Sample size requirements for training high-dimensional risk predictors

Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges

BACKGROUND

In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions.

METHODS

Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 "High-dimensional data" of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD.

RESULTS

The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided.

CONCLUSIONS

This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses.

Lessons and tips for designing a machine learning study using EHR data

Machine learning (ML) provides the ability to examine massive datasets and uncover patterns within data without relying on a priori assumptions such as specific variable associations, linearity in relationships, or prespecified statistical interactions. However, the application of ML to healthcare data has been met with mixed results, especially when using administrative datasets such as the electronic health record. The black box nature of many ML algorithms contributes to an erroneous assumption that these algorithms can overcome major data issues inherent in large administrative healthcare data. As with other research endeavors, good data and analytic design is crucial to ML-based studies. In this paper, we will provide an overview of common misconceptions for ML, the corresponding truths, and suggestions for incorporating these methods into healthcare research while maintaining a sound study design.

Sample size requirements for learning to classify with high-dimensional biomarker panels

A common problem in biomedical research is to calculate the sample size required to learn a classifier using a (possibly high-dimensional) panel of biomarkers. This paper describes a simple method based on a Gaussian approximation for calculating the predictive performance of the learned classifier given the size of the biomarker panel, the size of the training sample, and the optimal predictive performance (expressed as C-statistic Copt) of the biomarker panel that could be obtained if a training sample of unlimited size were available. Under the assumption that the biomarker effect sizes have the same correlation structure as the biomarkers, the required sample size does not depend upon these correlations, but only upon Copt and upon the sparsity of the distribution of effect sizes, defined by the proportion of biomarkers that have nonzero effects. To learn a classifier that extracts 80% of the predictive information, the required case sample size varies from about 0.1 cases per variable for a panel with Copt=0.9 and a sparse distribution of effect sizes (such that 1% of biomarkers have nonzero effect sizes) to nine cases per variable for a panel with Copt=0.75 and a diffuse distribution of effect sizes.

A strategy to build and validate a prognostic biomarker model based on RT-qPCR gene expression and clinical covariates

BACKGROUND

Construction and validation of a prognostic model for survival data in the clinical domain is still an active field of research. Nevertheless there is no consensus on how to develop routine prognostic tests based on a combination of RT-qPCR biomarkers and clinical or demographic variables. In particular, the estimation of the model performance requires to properly account for the RT-qPCR experimental design.

RESULTS

We present a strategy to build, select, and validate a prognostic model for survival data based on a combination of RT-qPCR biomarkers and clinical or demographic data and we provide an illustration on a real clinical dataset. First, we compare two cross-validation schemes: a classical outcome-stratified cross-validation scheme and an alternative one that accounts for the RT-qPCR plate design, especially when samples are processed by batches. The latter is intended to limit the performance discrepancies, also called the validation surprise, between the training and the test sets. Second, strategies for model building (covariate selection, functional relationship modeling, and statistical model) as well as performance indicators estimation are presented. Since in practice several prognostic models can exhibit similar performances, complementary criteria for model selection are discussed: the stability of the selected variables, the model optimism, and the impact of the omitted variables on the model performance.

CONCLUSION

On the training dataset, appropriate resampling methods are expected to prevent from any upward biases due to unaccounted technical and biological variability that may arise from the experimental and intrinsic design of the RT-qPCR assay. Moreover, the stability of the selected variables, the model optimism, and the impact of the omitted variables on the model performances are pivotal indicators to select the optimal model to be validated on the test dataset.