\DeclareMathOperator{\corr}{corr} \DeclareMathOperator{\var}{var}
The CoRpower
package assumes that $P(Y^{\tau}(1)=Y^{\tau}(0))=1$ for the biomarker sampling timepoint $\tau$, which renders the CoR parameter $P(Y=1 \mid S=s_1, Z=1, Y^{\tau}=0)$ equal to $P(Y=1 \mid S=s_1, Z=1, Y^{\tau}(1)=Y^{\tau}(0)=0)$, which links the CoR and biomarker-specific treatment efficacy (TE) parameters. Estimation of the latter requires outcome data in placebo recipients, and some estimation methods additionally require availability of a baseline immunogenicity predictor (BIP) of $S(1)$, the biomarker response at $\tau$ under assignment to treatment. In order to link power calculations for detecting a correlate of risk (CoR) and a correlate of TE (coTE), CoRpower
allows to export simulated data sets that are used in CoRpower
's calculations and that are extended to include placebo-group and BIP data for harmonized use by methods assessing biomarker-specific TE. This vignette aims to describe CoRpower
's algorithms, and the underlying assumptions, for simulating placebo-group and BIP data. The exported data sets include full rectangular data to allow the user to consider various biomarker sub-sampling designs, e.g., different biomarker case:control sampling ratios, or case-control vs. case-cohort designs.
Estimate $Spec(\phi_0)$ by $$\widehat{Spec}(\phi_0) = \frac{#{S^{\ast}_b \leq \phi_0, X^{\ast}_b \leq \theta_0}}{#{X^{\ast}_b \leq \theta_0}}\,$$ etc.
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