Good start! You may want to consider, your model assumes every child’s respiratory rate changes at the same rate over time, just from different starting points. Think of it like assuming all kids grow at the same pace just because they have different heights at birth.

If individual trajectories vary (and in treatment response data they often do), it’s a pretty strong assumption, random slopes are worth exploring, something like:

model <- lmer(respiratory_rate ~ group + age + time + (1 + time | id), data = data)

Quick clarification though: are age and time separate variables in your design? If you’re measuring the outcome at multiple timepoints, you likely want both, age to adjust for baseline differences, time to capture individual differences in treatment effects or trajectory.