As I understand it, you have 4 treatment groups - and for each child, you have several binary outcomes? You could build a score for each patient by adding the incidence of each potentially adverse outcome. Then compare the 4 groups based on the score.
a) if your score is the result of adding up a lot of binary outcomes (say 8 or more), then do a one-way ANOVA, assuming "normality" or your score.
b) If there are fewer scores (say, 4 items), then you could do a generalized linear model with binomial response and where "treatment group" is the explanatory variable.
If you go with Peter Flom's suggestion of doing a logistic regression on each outcome, be sure to adjust the p-value. Using 5% will boost the probability of a type 1 error somewhere in your results - so take something smaller. You want $1-(1-p)^r \leq 0.05$, where $r$ is the number of outcomes and $p$ will be the significance level for each test. For 4 outcomes, you want to go with a significance level of around 1% or 2%.