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Confidence intervals for rate ratio (RR) with independent binomial or Poisson rates.

Source: R/rrci.R
rrci.Rd

Confidence intervals for comparisons of two binomial or Poisson rates. This convenience wrapper function produces a selection of the methods below as appropriate for the selected distribution (binomial or Poisson) for the rate ratio (/relative risk) contrast (RR), with or without continuity adjustment.

  • SCAS (skewness-corrected asymptotic score)

  • Miettinen-Nurminen, Koopman, Gart-Nam Asymptotic Score methods

  • MOVER-W

  • MOVER-J (based on Jeffreys intervals)

  • Approximate normal (Katz log) methods (strongly advise this is not used for any purpose but included for reference)

Usage

rrci(
  x1,
  n1,
  x2,
  n2,
  distrib = "bin",
  level = 0.95,
  std_est = TRUE,
  cc = FALSE,
  precis = 6
)

Arguments

x1, x2

Numeric vectors of numbers of events in group 1 & group 2 respectively.

n1, n2

Numeric vectors of sample sizes (for binomial rates) or exposure times (for Poisson rates) in each group.

distrib

Character string indicating distribution assumed for the input data:
"bin" = binomial (default),
"poi" = Poisson.

level

Number specifying confidence level (between 0 and 1, default 0.95).

std_est

logical, specifying if the crude point estimate for the contrast value should be returned (TRUE, default) or the method-specific alternative point estimate consistent with a 0% confidence interval (FALSE).

cc

Number or logical (default FALSE) specifying (amount of) continuity adjustment. Numeric value between 0 and 0.5 is taken as the gamma parameter in Laud 2017, Appendix S2 (cc = TRUE translates to 0.5 for 'conventional' Yates adjustment).

precis

Number (default 6) specifying precision (i.e. number of decimal places) to be used in root-finding subroutine for the score confidence intervals. (Note other methods use closed-form calculations so are not affected.)

Value

A list containing the following components:

estimates

an array containing the confidence interval for RR using various methods. The methods shown depends on the cc argument (if cc = TRUE then the continuity-adjusted methods are given).

call

details of the function call.

References

Laud PJ. Equal-tailed confidence intervals for comparison of rates. Pharmaceutical Statistics 2017; 16:334-348.

Author

Pete Laud, p.j.laud@sheffield.ac.uk

Examples

# Selected example datasets from Newcombe 1998 and Fagerland et al. 2011
# (note Fagerland et al. appear to have the Miettinen-Nurminen method
#  labelled as Koopman)
rrci(
  x1 = c(5, 7), n1 = c(56, 34),
  x2 = c(0, 1), n2 = c(29, 34),
  precis = 4
)
#> $estimates
#> , , 5/56 vs 0/29
#> 
#>                     lower est    upper
#> SCAS               0.7696 Inf      Inf
#> Gart-Nam           0.7822 Inf      Inf
#> Miettinen-Nurminen 0.7175 Inf      Inf
#> Koopman            0.7257 Inf      Inf
#> MOVER-W            0.6292 Inf      Inf
#> MOVER-J            0.8753 Inf      Inf
#> Katz log           0.0000 Inf      Inf
#> Adjusted log       0.3287 Inf 100.3502
#> 
#> , , 7/34 vs 1/34
#> 
#>                     lower est    upper
#> SCAS               1.2383   7 129.3294
#> Gart-Nam           1.2532   7 130.8308
#> Miettinen-Nurminen 1.2086   7  43.0330
#> Koopman            1.2209   7  42.5757
#> MOVER-W            1.1537   7  41.9763
#> MOVER-J            1.2771   7  67.1689
#> Katz log           0.9096   7  53.8695
#> Adjusted log       0.9241   7  27.0523
#> 
#> 
#> $call
#> distrib   level      cc 
#>   "bin"  "0.95" "FALSE" 
#> 
# With conventional continuity adjustment
rrci(
  x1 = c(5, 7), n1 = c(56, 34),
  x2 = c(0, 1), n2 = c(29, 34),
  precis = 4, cc = TRUE
)
#> $estimates
#> , , 5/56 vs 0/29
#> 
#>                        lower est upper
#> SCAS_cc               0.4628 Inf   Inf
#> Gart-Nam_cc           0.4678 Inf   Inf
#> Miettinen-Nurminen_cc 0.4765 Inf   Inf
#> Koopman_cc            0.4810 Inf   Inf
#> MOVER-W_cc            0.4779 Inf   Inf
#> MOVER-J_cc            0.5654 Inf   Inf
#> 
#> , , 7/34 vs 1/34
#> 
#>                        lower est      upper
#> SCAS_cc               0.9360   7 27593.3534
#> Gart-Nam_cc           0.9456   7 43279.8893
#> Miettinen-Nurminen_cc 0.9424   7   149.5435
#> Koopman_cc            0.9512   7   147.7432
#> MOVER-W_cc            0.9712   7   136.6421
#> MOVER-J_cc            1.0356   7   282.5531
#> 
#> 
#> $call
#> distrib   level      cc 
#>   "bin"  "0.95"   "0.5" 
#> 
# With intermediate continuity adjustment
rrci(
  x1 = c(5, 7), n1 = c(56, 34),
  x2 = c(0, 1), n2 = c(29, 34),
  precis = 4, cc = 0.25
)
#> $estimates
#> , , 5/56 vs 0/29
#> 
#>                              lower est upper
#> SCAS_cc(0.25)               0.5853 Inf   Inf
#> Gart-Nam_cc(0.25)           0.5928 Inf   Inf
#> Miettinen-Nurminen_cc(0.25) 0.5788 Inf   Inf
#> Koopman_cc(0.25)            0.5847 Inf   Inf
#> MOVER-W_cc(0.25)            0.5444 Inf   Inf
#> MOVER-J_cc(0.25)            0.6838 Inf   Inf
#> 
#> , , 7/34 vs 1/34
#> 
#>                              lower est    upper
#> SCAS_cc(0.25)               1.0724   7 422.9320
#> Gart-Nam_cc(0.25)           1.0843   7 437.4584
#> Miettinen-Nurminen_cc(0.25) 1.0643   7  71.7594
#> Koopman_cc(0.25)            1.0746   7  70.9530
#> MOVER-W_cc(0.25)            1.0563   7  66.8112
#> MOVER-J_cc(0.25)            1.1453   7 121.2444
#> 
#> 
#> $call
#> distrib   level      cc 
#>   "bin"  "0.95"  "0.25" 
#>