188.Proportions and their Confidence Intervals_jingju

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188.Proportions and their Confidence Intervals

(2013-05-22 06:16:11)

标签：

rates

ci

杂谈

分类：统计分享

Introduction

A proportion refers to the fraction of the total that possesses a certain attribute. Estimating the confidence interval for the binomial proportion is not a challenge any more in statistics. The FREQ procedure in SAS will do the entire job for you without programming any formula.
The following analysis was from a simulated study which is involving four different groups, i.e., test, placebo, standard and other, during a certain period of time, to compare the crude proportions of positive responses to a specific test among the four groups. Of note, in the data, there is a zero count in group 'other' that may cause estimation problems in some methods, in particular, the classical method of calculating a Wald confidence interval.

Code

proc format;

value OTfmt

1 ='positive' 2 ='negative' 3 ='unknown'

;

run;

data respire;

input treat $ outcome count @@;

datalines;

test 1 20 test 2 120 test 3 2

placebo 1 48 placebo 2 96 placebo 3 2

standard 1 34 standard 2 108 standard 3 3

other 1 0 other 2 3 other 2 1 other 3 2

;

proc freq data =respire order=data noprint;

weight count/zeros; *Not miss the zero counts;

tables treat*outcome/list out =list; format outcome OTfmt.;

run;

ods select BinomialProp BinomialCLs;

proc freq data =list order=data;

by treat notsorted;

tables outcome/binomial(all); *Option ALL since SAS 9.2 version;

weight count/zeros; format outcome OTfmt.;

run;

Results (selected)

Proportion of positive response for test group.

The SAS System 18:10 Tuesday, May 21, 2013 1

------------------------------------------- treat=test -------------------------------------------

The FREQ Procedure

Binomial Proportion

for outcome = positive

-------------------------------------------

Proportion 0.1408

ASE 0.0292

Type 95% Confidence Limits

Wald 0.0836 0.1981

Wilson 0.0931 0.2075

Agresti-Coull 0.0923 0.2083

Jeffreys 0.0911 0.2051

Clopper-Pearson (Exact) 0.0882 0.2091

Proportion of positive response for other group. As seen, there is no or a degenerate confidence interval (0,0) in Wald method.

------------------------------------------ treat=other -------------------------------------------

The FREQ Procedure

Binomial Proportion

for outcome = positive

-------------------------------------------

Proportion 0.0000

ASE 0.0000

Type 95% Confidence Limits

Wald 0.0000 0.0000

Wilson 0.0000 0.3903

Agresti-Coull 0.0000 0.4428

Jeffreys 0.0000 0.3304

Clopper-Pearson (Exact) 0.0000 0.4593

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