PubMed · 1489453
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J M Burke, C P Solomon. Ordinal and interval data analysis.. https://doi.org/10.1007/bf02599468
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The fraction of proteins that retain wild-type function after mutation has long been observed to decline exponentially as the average number of mutations per gene increases. Recently, several groups have used error-prone polymerase chain reactions (PCR) to generate libraries with 15 to 30 mutations per gene, on average, and have reported that orders of magnitude more proteins retain function than would be expected from the low-mutation-rate trend. Proteins with improved or novel function were isolated disproportionately from these high-error-rate libraries, leading to claims that high mutation rates unlock regions of sequence space that are enriched in positively coupled mutations. Here, we show experimentally that error-prone PCR produces a broader non-Poisson distribution of mutations consistent with a detailed model of PCR. As error rates increase, this distribution leads directly to the observed excesses in functional clones. We then show that while very low mutation rates result in many functional sequences, only a small number are unique. By contrast, very high mutation rates produce mostly unique sequences, but few retain function. Thus an optimal mutation rate exists that balances uniqueness and retention of function. Overall, high-error-rate mutagenesis libraries are enriched in improved sequences because they contain more unique, functional clones. Our findings demonstrate how optimal error-prone PCR mutation rates may be calculated, and indicate that "optimal" rates depend on both the protein and the mutagenesis protocol.
Group randomized trials (GRT) are often designed with relatively little preliminary data available to estimate key parameters. In this paper, however, the opposite situation is considered-very good baseline data are available on the primary outcome of interest. These data can then be used to inform key design and analysis decisions such as (i) should the trial be designed as an unmatched or pair-matched study, or stratified in some other fashion; (ii) is analysis of "change from baseline" preferable to using end-of-study data alone; and (iii) what power might be expected by pursuing these various strategies. The results are applied to a GRT for sexually transmitted diseases prevention in Peru.