Power

Power will depend on the study design used -- case-cohort v. case-control -- due to the differences in the number of “controls”. As the proposed method for this study (SKAT) does not conform to a typical power calculation, certain simplifying assumptions are used.

Given the lack of a power model for SKAT, an unmatched case-control design was

log-additive, gene only, unmatched case-control model was assumed. Two-sided Type 1 error of 0.05 was used for both study designs. Initial calculations also included a Bonferroni correction using the assumed number of genes in each pathway. For inflammatory genes the Bonferroni corrected p value= 0.002 and for cell cycle genes p=0.006. Baseline risk was calculated in the cohort.

The case:control ratio was estimated using a hypothetical case-cohort study design. For the hypothetical study a ‘cohort’ was constructed by using the N=523 women in the existing PIN1/2 subcohort and adding the non-cases and an appropriate number of cases from each of the two (PIN1/2 non-subcohort, PIN 3) remaining sampling groups. The appropriate number of cases was chosen to reflect the distribution of cases in the established subcohort (PIN1/2= 87 non-cases and 53 cases, PIN3= 218 non-cases and 134 cases). The total reconstructed cohort was

composed of 1015 women. Table 2.12 outlines the criteria used for each outcome for the power calculations.

Table 2.11 Criteria used in power calculations

Outcome Risk Cases Case:Control Ratio Case-Cohort N=1015

Preterm birth 12% 347 3

SGA 10% 216 5

Isolated PIH 15% 454 2

PE 8% 217 5

Table 2.12 Range of odds ratios with 80% power for each outcome with the specified type 1 error

PTB SGA GHTN PE

Type 1 error Type 1 error Type 1 error Type 1 error

MAF 0.002 0.005 0.05 0.002 0.005 0.05 0.002 0.005 0.05 0.002 0.005 0.05 10% 1.7 1.7 1.5 1.9 1.8 1.6 1.7 1.6 1.5 1.9 1.8 1.6 20% 1.5 1.5 1.4 1.7 1.6 1.5 1.5 1.5 1.4 1.7 1.6 1.5 30% 1.5 1.4 1.3 1.6 1.5 1.4 1.5 1.4 1.3 1.6 1.5 1.4 40% 1.5 1.4 1.3 1.6 1.5 1.4 1.4 1.4 1.3 1.6 1.5 1.4 Abbreviations: PTB preterm birth, SGA small for gestational age, GHTN gestational hypertension, PE preeclampsia, MAF minor allele frequency.

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For the more common outcomes of PTB and GHTN power is adequate at or below OR 1.7 within the full range of MAF. For the less common outcomes however power is adequate only below an OR of 1.9 (Table 2.13).

The applicability of this approach to power calculations is limited given the study design.

The SKAT model will be based on genes and not on single SNPs. While this should increase the overall power to detect a relevant gene, the association between MAF for a single SNP and the resulting power is not as clear.

The Quanto program used for the power calculation relies on an unmatched case-control design. Due to the presence of cases in both the case group and the control group in a case- cohort design, the Quanto method likely under estimates power for the case-cohort design.

The outcomes above are not mutually exclusive and non-independent. “Pure” case groups would be quite small with much lower power.

The above calculations include women of both races. Racially stratified analyses will have much lower power.

The assumption of the Quanto power calculation is that there is a single causative SNP. The power calculated reflects the ability to detect the single causative SNP among a large number of null SNPs.

An alternative approach to power calculation assumes that there exists more than one causative SNP and seeks to assess power to find one of many causative SNPs.222 Under this framework, Table 2.14 outlines the number of causative SNPs which must be assumed to be present to have 80% to find one of them given the range of power to find a single SNP if only 1

SNP is causative. For instance if the power to find a single causative SNP is 2%, the presence of 80 causative SNPs would result in 80% power to find one of them.

Table 2.13 Power to detect multiple risk alleles

Power for a single allele assuming only 1 risk

allele

Number of risk alleles needed to have 80% power to find 1 SNP 0.01 >100 0.02 80 0.03 53 0.04 40 0.05 32 0.06 27 0.08 20 0.10 16 0.12 13 0.15 10 0.20 8 0.25 6 0.30 5

In this study an assumption of 15-20 underlying risk alleles seems reasonable. This would place the target single SNP power in the range of 8% to 10%. Although the previous power calculation suggested adequate single SNP power below OR 1.7-1.9, SNP effects are likely to be much more modest.

Given that sample size, baseline risk and MAF are fixed in this study, the only variable which can be modified to influence power is the Type 1 error. Type 1 error can be considered as a function of the number of tests conducted, with more tests resulting in a lower type 1 error due to multiple comparisons.

Quanto was again used to estimate power for an OR of 1.4 at a range of MAF given four different type 1 errors. Specifications within Quanto were the same as presented in Table 2.12. Given the similarity between power calculations for SGA and PE, only SGA is presented. The

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candidate type 1 errors were chosen based on convenient Bonferroni corrections. The Bonferroni correction for the number of genes in the inflammatory pathway is 0.002. At the other extreme the Bonferroni correction for the total number of SNPs is 0.0001. Midway

between these values, assuming 200 SNPs for analysis would result in a Bonferroni correction of 0.0002 and assuming 100 SNPs would result in a Bonferroni correction of 0.0005.

Table 2.14 Power with OR 1.4 to find one allele with a range of MAF and Type 1 error

PTB SGA GHTN

Type 1 error Type 1 error Type 1 error

MAF 0.0001 0.0002 0.0005 0.002 0.0001 0.0002 0.0005 0.002 0.0001 0.0002 0.0005 0.002 10% 0.08 0.10 0.15 0.26 0.03 0.05 0.07 0.15 0.10 0.13 0.19 0.31 20% 0.25 0.30 0.39 0.54 0.11 0.15 0.21 0.34 0.32 0.38 0.48 0.63 30% 0.38 0.45 0.55 0.69 0.19 0.27 0.32 0.46 0.49 0.56 0.65 0.78 40% 0.46 0.53 0.62 0.76 0.23 0.29 0.37 0.53 0.57 0.64 0.72 0.84

Abbreviations: PTB preterm birth, SGA small for gestational age, GHTN gestational hypertension, PE preeclampsia, MAF minor allele frequency.

Table 2.15 suggests that for the more common outcomes of PTB and GHTN, the study has 80% power to detect a single SNP with OR 1.4 assuming that there are at least 20 causative SNPs on the panel. With a MAF >10% the number of causative SNPs falls to 6. For SGA an assumption of 53 causative SNPs would be needed at the most stringent type 1 error and lowest MAF. However at less stringent type 1 error levels the assumptions about the number of causative SNPs becomes more reasonable (fewer than 30 and often fewer than 10).

As a way of informing the number of SNPs which could reasonably proceed to Stage 2, a goal of a single SNP power of 8%-10% suggests that a type 1 error of 0.0002 to 0.0005 would be a reasonable choice. This type 1 error corresponds to the analysis of 100-200 SNPs in Stage 2. The number of genes that would result in this number of SNPs will depend on the gene.