Binomial exact confidence intervals for multiple proportions

Question

I am trying to calculate a whole long list of binomial confidence intervals for proportions. I have a list of samples with a column for village number (24 villages) and a column with + or - for the test result (PCR). I need to know the proportion of + test results in each village and the corresponding confidence intervals. The code below gives me the confidence intervals for the proportion of the whole set but I need to break it down by village.

a = sum(dat$PCR=='+')
p = length(dat$PCR)
binom.test(a, p, p = 0.5,
       alternative = c("two.sided", "less", "greater"),
       conf.level = 0.95)

If you show us a sample of your data (paste into question the output dput(data_sample)) it will be easier to help you. — eipi10

eipi10 eipi10 · Accepted Answer · 2017-04-24T05:48:04

Here's a tidyverse approach, illustrated with fake data:

library(tidyverse)
library(broom)

# Fake data
set.seed(2)
dat = data.frame(village=rep(LETTERS[1:24], each=100), 
                 PCR=sample(c("+","-"), 100*24, replace=TRUE))

# Set "+" to be the reference level
dat$PCR = factor(dat$PCR, levels=c("+","-"))

Now, the code below first splits dat by village and feeds the result to map_df. map_df runs binom.test on the data for each level of village. binom.test returns a list, but wrapping it in tidy turns the output of binom.test into a "tidy" data frame. So we end up with a data frame where each row is the output of binom.test for one village.

split(dat, dat$village) %>% 
        map_df(~ tidy(binom.test(table(.x$PCR), p=0.5, 
                      alternative = c("two.sided", "less", "greater"),
                      conf.level = 0.95)), .id="Village")

binom.test.results

   Village estimate statistic    p.value parameter  conf.low conf.high              method alternative
1        A     0.55        55 0.36820162       100 0.4472802 0.6496798 Exact binomial test   two.sided
2        B     0.54        54 0.48411841       100 0.4374116 0.6401566 Exact binomial test   two.sided
3        C     0.48        48 0.76435343       100 0.3790055 0.5822102 Exact binomial test   two.sided
4        D     0.55        55 0.36820162       100 0.4472802 0.6496798 Exact binomial test   two.sided
5        E     0.43        43 0.19334790       100 0.3313910 0.5328663 Exact binomial test   two.sided
6        F     0.47        47 0.61729941       100 0.3694052 0.5724185 Exact binomial test   two.sided
7        G     0.49        49 0.92041076       100 0.3886442 0.5919637 Exact binomial test   two.sided
8        H     0.49        49 0.92041076       100 0.3886442 0.5919637 Exact binomial test   two.sided
9        I     0.53        53 0.61729941       100 0.4275815 0.6305948 Exact binomial test   two.sided
10       J     0.50        50 1.00000000       100 0.3983211 0.6016789 Exact binomial test   two.sided
11       K     0.49        49 0.92041076       100 0.3886442 0.5919637 Exact binomial test   two.sided
12       L     0.50        50 1.00000000       100 0.3983211 0.6016789 Exact binomial test   two.sided
13       M     0.45        45 0.36820162       100 0.3503202 0.5527198 Exact binomial test   two.sided
14       N     0.59        59 0.08862608       100 0.4871442 0.6873800 Exact binomial test   two.sided
15       O     0.41        41 0.08862608       100 0.3126200 0.5128558 Exact binomial test   two.sided
16       P     0.50        50 1.00000000       100 0.3983211 0.6016789 Exact binomial test   two.sided
17       Q     0.54        54 0.48411841       100 0.4374116 0.6401566 Exact binomial test   two.sided
18       R     0.52        52 0.76435343       100 0.4177898 0.6209945 Exact binomial test   two.sided
19       S     0.44        44 0.27125302       100 0.3408360 0.5428125 Exact binomial test   two.sided
20       T     0.55        55 0.36820162       100 0.4472802 0.6496798 Exact binomial test   two.sided
21       U     0.47        47 0.61729941       100 0.3694052 0.5724185 Exact binomial test   two.sided
22       V     0.52        52 0.76435343       100 0.4177898 0.6209945 Exact binomial test   two.sided
23       W     0.54        54 0.48411841       100 0.4374116 0.6401566 Exact binomial test   two.sided
24       X     0.51        51 0.92041076       100 0.4080363 0.6113558 Exact binomial test   two.sided

Binomial exact confidence intervals for multiple proportions

1 Answers