Beyond the E-Value: Stratified Statistics for Protein Domain Prediction

E-values have been the dominant statistic for protein sequence analysis for the past two decades: from identifying statistically significant local sequence alignments to evaluating matches to hidden Markov models describing protein domain families. Here we formally show that for “stratified” multiple hypothesis testing problems—that is, those in which statistical tests can be partitioned naturally—controlling the local False Discovery Rate (lFDR) per stratum, or partition, yields the most predictions across the data at any given threshold on the FDR or E-value over all strata combined. For the important problem of protein domain prediction, a key step in characterizing protein structure, function and evolution, we show that stratifying statistical tests by domain family yields excellent results. We develop the first FDR-estimating algorithms for domain prediction, and evaluate how well thresholds based on q-values, E-values and lFDRs perform in domain prediction using five complementary approaches for estimating empirical FDRs in this context. We show that stratified q-value thresholds substantially outperform E-values. Contradicting our theoretical results, q-values also outperform lFDRs; however, our tests reveal a small but coherent subset of domain families, biased towards models for specific repetitive patterns, for which weaknesses in random sequence models yield notably inaccurate statistical significance measures. Usage of lFDR thresholds outperform q-values for the remaining families, which have as-expected noise, suggesting that further improvements in domain predictions can be achieved with improved modeling of random sequences. Overall, our theoretical and empirical findings suggest that the use of stratified q-values and lFDRs could result in improvements in a host of structured multiple hypothesis testing problems arising in bioinformatics, including genome-wide association studies, orthology prediction, and motif scanning.Author Summary: Despite decades of research, it remains a challenge to distinguish homologous relationships between proteins from sequence similarities arising due to chance alone. This is an increasingly important problem as sequence database sizes continue to grow, and even today many computational analyses require that the statistics of billions of sequence comparisons be assessed automatically. Here we explore statistical significance evaluation on data that is stratified—that is, naturally partitioned into subsets that may differ in their amount of signal—and find a theoretically optimal criterion for automatically setting thresholds of significance for each stratum. For the task of domain prediction, an important component of efforts to annotate protein sequences and identify remote sequence homologs, we empirically show that our stratified analysis of statistical significance greatly improves upon a combined analysis. Further, we identify weaknesses in the prevailing random sequence model for assessing statistical significance for a small subset of domain families with repetitive sequence patterns and known biological, structural, and evolutionary properties. Our theoretical findings in statistics are relevant not only for identifying protein domains, but for arbitrary stratified problems in genomics and beyond.