Numerical precision issue: p-values of zero in MaAsLin3 (possibly related to multcomp)

Downstream analysis and statistics MaAsLin
1

Hi,

I encountered a numerical precision issue in MaAsLin3 where an abundance association returned a p-value of exactly zero, resulting in individual and joint FDR values of zero.

I investigated this and found that the issue may originate from the multcomp package, which MaAsLin3 uses for median-comparison testing.

The underlying linear regression produced a coefficient of 0.05755 and a standard error of 0.00634, which I could reproduce independently. However, testing against the reported median null hypothesis using multcomp::glht() also returned a p-value of zero.

For the corresponding simplified contrast (t = 8.85), I obtained:

# Numerically unstable calculation
2 * (1 - pt(abs(t_stat), df))
# 0

# Numerically stable calculation
2 * pt(abs(t_stat), df, lower.tail = FALSE)
# 4.76e-18

This suggests that the zero p-value results from numerical precision loss when calculating upper-tail probabilities, rather than an issue with the underlying regression.

Is this a known issue, and would it be more appropriate to address it with developers of multcomp?

Thanks for your help and for maintaining MaAsLin3!

Best wishes,
Daniel

2

Hi,

Do you need the exact value or is it fine to just treat it as “<2e^-16” (which I think is the R cut-off in this case)? Presumably the p-value is very very small and exactly how small shouldn’t affect subsequent analyses.

Will

3

Hi Will,

Yes, treating it as <2e-16 is fine. Thank you for clarifying!

Best,
Daniel