 0.5. It is perhaps because there is no treatment effect when φBj = 0.5, and more historical trials include larger variations in the model, which reduces the accuracy of the prediction. Regarding the precision of RR prediction, the average width of the 95% CIs is smaller when N is larger and φBj increases. The detailed simulation results are presented in Additional file 1: Table S3.Figure 4

Bottom Line: PPV and NPV are employed to describe the patient-level relationship between the biomarker and the clinical outcome.It could be applied in drug development.But the practical problems in applications have to be studied in further research.

View Article: PubMed Central - PubMed

Affiliation: Department of Health Statistics, School of Preventive Medicine, Fourth Military Medical University, No, 169 Changle West Road, Xi'an, Shaanxi, China. jielaixia@yahoo.com.

ABSTRACT

Background: Early biomarkers are helpful for predicting clinical endpoints and for evaluating efficacy in clinical trials even if the biomarker cannot replace clinical outcome as a surrogate. The building and evaluation of an association model between biomarkers and clinical outcomes are two equally important concerns regarding the prediction of clinical outcome. This paper is to address both issues in a Bayesian framework.

Methods: A Bayesian meta-analytic approach is proposed to build a prediction model between the biomarker and clinical endpoint for dichotomous variables. Compared with other Bayesian methods, the proposed model only requires trial-level summary data of historical trials in model building. By using extensive simulations, we evaluate the link function and the application condition of the proposed Bayesian model under scenario (i) equal positive predictive value (PPV) and negative predictive value (NPV) and (ii) higher NPV and lower PPV. In the simulations, the patient-level data is generated to evaluate the meta-analytic model. PPV and NPV are employed to describe the patient-level relationship between the biomarker and the clinical outcome. The minimum number of historical trials to be included in building the model is also considered.

Results: It is seen from the simulations that the logit link function performs better than the odds and cloglog functions under both scenarios. PPV/NPV ≥0.5 for equal PPV and NPV, and PPV + NPV ≥1 for higher NPV and lower PPV are proposed in order to predict clinical outcome accurately and precisely when the proposed model is considered. Twenty historical trials are required to be included in model building when PPV and NPV are equal. For unequal PPV and NPV, the minimum number of historical trials for model building is proposed to be five. A hypothetical example shows an application of the proposed model in global drug development.

Conclusions: The proposed Bayesian model is able to predict well the clinical endpoint from the observed biomarker data for dichotomous variables as long as the conditions are satisfied. It could be applied in drug development. But the practical problems in applications have to be studied in further research.

Show MeSH
Related in: MedlinePlus