Confidence Interval for ratio (response time 2 / response time 1) We have a population of n=1000, nine binary responses (0 symptom absent, 1 present), and 2 timepoints. Note that some of the responses are heavily skewed, only 1% of the subjects are in the "symptom present" category at baseline for the most skewed response. 
We calculate the change over time as ratio: 
participants with symptoms present at time2 / participants with symptoms present at time1. 
This leads to increases between 100% and 600%. 
Now we want to examine the confidence intervals around these changes. How would you go about this?
 A: In your case, you've calculated a special case of a Rate Ratio (RR) since you have $n=1000$ in your denominator at time $t=1$ and $t=2$. For independent data, you can calculate a confidence interval using a binomial model for risk using the following formula:
$RR = a / b$
$\log \left( RR \right) = \log(a) - \log(b)$
$\mbox{SE} \left( \log \left( RR \right) \right) = 1/a + 1/b$
So the 95% CI is
$\mbox{Lower} = \exp \left(\log(a) - \log(b) - 1.96 * (1/a + 1/b) \right)$
$\mbox{Upper} = \exp \left(\log(a) - \log(b) + 1.96 * (1/a + 1/b) \right)$
Note it's not a symmetric interval!
For dependent data, you can estimate a matched-pair odds ratio using a similar formulation. Except for these data you must consider the 2 by 2 contingency table of the following form
$$
\begin{array}{ccc}
 & \text{Status at Baseline} & \\
& Case & Control \\
\text{Status at Followup} & & \\
Case & a & b \\
Control & c & d\\
\end{array}
$$
The Mcnemar's paired odds ratio is $b / c$. 
Note this is actually an odds ratio, not a risk ratio. However, inference about whether the status at follow-up was more likely to produce cases is equivalently tested by determining whether this odds ratio is equal to 1.
The 95% confidence interval for the matched pair odds ratio is given by:
$\text{Lower} = \exp \left( \log \left( b / c \right) - 1.96 * (1/b + 1/c)\right)$
$\text{Upper} = \exp \left( \log \left( b / c \right) + 1.96 * (1/b + 1/c)\right)$
To actually get a confidence interval for the risk ratio, you would have to make some assumptions about the correlation structure of the data using a GLM. However, it's much more common to see analyses of paired binary data using the McNemar's test.
