pairwiseCI (version 0.1-19)

pairwiseCImethodsProp: Confidence intervals for two sample comparisons of binomial proportions

Description

For the comparison of two independent samples of binomial observations, confidence intervals for the difference (RD), ratio (RR) and odds ratio (OR) of proportions are implemented.

Usage

Prop.diff(x, y, conf.level=0.95, alternative="two.sided", CImethod=c("NHS", "CC", "AC"), ...)
Prop.ratio(x, y, conf.level=0.95, alternative="two.sided", CImethod=c("Score", "GNC"))
Prop.or(x, y, conf.level=0.95, alternative="two.sided", CImethod=c("Exact", "Woolf"), ...)

Arguments

x

observations of the first sample: either a vector with number of success and failure, or a data.frame with two columns (the success and failures))

y

observations of the second sample: either a vector with number of success and failure, or a data.frame with two columns (the success and failures))

alternative

character string, either "two.sided", "less" or "greater"

conf.level

the comparisonwise confidence level of the intervals, where 0.95 is default

CImethod

a single character string, see below for details

...

further arguments to be passed to the individual methods, see details

Value

• A list containing:
• conf.int
  a vector containing the lower and upper confidence limit
• estimate
  a single named value

Details

Generally, the input are two vectors x and y giving the number of successes and failures in the two samples, or, alternatively, two data.frames x and y each containing one column for the successes and one column for the failures, and the rows containing repeated observations from the same treatment. Please note, that except for function prop.or with CImethod="Quasibinomial" the confidence intervals available in this function are based on sums over the rows of x and y and hence do NOT APPROPRIATELY account for extra-binomial variability between repeated observations for the same treatment!

• Prop.diffcalculates the asymptotic Continuity Corrected confidence interval for the difference of proportions by callingprop.testin packagestats. See?prop.testfor details. NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!
• Prop.diffwithCImethod="AC"Calculates the Agresti-Caffo-Interval (Agresti and Caffo, 2000). NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!
• Prop.diffwithCImethod="NHS"Calculates Newcombes Hybrid Score Interval (Newcombe, 1998). NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!
• Prop.ratiowithCImethod="GNC"calculates the crude interval for the ratio of proportions according to Gart and Nam (1988), based on normal approximation on the log-scale. NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!
• Prop.ratiowithCImethod="Score"calculates the Score interval for the ratio of proportions according to Gart and Nam (1988), based on a Chi-Square approximation. NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!
• Prop.orwithCImethod="Woolf"calculates the adjusted Woolf confidence interval for the odds ratio of proportions as, e.g., described in Lawson (2005). NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!
• Prop.orwithCImethod="Exact"calculates the exact confidence interval for the odds ratio of proportions corresponding to Fishers exact test, by calling tofisher.testinstats. For details, see?fisher.test. NOTE: When there are repeated observations (input as a data.frame with several rows), intervals are calculated based on the sums over the rows!

References

• Newcombe R.G. (1998):Interval Estimation for the Difference Between Independent Proportions: Comparison of Eleven Methods. Statistics in Medicine 17, 873-890.
• Agresti, A. and Caffo, B. (2000):Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. American Statistician 54 (4), 280-288.
• Gart, JJ and Nam, J (1988): Approximate interval estimation of the ratio of binomial parameters: A review and corrections for skewness. Biometrics 44, 323-338.Dann, RS and Koch, GG (2005): Review and evaluation of methods for computing confidence intervals for the ratio of two proportions and considerations for non-inferiority clinical trials. Journal of Biopharmaceutical Statistics, 15, 85-107.
• Lawson, R (2005): Small sample confidence intervals for the odds ratio. Communication in Statistics Simulation and Computation, 33, 1095-1113.
• Venables WN and Ripley BD (2002). Modern Applied Statistics with S. Fourth Edition. Springer New York.

Examples

# The rooting data.

data(rooting)

# the first comparison should be the same as:

Age5_PosB_IBA0 <- subset(rooting,
 Age=="5" & Position=="B" & IBA=="0")[,c("root", "noroot")]
Age5_PosB_IBA0.5 <- subset(rooting,
 Age=="5" & Position=="B" & IBA=="0.5")[,c("root", "noroot")]

Age5_PosB_IBA0
Age5_PosB_IBA0.5

Prop.diff(x=Age5_PosB_IBA0, y=Age5_PosB_IBA0.5)

Prop.ratio(x=Age5_PosB_IBA0, y=Age5_PosB_IBA0.5)

Prop.or(x=Age5_PosB_IBA0, y=Age5_PosB_IBA0.5)

# is the same as input two vectors x,y each containing
# the count of successes and the count of failures

 colSums(Age5_PosB_IBA0)
 colSums(Age5_PosB_IBA0.5)

Prop.diff(x=c(16,32),y=c(29,19))

Prop.ratio(x=c(16,32),y=c(29,19))

Prop.or(x=c(16,32),y=c(29,19))

# # # 

# Comparison with original papers:

# Risk difference:

# Risk difference, CC

# Continuity corrected interval:

# 1.Comparison with results presented in Newcombe (1998),
# Table II, page 877, 10. Score, CC
# column 1 (a): 56/70-48/80: [0.0441; 0.3559]


Prop.diff(x=c(56,70-56),y=c(48,80-48), alternative="two.sided",
 conf.level=0.95, CImethod="CC")


# I. Risk difference, NHS

# Newcombes Hybrid Score interval:

# 1.Comparison with results presented in Newcombe (1998),
# Table II, page 877, 10. Score, noCC
# column 1 (a): 56/70-48/80: [0.0524; 0.3339]


Prop.diff(x=c(56,70-56),y=c(48,80-48), alternative="two.sided",
 conf.level=0.95, CImethod="NHS")


Prop.diff(x=c(56,70-56),y=c(48,80-48), alternative="greater",
 conf.level=0.975, CImethod="NHS")

Prop.diff(x=c(56,70-56),y=c(48,80-48), alternative="less",
 conf.level=0.975, CImethod="NHS")


# 2.Comparison with results presented in Newcombe (1998),
# Table II, page 877, 10. Score, noCC
# column 2 (b): 9/10-3/10: [0.1705; 0.8090]


Prop.diff(x=c(9,1),y=c(3,7), alternative="two.sided",
 conf.level=0.95, CImethod="NHS")


# 3.Comparison with results presented in Newcombe (1998),
# Table II, page 877, 10. Score, noCC
# column 2 (h): 10/10-0/10: [0.6075; 1.000]


Prop.diff(x=c(10,0),y=c(0,10), alternative="two.sided",
 conf.level=0.95, CImethod="NHS")


# II. Risk ratio, Score
# Score interval according to Gart and Nam (1988)

# 1.Comparison with results presented in Gart and Nam (1998),
# Section 5 (page 327), Example 1
# x1/n1=8/15 x0/n0=4/15:
# Log: [0.768, 4.65]
# Score: [0.815; 5.34]

# Log (GNC)
Prop.ratio(x=c(8,7),y=c(4,11), alternative="two.sided",
 conf.level=0.95, CImethod="GNC")

# Score (Score)
Prop.ratio(x=c(8,7),y=c(4,11), alternative="two.sided",
 conf.level=0.95, CImethod="Score")

Prop.ratio(x=c(8,7),y=c(4,11), alternative="less",
 conf.level=0.975, CImethod="Score")

Prop.ratio(x=c(8,7),y=c(4,11), alternative="greater",
 conf.level=0.975, CImethod="Score")



# 2.Comparison with results presented in Gart and Nam (1998),
# Section 5 (page 328), Example 2
# x1/n1=6/10 x0/n0=6/20:
# Log: [0.883, 4.32]
# Score: [0.844; 4.59]

# Log (GNC)
Prop.ratio(x=c(6,4),y=c(6,14), alternative="two.sided",
 conf.level=0.95, CImethod="GNC")

# Score (Score)
Prop.ratio(x=c(6,4),y=c(6,14), alternative="two.sided",
 conf.level=0.95, CImethod="Score")