Secondary analysis
The strength of the effect of the individual offer increased as more family members received a prior or contemporaneous offer of the incentive, further supporting the main hypothesis. Effect sizes increased from 6.5% (95% CI: 5.3–7.7) among participants with no family members who received the offer to 26.3% (95% CI: 23.5–29.0) among participants with three family members who received it. The effect size of the individual incentive appeared not to change substantially when four (RD: 25.5, 95% CI: 20.2–30.7) or five or more (RD: 24.8, 95% CI: 20.7–28.9) family members received the offer. A linear trend test showed that for each additional family member who was offered the incentive, the risk difference for the effect of the incentive on testing uptake increased by 4.8% (95% CI: 2.4−7.2) on average.