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The phrase "are substantially higher when" is correct and usable in written English.
It can be used in contexts where you are comparing values or conditions that lead to a significant increase in something.
Example: "The costs of production are substantially higher when raw materials are sourced from overseas."
Alternatives: "are significantly greater when" or "are much higher when".
Exact(3)
Similarly, health survey participation and response rates are substantially higher when the default strategy is opt-out compared with opt-in [ 45, 46].
For all three outcomes, the estimates are substantially higher when based on mortality, although for CB and emphysema few RRs are so based.
Nonetheless accuracies and F-scores are substantially higher when using CRFs compared with SVMs, reflecting that classification using sequence models is beneficial in recognizing the semantic classes of these sentences.
Similar(57)
Both the separation efficiency and injection repeatability were found to be substantially higher when using the novel volumetric injection approach compared to electrokinetic injection (performed in the same chip).
The specificity of the ALS assay was substantially higher when healthy controls were considered instead of non-TB controls (data not shown).
Not surprisingly, bacterial diversity was substantially higher when determined by 16S rRNA gene-based pyrosequencing analysis as compared to the culture-based analyses.
While this figure is lower than that reported for ancient material retrieved from permafrost-preserved mammoth samples [32], [47], it is substantially higher when compared to other palaeogenetic studies where the proportion of endogenous sequences was estimated at between ∼0.3%–6.0% [48], [49], [50], [51].
Moreover, the estimates of πS and πN were substantially higher when rare variants were included (table 1).
This rate is substantially higher when compared with previously reported rates of stroke in AF patients with or without CKD.
Compared to conventional doxorubicin, intratumoural doxorubicin levels in tumour-bearing mice were substantially higher when using PLD.
Similarity Indices obtained using the DP algorithm were substantially higher when crossbreeding was assumed compared to when random mating was assumed (Table 6).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com