The summary() method for objects of class multisimsum returns confidence intervals for performance measures based on Monte Carlo standard errors.
Usage
# S3 method for multisimsum
summary(object, ci_level = 0.95, df = NULL, stats = NULL, ...)Arguments
- object
An object of class
multisimsum.- ci_level
Significance level for confidence intervals based on Monte Carlo standard errors. Ignored if a
multisimsumobject with control parametermcse = FALSEis passed.- df
Degrees of freedom of a t distribution that will be used to calculate confidence intervals based on Monte Carlo standard errors. If
NULL(the default), quantiles of a Normal distribution will be used instead.- stats
Summary statistics to include; can be a scalar value or a vector (for multiple summary statistics at once). Possible choices are:
nsim, the number of replications with non-missing point estimates and standard error.thetamean, average point estimate.thetamedian, median point estimate.se2mean, average standard error.se2median, median standard error.bias, bias in point estimate.rbias, relative (to the true value) bias in point estimate.empse, empirical standard error.mse, mean squared error.relprec, percentage gain in precision relative to the reference method.modelse, model-based standard error.relerror, relative percentage error in standard error.cover, coverage of a nominallevel\becover, bias corrected coverage of a nominallevel\power, power of a (1 -level)\ Defaults toNULL, in which case all possible summary statistics are included.
- ...
Ignored.
Examples
data(frailty)
ms <- multisimsum(
data = frailty, par = "par", true = c(
trt = -0.50,
fv = 0.75
), estvarname = "b", se = "se", methodvar = "model",
by = "fv_dist"
)
#> 'ref' method was not specified, Cox, Gamma set as the reference
sms <- summary(ms)
sms
#> Values are:
#> Point Estimate (Monte Carlo Standard Error)
#>
#>
#> Parameter: fv
#>
#> Non-missing point estimates/standard errors:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 976 1000 971 1000
#> Log-Normal 957 1000 997 1000
#>
#> Average point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.7376 0.9799 0.7321 0.9847
#> Log-Normal 0.6436 0.7325 0.6434 0.7348
#>
#> Median point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.7271 0.9566 0.7225 0.9597
#> Log-Normal 0.6365 0.7182 0.6324 0.7199
#>
#> Average variance:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0203 0.0600 0.0202 0.0498
#> Log-Normal 0.0156 0.0230 0.0158 0.0254
#>
#> Median variance:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0193 0.0483 0.0191 0.0442
#> Log-Normal 0.0149 0.0206 0.0149 0.0235
#>
#> Bias in point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma
#> Gamma -0.0124 (0.0045) 0.2299 (0.0076) -0.0179 (0.0044)
#> Log-Normal -0.1064 (0.0043) -0.0175 (0.0049) -0.1066 (0.0041)
#> RP(P), Log-Normal
#> 0.2347 (0.0077)
#> -0.0152 (0.0050)
#>
#> Relative bias in point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma -0.0165 (NA) 0.3066 (0.0101) -0.0239 (NA) 0.3130 (0.0103)
#> Log-Normal -0.1419 (NA) -0.0233 (0.0066) -0.1421 (NA) -0.0203 (0.0066)
#>
#> Empirical standard error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.1421 (0.0032) 0.2406 (0.0054) 0.1387 (0.0031) 0.2438 (0.0055)
#> Log-Normal 0.1320 (0.0030) 0.1554 (0.0035) 0.1307 (0.0029) 0.1570 (0.0035)
#>
#> % gain in precision relative to method Cox, Gamma:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0000 (0.0000) -65.1290 (0.6149) 5.0048 (0.0507) -66.0342 (0.5911)
#> Log-Normal 0.0000 (0.0000) -27.8283 (1.5037) 2.0492 (0.0466) -29.3058 (1.4591)
#>
#> Mean squared error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0203 (0.0010) 0.1107 (0.0055) 0.0195 (0.0009) 0.1145 (0.0057)
#> Log-Normal 0.0287 (0.0010) 0.0244 (0.0011) 0.0284 (0.0010) 0.0248 (0.0012)
#>
#> Model-based standard error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.1426 (0.0008) 0.2449 (0.0027) 0.1420 (0.0008) 0.2232 (0.0019)
#> Log-Normal 0.1249 (0.0008) 0.1517 (0.0013) 0.1258 (0.0007) 0.1594 (0.0011)
#>
#> Relative % error in standard error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma
#> Gamma 0.3574 (2.3463) 1.7896 (2.5449) 2.3922 (2.3950)
#> Log-Normal -5.3912 (2.2452) -2.3382 (2.3301) -3.7112 (2.2300)
#> RP(P), Log-Normal
#> -8.4531 (2.1890)
#> 1.5422 (2.3713)
#>
#> Coverage of nominal 95% confidence interval:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.9201 (0.0087) 0.9220 (0.0085) 0.9300 (0.0082) 0.9030 (0.0094)
#> Log-Normal 0.7503 (0.0140) 0.9020 (0.0094) 0.7683 (0.0134) 0.9280 (0.0082)
#>
#> Bias-eliminated coverage of nominal 95% confidence interval:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.9334 (0.0080) 0.8980 (0.0096) 0.9434 (0.0074) 0.8930 (0.0098)
#> Log-Normal 0.9164 (0.0089) 0.9130 (0.0089) 0.9308 (0.0080) 0.9360 (0.0077)
#>
#> Power of 5% level test:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000)
#> Log-Normal 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000)
#>
#> --------------------------------------------------------------------------------
#>
#> Parameter: trt
#>
#> Non-missing point estimates/standard errors:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 1000 1000 971 1000
#> Log-Normal 1000 1000 997 1000
#>
#> Average point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma -0.5006 -0.5013 -0.5003 -0.5015
#> Log-Normal -0.5006 -0.5014 -0.5006 -0.5016
#>
#> Median point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma -0.5011 -0.5021 -0.5010 -0.5025
#> Log-Normal -0.5014 -0.5021 -0.5014 -0.5022
#>
#> Average variance:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0026 0.0026 0.0026 0.0026
#> Log-Normal 0.0023 0.0023 0.0023 0.0023
#>
#> Median variance:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0026 0.0026 0.0026 0.0026
#> Log-Normal 0.0022 0.0022 0.0022 0.0022
#>
#> Bias in point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma
#> Gamma -0.0006 (0.0016) -0.0013 (0.0016) -0.0003 (0.0016)
#> Log-Normal -0.0006 (0.0015) -0.0014 (0.0015) -0.0006 (0.0015)
#> RP(P), Log-Normal
#> -0.0015 (0.0016)
#> -0.0016 (0.0015)
#>
#> Relative bias in point estimate:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0011 (0.0032) 0.0027 (0.0032) 0.0006 (NA) 0.0031 (0.0032)
#> Log-Normal 0.0012 (0.0030) 0.0028 (0.0030) 0.0013 (NA) 0.0032 (0.0030)
#>
#> Empirical standard error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0508 (0.0011) 0.0509 (0.0011) 0.0506 (0.0011) 0.0509 (0.0011)
#> Log-Normal 0.0474 (0.0011) 0.0474 (0.0011) 0.0473 (0.0011) 0.0474 (0.0011)
#>
#> % gain in precision relative to method Cox, Gamma:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0000 (0.0000) -0.4457 (0.1133) 0.4394 (0.0845) -0.5782 (0.1641)
#> Log-Normal 0.0000 (0.0000) -0.1417 (0.1367) 0.0918 (0.0853) -0.2078 (0.1589)
#>
#> Mean squared error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0026 (0.0001) 0.0026 (0.0001) 0.0026 (0.0001) 0.0026 (0.0001)
#> Log-Normal 0.0022 (0.0001) 0.0022 (0.0001) 0.0022 (0.0001) 0.0022 (0.0001)
#>
#> Model-based standard error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.0506 (0.0000) 0.0507 (0.0000) 0.0506 (0.0000) 0.0507 (0.0000)
#> Log-Normal 0.0475 (0.0000) 0.0475 (0.0000) 0.0475 (0.0000) 0.0475 (0.0000)
#>
#> Relative % error in standard error:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma
#> Gamma -0.2017 (2.2346) -0.3890 (2.2304) -0.0544 (2.2710)
#> Log-Normal 0.2507 (2.2438) 0.1815 (2.2423) 0.3319 (2.2490)
#> RP(P), Log-Normal
#> -0.4330 (2.2294)
#> 0.2101 (2.2429)
#>
#> Coverage of nominal 95% confidence interval:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.9500 (0.0069) 0.9490 (0.0070) 0.9506 (0.0070) 0.9500 (0.0069)
#> Log-Normal 0.9410 (0.0075) 0.9420 (0.0074) 0.9428 (0.0074) 0.9430 (0.0073)
#>
#> Bias-eliminated coverage of nominal 95% confidence interval:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 0.9500 (0.0069) 0.9500 (0.0069) 0.9506 (0.0070) 0.9490 (0.0070)
#> Log-Normal 0.9420 (0.0074) 0.9400 (0.0075) 0.9428 (0.0074) 0.9410 (0.0075)
#>
#> Power of 5% level test:
#> fv_dist Cox, Gamma Cox, Log-Normal RP(P), Gamma RP(P), Log-Normal
#> Gamma 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000)
#> Log-Normal 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000) 1.0000 (0.0000)