# Example R packages required
library(cardx) R vs SAS Confidence Intervals for Proportions
Introduction
The methods to use for calculating a confidence interval (CI) for a proportion depend on the type of proportion you have.
1 sample proportion (1 proportion calculated from 1 group of subjects)
2 sample proportions and you want a CI for the difference in the 2 proportions.
If the 2 samples come from 2 independent samples (different subjects in each of the 2 groups)
If the 2 samples are matched (i.e. the same subject has 2 results, one on each group [paired data]).
The method selected is also dependent on whether your proportion is close to 0 or 1 (or near to the 0.5 midpoint), and your sample size.
For more technical derivation and reasons why you would use one method above another see the corresponding SAS page.
The tables below provide an overview of findings from R & SAS, for calculation of CIs, for a Single Sample Proportion and for calculation of a difference between 2 matched pair proportions or 2 independent sample proportions.
General Comparison Table For Single Sample Proportions
See the corresponding SAS page and R page for results showing a single set of data run through both SAS and R.
| Analysis of One Sample Proportion | Supported in R | Supported in SAS | Results Match |
|---|---|---|---|
| Clopper-Pearson Exact | Yes {cardx} | Yes (default) | Yes |
| Normal approximation (Wald Method) | Yes {cardx} | Yes (default) | Yes |
| Normal approximation (Wald Method) with continuity correction | Yes {cardx} | Yes | Yes |
| Wilson (Score, Altman, Newcombe) method | Yes {cardx} | Yes | Yes |
| Wilson (Score, Altman, Newcombe) method with continuity correction | Yes {cardx} | Yes | Yes |
| Agresti Coull | Yes {cardx} | Yes | Yes |
| Jeffreys Bayesian HPD | Yes {cardx} | Yes | Yes |
| midp | Yes {PropCIs} | Yes | results match to the 3rd decimal place |
| Blaker | Yes {PropCIs} | Yes | results match to the 5th decimal place |
| Wilson Stratified score | Yes {cardx} | No | NA |
General Comparison Table For Two Matched Samples Proportions
| Analysis of Two Matched Sample Proportions | Supported in R | Supported in SAS | Notes |
|---|---|---|---|
| Exact method | Yes {ExactCIdiff} | No | |
| Normal approximation (Wald Method) | No | No (proc freq does CIs for the risk difference, not the difference between two proportions) | Using the equations provided in the SAS page, You could do this programatically in either package |
| Wilson (Score method or the Altman, Newcombe method) | No | No (proc freq does CIs for the risk difference, not the difference between two proportions) | Using the equations provided in the SAS page, You could do this programatically in either package |
Calculating the Normal approximation and Wilson methods by hand and comparing it to the Exact method gave similar results for the 1 example demonstrated indicating as long as the proportion of responders is not close to 0 or 1, then the faster computation of the approximation methods may be easier to implement than the exact method and produce similar results. Hence {ExactCIdiff} is not recommended for most scenarios.
| Method Name | Calculated Using matched pair example from R & SAS pages | Lower 95% CI | Upper 95% CI |
|---|---|---|---|
| Exact | R | -0.00339 | 0.38065 |
| Normal | by hand using equation from SAS page | 0.00911 | 0.38289 |
| Wilson | by hand using equation from SAS page | 0.00032 | 0.36739 |
General Comparison Table For Two Independent Samples Proportions
| Analysis of Two Independant Sample Proportions | Supported in R | Supported in SAS | Results Match |
|---|---|---|---|
| Normal approximation (Wald Method) | Yes {cardx} ard_stats_prop_test function uses stats::prop.test |
Yes (default) | Yes and results match by hand calculation Note that documentation for stats::prop.test says it’s using newcombe method. However, the results match the Normal Approximation (wald) method. |
| Normal approximation (Wald Method) with continuity correction | Yes {cardx} as per above but with correct=TRUE | Yes | Yes Note that documentation for stats::prop.test says it’s using newcombe method. However, the results match the Normal Approximation (wald) method. |
| Wilson (Score, Altman, Newcombe) method | No | Yes | SAS results match by hand calculation |
| Wilson (Score, Altman, Newcombe) method with continuity correction | No | Yes | SAS results match by hand calculation |
Prerequisites: R Packages
See the R page for more detail.