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Stratification bias in low signal microarray studies.

Parker BJ, Günter S, Bedo J - BMC Bioinformatics (2007)

Bottom Line: In simulation studies using 10-fold cross-validation, AUC values of less than 0.3 can be observed on random datasets rather than the expected 0.5.Therefore for model selection and evaluation of microarray and other small biological datasets, these methods should be used and unstratified versions avoided.In particular, the commonly used (unbalanced) leave-one-out cross-validation should not be used to estimate AUC for small datasets.

View Article: PubMed Central - HTML - PubMed

Affiliation: Statistical Machine Learning Group, NICTA, Canberra, Australia. brian.bj.parker@gmail.com

ABSTRACT

Background: When analysing microarray and other small sample size biological datasets, care is needed to avoid various biases. We analyse a form of bias, stratification bias, that can substantially affect analyses using sample-reuse validation techniques and lead to inaccurate results. This bias is due to imperfect stratification of samples in the training and test sets and the dependency between these stratification errors, i.e. the variations in class proportions in the training and test sets are negatively correlated.

Results: We show that when estimating the performance of classifiers on low signal datasets (i.e. those which are difficult to classify), which are typical of many prognostic microarray studies, commonly used performance measures can suffer from a substantial negative bias. For error rate this bias is only severe in quite restricted situations, but can be much larger and more frequent when using ranking measures such as the receiver operating characteristic (ROC) curve and area under the ROC (AUC). Substantial biases are shown in simulations and on the van 't Veer breast cancer dataset. The classification error rate can have large negative biases for balanced datasets, whereas the AUC shows substantial pessimistic biases even for imbalanced datasets. In simulation studies using 10-fold cross-validation, AUC values of less than 0.3 can be observed on random datasets rather than the expected 0.5. Further experiments on the van 't Veer breast cancer dataset show these biases exist in practice.

Conclusion: Stratification bias can substantially affect several performance measures. In computing the AUC, the strategy of pooling the test samples from the various folds of cross-validation can lead to large biases; computing it as the average of per-fold estimates avoids this bias and is thus the recommended approach. As a more general solution applicable to other performance measures, we show that stratified repeated holdout and a modified version of k-fold cross-validation, balanced, stratified cross-validation and balanced leave-one-out cross-validation, avoids the bias. Therefore for model selection and evaluation of microarray and other small biological datasets, these methods should be used and unstratified versions avoided. In particular, the commonly used (unbalanced) leave-one-out cross-validation should not be used to estimate AUC for small datasets.

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Related in: MedlinePlus

Simulation results using DLDA and 10-fold unstratified CV for a weak signal. Same experimental setup as in additional figure 1(a), but d' = 0.5.
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Figure 2: Simulation results using DLDA and 10-fold unstratified CV for a weak signal. Same experimental setup as in additional figure 1(a), but d' = 0.5.

Mentions: The grey lines in figures 1, 2, 3, 5, 6, 7 and 8 show the optimal values for AUC and the optimal (Bayes) error rate for class proportion 0.5. If both optimal AUC and error rate are shown, the line for AUC is solid. The R code and data for the experiments are available from the authors upon request.


Stratification bias in low signal microarray studies.

Parker BJ, Günter S, Bedo J - BMC Bioinformatics (2007)

Simulation results using DLDA and 10-fold unstratified CV for a weak signal. Same experimental setup as in additional figure 1(a), but d' = 0.5.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2211509&req=5

Figure 2: Simulation results using DLDA and 10-fold unstratified CV for a weak signal. Same experimental setup as in additional figure 1(a), but d' = 0.5.
Mentions: The grey lines in figures 1, 2, 3, 5, 6, 7 and 8 show the optimal values for AUC and the optimal (Bayes) error rate for class proportion 0.5. If both optimal AUC and error rate are shown, the line for AUC is solid. The R code and data for the experiments are available from the authors upon request.

Bottom Line: In simulation studies using 10-fold cross-validation, AUC values of less than 0.3 can be observed on random datasets rather than the expected 0.5.Therefore for model selection and evaluation of microarray and other small biological datasets, these methods should be used and unstratified versions avoided.In particular, the commonly used (unbalanced) leave-one-out cross-validation should not be used to estimate AUC for small datasets.

View Article: PubMed Central - HTML - PubMed

Affiliation: Statistical Machine Learning Group, NICTA, Canberra, Australia. brian.bj.parker@gmail.com

ABSTRACT

Background: When analysing microarray and other small sample size biological datasets, care is needed to avoid various biases. We analyse a form of bias, stratification bias, that can substantially affect analyses using sample-reuse validation techniques and lead to inaccurate results. This bias is due to imperfect stratification of samples in the training and test sets and the dependency between these stratification errors, i.e. the variations in class proportions in the training and test sets are negatively correlated.

Results: We show that when estimating the performance of classifiers on low signal datasets (i.e. those which are difficult to classify), which are typical of many prognostic microarray studies, commonly used performance measures can suffer from a substantial negative bias. For error rate this bias is only severe in quite restricted situations, but can be much larger and more frequent when using ranking measures such as the receiver operating characteristic (ROC) curve and area under the ROC (AUC). Substantial biases are shown in simulations and on the van 't Veer breast cancer dataset. The classification error rate can have large negative biases for balanced datasets, whereas the AUC shows substantial pessimistic biases even for imbalanced datasets. In simulation studies using 10-fold cross-validation, AUC values of less than 0.3 can be observed on random datasets rather than the expected 0.5. Further experiments on the van 't Veer breast cancer dataset show these biases exist in practice.

Conclusion: Stratification bias can substantially affect several performance measures. In computing the AUC, the strategy of pooling the test samples from the various folds of cross-validation can lead to large biases; computing it as the average of per-fold estimates avoids this bias and is thus the recommended approach. As a more general solution applicable to other performance measures, we show that stratified repeated holdout and a modified version of k-fold cross-validation, balanced, stratified cross-validation and balanced leave-one-out cross-validation, avoids the bias. Therefore for model selection and evaluation of microarray and other small biological datasets, these methods should be used and unstratified versions avoided. In particular, the commonly used (unbalanced) leave-one-out cross-validation should not be used to estimate AUC for small datasets.

Show MeSH
Related in: MedlinePlus