Genome-wide screens for effective siRNAs through assessing the size of siRNA effects

BMC Research Notes

Table 1 SSMD-based decision rules and their false negative levels (FNLs) and restricted false positive levels (RFPLs) for hit selection in RNAi HTS experiments

I: Select up-regulated siRNAs (c₁ ≥ c₂ ≥ 0)
Selection Criterion	FNL	RFPL
Ia: $\hat{β}$ ≥ β*	$F_{t (ν, b c_{1})} (\frac{β *}{k})$	$1 - F_{t (ν, b c_{2})} (\frac{β *}{k})$
Ib: $\hat{β} \geq k Q_{t (ν, b c_{1})} (α_{1})$	α ₁	$1 - F_{t (ν, b c_{2})} (Q_{t (ν, b c_{1})} (α_{1}))$
Ic: $\hat{β} \geq k Q_{t (ν, b c_{2})} (1 - α_{2})$	$F_{t (ν, b c_{1})} (Q_{t (ν, b c_{2})} (1 - α_{2}))$	α ₂
II: Select down-regulated siRNAs ( c₁ ≤ c₂ ≤ 0)
Selection Criterion	FNL	RFPL
IIa: $\hat{β}$ ≤ β*	$1 - F_{t (ν, b c_{1})} (\frac{β *}{k})$	$F_{t (ν, b c_{2})} (\frac{β *}{k})$
IIb: $\hat{β} \leq k Q_{t (ν, b c_{1})} (1 - α_{1})$	α ₁	$F_{t (ν, b c_{2})} (Q_{t (ν, b c_{1})} (1 - α_{1}))$
IIc: $\hat{β} \leq k Q_{t (ν, b c_{2})} (α_{2})$	$1 - F_{t (ν, b c_{1})} (Q_{t (ν, b c_{2})} (α_{2}))$	α ₂

Notes:
(i) $\hat{β}$ is the estimate of SSMD and β* is a cutoff of SSMD; $\hat{β}$ = kT where T has a noncentral t-distribution with degree of freedom ν and non-central parameter bβ, namely T ~t(ν, bβ); F_{t(ν, bβ)}(·) and Q_{t(ν, bβ)}(α) are the cumulative distribution function and the α quantile of t(ν, bβ) respectively.
(ii) For an unpaired difference, $\hat{β} = \frac{{\bar{X}}_{1} - {\bar{X}}_{2}}{\sqrt{\frac{2}{K} ((n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2})}}$ and $T = \frac{({\bar{X}}_{1} - {\bar{X}}_{2}) / \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}}}{\sqrt{((n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}) / (N - 2)}}$ where $K = 2 \cdot {(\frac{Γ (\frac{N - 2}{2})}{Γ (\frac{N - 3}{2})})}^{2} \approx N - 3.5$ , N = n₁ + n₂, and n₁, ${\bar{X}}_{1}$ , s₁, n₂, ${\bar{X}}_{2}$ , s₂ are sample size, mean and standard deviation in two groups respectively; $k = \sqrt{\frac{K}{2 (N - 2)} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}$ , ν = N - 2, $b = \frac{\sqrt{2}}{\sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}}}$ .
(iii) For a paired difference, $\hat{β} = \frac{Γ (\frac{n - 1}{2})}{Γ (\frac{n - 2}{2})} \sqrt{\frac{2}{n - 1}} \frac{\bar{D}}{s_{D}}$ and $T = \frac{\sqrt{n} \bar{D}}{s_{D}}$ where n, $\bar{D}$ and s_Dare sample size, sample mean and standard deviation of a paired difference respectively; $k = \frac{Γ (\frac{n - 1}{2})}{Γ (\frac{n - 2}{2})} \sqrt{\frac{2}{n (n - 1)}}$ , ν = n - 1, $b = \sqrt{n}$ .

ISSN: 1756-0500