Algorithm 1.

DSILT Algorithm.

Input: ${𝓓}^{(\text{m})}$ at the $m^{\text{th}}$ DC for $m\in [M]$.
1.	For each $k\in [K]$, fit integrative sparse regression under DataSHIELD with ${𝓓}_{[-k]}^{(•)}$:
	(a) At the $m^{\text{th}}$ DC, construct cross-fitted summary statistics based on local LASSO estimator, and send them to the AC;
	(b) Obtain the integrative estimator ${\tilde{\mathit{\beta }}}_{[-k]}^{(•)}$ at AC and send them back to each DC.
2.	Obtain debiased group test statistics:
	(a) For each $k$, at the $m^{\text{th}}$ DC, obtain the updated summary statistics based on ${\tilde{\mathit{\beta }}}_{[-k]}^{(•)}$ and ${𝓓}_{[k]}^{(\text{m})}$, and send them to the AC;
	(b) At the AC, construct cross-fitted debiased group estimators $\left\{{\breve{\zeta }}_j,j\in 𝓗\right\}$.
3.	Construct a multiple testing procedure based on the test statistics from Step 2.