Hi organizers, I've been working through the PGK2 selection data and have a few questions about how the Z-score columns are computed. The wiki cites Faver et al. (2019) and gives Z = (observed − expected)/σ, but the empirical behaviour of these columns has some features I'd like to understand better before building on them. Observations from PGK2_selection.parquet (7,703,070 rows): 1. **zscore_PGK2 is strictly positive.** The range is [0.0042, 2.6208], with no negative or zero values anywhere in the file. Only 11 rows exceed 2. 2. **zscore\_PGK2 is close to proportional to count\_PGK2 within a sub-library.** Regressing Z on count through the origin for rows with count > 10 gives R² ≥ 0.96 in every sub-library with more than a handful of such rows, with slopes ranging from 0.0022 (qDOS11, qDOS18\_3) to 0.0127 (qDOS42\_2) 3. **At fixed count, zscore still varies substantially**, with qDOS11 singletons for example spanning roughly 0.003 to 0.47. Questions: - **How is the expected count defined?** Is it derived from sequencing of the naive (pre-selection) library, or computed from building-block marginal frequencies within the selection data itself, or something else? - **What is σ?** Point 2 suggests something roughly constant per sub-library rather than √(expected). - **Are negative Z values possible in principle, and have they been clipped or otherwise not computed?** Under a marginal-frequency expectation I'd expect compounds that underperform their building blocks' predicted enrichment to be common, and it isn't obvious to me where that population is in the file. - **Are Z values comparable across sub-libraries?** Given the spread in point 2, I want to check whether a global Z ranking is appropriate or whether within-library ranking is the intended use. Happy to share code for any of the above if useful. Thanks! - Alex

Created by Alex Izvorski memes
Seth (@vonboss) - Thanks, that's a very helpful explanation. A follow-up request: would it be possible to release the naive sequencing data - the read counts from the pre-selection library run? With those in hand we could compute enrichment as po/pi directly. Recovering pi by inverting the Z-score is unreliable, and in any case I assume pi is modelled from per-synthon frequencies rather than read out directly for every molecule. If the raw naive data isn't available, the naive synthon frequencies would also be useful. Thanks! — Alex
Alex (@memes), The normalized Z-score was calculated by the data producer (Baylor College of Medicine). I am not clear on all of the implementation details, but here is my current understanding: 1. **Expected counts:** Conceptually, the Z-score can be understood as comparing the observed count of a molecule in the protein selection with the count expected based on its representation in the naïve library. In practice, however, the normalized Z-score calculation only requires the corresponding proportions: ($p_i$), the proportion of reads for a molecule in the naïve sequencing experiment, and ($p_o$), its proportion in the protein selection. The Faver normalized Z-score is: $z_n = \frac{p_o-p_i}{\sqrt{p_i(1-p_i)}}$ 2. **Standard deviation:** Faver et al. starts with the binomial sampling model, where the standard deviation of the count is ($\sqrt{n p_i(1-p_i)}$). The normalized Z-score removes the dependence on sequencing depth by dividing the conventional Z-score by ($\sqrt n$), leaving ($\sqrt{p_i(1-p_i)}$) in the denominator. Thus, the Z-score reflects the difference between the observed and expected proportions relative to the sampling variability expected under the binomial model. 3. **Negative Z-scores:** Negative values should be theoretically possible when the observed count is below the expected count. However, I have not seen negative normalized Z-score values in the other datasets we've received from Baylor, and I am not aware of any clipping or filtering. It is possible that the expected count is <1 for essentially all molecules represented in the file. 4. **Comparability across sub-libraries:** It is common practice in DEL analysis to calculate enrichment metrics separately for different sub-libraries. One motivation for the Faver normalized Z-score was specifically to facilitate comparison of enrichment across parallel DEL selections. So, in principle, the normalized Z-score can be used to compare and rank compounds across sub-libraries. However, we have not independently validated how well normalized Z-scores perform for comparing compounds across sub-libraries.
Hello Alex ( @memes ), I think @vonboss and @jmchap might have the answers you are looking for. Luca

Clarification on the definition of the zscore columns page is loading…