Statistical analysis
cirrhosis
REGRESSION, CIRRHOSIS
We estimated a 10% base response rate for the usual care arm based on prior studies and outreach programs. Based on a preliminary data review, we estimated that we would be able to identify approximately 600 eligible patients across the 3 batches. This sample size would provide 80% power to detect a 13 percentage point increase in response rate for the Letter + Order arm compared to the Usual Care arm (estimated 23%) and a 13 percentage point increase for the Letter + Order + Incentive arm compared to the Letter + Order arm (estimated 36%) using a two-tailed chi-squared test of proportions and a type 1 error rate of 0.025, accounting for 2 pairwise comparisons with Bonferroni correction (0.05/2).The chi-squared test of proportions was used to calculate the differences, 95% CIs, and We performed prespecified exploratory subgroup analyses for the primary outcome by age, sex, race/ethnicity, income, etiology of cirrhosis, provider and specialty, prior gastrointestinal clinic visits, and patient portal status. ORs for the treatment effects within subgroups were calculated using a multivariable logistic regression model with interaction terms. The treatment-by-subgroup interaction terms were analyzed one at a time in separate multivariable models. For the purposes of these analyses, age and income were represented as categorical variables. All analyses were performed using Stata version 15.0 (Stata Corp LP, College Station, Texas).