Mantel-Haenszel method, CI for common RR over strata or clusters with sparse data.

Estimates confidence intervals for the risk ratio or prevented fraction from clustered or stratified data, using a Mantel-Haenszel estimator for sparse data.

Usage

RRmh(
  formula = NULL,
  data = NULL,
  compare = c("vac", "con"),
  Y,
  alpha = 0.05,
  pf = TRUE,
  rnd = 3
)

Arguments

formula: Formula of the form cbind(y, n) ~ x + cluster(w), where Y is the number positive, n is the group size, x is a factor with two levels of treatment, and w is a factor indicating the clusters.
data: data.frame containing variables for formula
compare: Text vector stating the factor levels: compare[1] is the vaccinate group to which compare[2] (control or reference) is compared.
Y: Matrix of data, \(K \times 4\). Each row is a stratum or cluster. The columns are \(y1, n1, y2, n2\), where the y's are the number of positive in each group, and the n is the total in each group. Group 1 corresponds to vaccinates and group 2 are controls or reference. If data entered by formula and dataframe, Y is generated automatically.
alpha: Complement of the confidence level.
pf: Estimate RR or its complement PF?
rnd: Number of digits for rounding. Affects display only, not estimates.

Value

An object of class rr1 with the following fields.

estimate: vector of point and interval estimates: point estimate, lower confidence limit, upper confidence limit
estimator: either "PF" or "RR"
y: data.frame of restructured input
rnd: how many digits to round the display
alpha: complement of confidence level

Details

Based on the Mantel-Haenszel (1959) procedure for sparse data developed by Greenland and Robins (1985). The confidence limits are based on asymptotic normality of the log(risk ratio). Agresti and Hartzel (2000) favor this procedure for small, sparse data sets, but they warn that it is less efficient than maximum likelihood for large data sets.

Note

If either all y1's or all y2's are zero, a division by zero may occur, and a NaN returned for some values.

Vignette Examples for Stratified Designs forthcoming with more examples.

Call to this function may be one of two formats: (1) specify data and formula or (2) as a matrix Y

RRmh(formula, data, compare = c("b", "a"), pf = TRUE, alpha = 0.05, rnd = 3)

RRmh(Y, pf = TRUE, alpha = 0.05, rnd = 3)

References

Mantel N, Haenszel W, 1959. Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute 22:719-748.

Greenland S, Robins JM, 1985. Estimation of a common effect parameter from sparse follow-up data. Biometrics 41: 55-68. Errata, 45: 1323-1324.

Agresti A, Hartzel J, 2000. Strategies for comparing treatments on a binary response with multi-centre data. Statistics in Medicine 19: 1115-1139.

Lachin JM, 2000. Biostatistical Methods: The Assessment of Relative Risks (Wiley, New York), Sec. 4.3.1.

Author

PF-package

Examples


## Table 1 from Gart (1985)
##  as data frame

# tx group "b" is control
RRmh(cbind(y, n) ~ tx + cluster(clus),
     Table6,
     compare = c("a", "b"), pf = FALSE)
#> 
#> RR 
#> 95% interval estimates
#> 
#>   RR   LL   UL 
#> 2.67 1.37 5.23 
#> 

# RR
# 95% interval estimates
#
#   RR   LL   UL
# 2.67 1.37 5.23
#

## or as matrix
RRmh(Y = table6, pf = FALSE)
#> 
#> RR 
#> 95% interval estimates
#> 
#>   RR   LL   UL 
#> 2.67 1.37 5.23 
#> 

# RR
# 95% interval estimates
#
#   RR   LL   UL
# 2.67 1.37 5.23