# Modeling Proportions & Percents

Can Joinpoint be used to model proportions or percents?

### Answer:

Joinpoint can be used to model proportions or percents, and for consistency, assume that percents are transformed to proportions before analysis.

For confidence intervals of the model parameters and related p-values, Joinpoint assumes that the data being analyzed arises from a normal distribution or the number of observations is large enough to use the asymptotic normality of the estimated model parameters.

If ni is the sample size for the ith observation and is large enough that both ni pi and ni(1-pi) are larger than or equal to 10, then the sample proportions can be considered to asymptotically follow a normal distribution with standard error equal to $\sqrt{p_i \left( 1 - p_i \right) / n_i}$.

If the proportions arise from a complex survey, then the standard error from a complex survey analysis statistical package (e.g. SUDAAN) can be used. If ni is not large enough for a normal approximation (that is, either ni pi or ni(1-pi) or both are smaller than 10), then the distribution may be skewed, and Joinpoint results based on asymptotic normality may not be accurate unless the number of observations is large.

To correct heteroscedasticity, one would want to incorporate the standard errors of the proportions and the standard error of $\sqrt{p_i \left( 1 - p_i \right) / n_i}$ can be used. These are the standard errors that are automatically computed and incorporated when proportions are calculated within Joinpoint. If ni is not available, but all the proportions are in approximately the same range, and the sample sizes are known to be approximately the same, then it may not be necessary to enter the standard errors (i.e. in this case all the standard errors are approximately the same, which is the implicit assumption in Joinpoint if no standard errors are entered).

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