Get standardized estimates using the g-formula with and separate models for each exposure level in the data
Source:R/standardize_custom.R
standardize_level.RdGet standardized estimates using the g-formula with and separate models for each exposure level in the data
Usage
standardize_level(
fitter_list,
arguments,
predict_fun_list,
data,
values,
B = NULL,
ci_level = 0.95,
contrasts = NULL,
reference = NULL,
seed = NULL,
times = NULL,
transforms = NULL,
progressbar = TRUE
)Arguments
- fitter_list
The function to call to fit the data (as a list).
- arguments
The arguments to be used in the fitter function as a
list.- predict_fun_list
The function used to predict the means/probabilities for a new data set on the response level. For survival data, this should be a matrix where each column is the time, and each row the data (as a list).
- data
The data.
- values
A named list or data.frame specifying the variables and values at which marginal means of the outcome will be estimated.
- B
Number of nonparametric bootstrap resamples. Default is
NULL(no bootstrap).- ci_level
Coverage probability of confidence intervals.
- contrasts
A vector of contrasts in the following format: If set to
"difference"or"ratio", then \(\psi(x)-\psi(x_0)\) or \(\psi(x) / \psi(x_0)\) are constructed, where \(x_0\) is a reference level specified by thereferenceargument. Has to beNULLif no references are specified.- reference
A vector of reference levels in the following format: If
contrastsis notNULL, the desired reference level(s). This must be a vector or list the same length ascontrasts, and if not named, it is assumed that the order is as specified in contrasts.- seed
The seed to use with the nonparametric bootstrap.
- times
For use with survival data. Set to
NULLotherwise.- transforms
A vector of transforms in the following format: If set to
"log","logit", or"odds", the standardized mean \(\theta(x)\) is transformed into \(\psi(x)=\log\{\theta(x)\}\), \(\psi(x)=\log[\theta(x)/\{1-\theta(x)\}]\), or \(\psi(x)=\theta(x)/\{1-\theta(x)\}\), respectively. If the vector isNULL, then \(\psi(x)=\theta(x)\).- progressbar
Logical, if TRUE will print bootstrapping progress to the console
Value
An object of class std_custom. Obtain numeric results using tidy.std_custom.
This is a list with the following components:
- res_contrast
An unnamed list with one element for each of the requested contrasts. Each element is itself a list with the elements:
- B
The number of bootstrap replicates
- estimates
Estimated counterfactual means and standard errors for each exposure level
- fit_outcome
The estimated regression model for the outcome
- estimates_boot
A list of estimates, one for each bootstrap resample
- exposure_names
A character vector of the exposure variable names
- times
The vector of times at which the calculation is done, if relevant
- est_table
Data.frame of the estimates of the contrast with inference
- transform
The transform argument used for this contrast
- contrast
The requested contrast type
- reference
The reference level of the exposure
- ci_level
Confidence interval level
- res
A named list with the elements:
- B
The number of bootstrap replicates
- estimates
Estimated counterfactual means and standard errors for each exposure level
- fit_outcome
The estimated regression model for the outcome
- estimates_boot
A list of estimates, one for each bootstrap resample
- exposure_names
A character vector of the exposure variable names
- times
The vector of times at which the calculation is done, if relevant
Details
See standardize. The difference is here that different models
can be fitted for each value of x in values.
References
Rothman K.J., Greenland S., Lash T.L. (2008). Modern Epidemiology, 3rd edition. Lippincott, Williams & Wilkins.
Sjölander A. (2016). Regression standardization with the R-package stdReg. European Journal of Epidemiology 31(6), 563-574.
Sjölander A. (2016). Estimation of causal effect measures with the R-package stdReg. European Journal of Epidemiology 33(9), 847-858.
Examples
require(survival)
prob_predict.coxph <- function(object, newdata, times) {
fit.detail <- suppressWarnings(basehaz(object))
cum.haz <- fit.detail$hazard[sapply(times, function(x) max(which(fit.detail$time <= x)))]
predX <- predict(object = object, newdata = newdata, type = "risk")
res <- matrix(NA, ncol = length(times), nrow = length(predX))
for (ti in seq_len(length(times))) {
res[, ti] <- exp(-predX * cum.haz[ti])
}
res
}
set.seed(68)
n <- 500
Z <- rnorm(n)
X <- rbinom(n, 1, prob = 0.5)
T <- rexp(n, rate = exp(X + Z + X * Z)) # survival time
C <- rexp(n, rate = exp(X + Z + X * Z)) # censoring time
U <- pmin(T, C) # time at risk
D <- as.numeric(T < C) # event indicator
dd <- data.frame(Z, X, U, D)
x <- standardize_level(
fitter_list = list("coxph", "coxph"),
arguments = list(
list(
formula = Surv(U, D) ~ X + Z + X * Z,
method = "breslow",
x = TRUE,
y = TRUE
),
list(
formula = Surv(U, D) ~ X,
method = "breslow",
x = TRUE,
y = TRUE
)
),
predict_fun_list = list(prob_predict.coxph, prob_predict.coxph),
data = dd,
times = seq(1, 5, 0.1),
values = list(X = c(0, 1)),
B = 100,
reference = 0,
contrasts = "difference"
)
#>
|
| | 0%
|
|= | 1%
|
|= | 2%
|
|== | 3%
|
|== | 4%
|
|=== | 5%
|
|=== | 6%
|
|==== | 7%
|
|==== | 8%
|
|===== | 9%
|
|===== | 10%
|
|====== | 11%
|
|====== | 12%
|
|======= | 13%
|
|======= | 14%
|
|======== | 15%
|
|======== | 16%
|
|========= | 17%
|
|========= | 18%
|
|========== | 19%
|
|========== | 20%
|
|=========== | 21%
|
|=========== | 22%
|
|============ | 23%
|
|============ | 24%
|
|============= | 25%
|
|============= | 26%
|
|============== | 27%
|
|============== | 28%
|
|=============== | 29%
|
|=============== | 30%
|
|================ | 31%
|
|================ | 32%
|
|================= | 33%
|
|================= | 34%
|
|================== | 35%
|
|================== | 36%
|
|=================== | 37%
|
|=================== | 38%
|
|==================== | 39%
|
|==================== | 40%
|
|===================== | 41%
|
|===================== | 42%
|
|====================== | 43%
|
|====================== | 44%
|
|======================= | 45%
|
|======================= | 46%
|
|======================== | 47%
|
|======================== | 48%
|
|========================= | 49%
|
|========================= | 51%
|
|========================== | 52%
|
|========================== | 53%
|
|=========================== | 54%
|
|=========================== | 55%
|
|============================ | 56%
|
|============================ | 57%
|
|============================= | 58%
|
|============================= | 59%
|
|============================== | 60%
|
|============================== | 61%
|
|=============================== | 62%
|
|=============================== | 63%
|
|================================ | 64%
|
|================================ | 65%
|
|================================= | 66%
|
|================================= | 67%
|
|================================== | 68%
|
|================================== | 69%
|
|=================================== | 70%
|
|=================================== | 71%
|
|==================================== | 72%
|
|==================================== | 73%
|
|===================================== | 74%
|
|===================================== | 75%
|
|====================================== | 76%
|
|====================================== | 77%
|
|======================================= | 78%
|
|======================================= | 79%
|
|======================================== | 80%
|
|======================================== | 81%
|
|========================================= | 82%
|
|========================================= | 83%
|
|========================================== | 84%
|
|========================================== | 85%
|
|=========================================== | 86%
|
|=========================================== | 87%
|
|============================================ | 88%
|
|============================================ | 89%
|
|============================================= | 90%
|
|============================================= | 91%
|
|============================================== | 92%
|
|============================================== | 93%
|
|=============================================== | 94%
|
|=============================================== | 95%
|
|================================================ | 96%
|
|================================================ | 97%
|
|================================================= | 98%
|
|================================================= | 99%
|
|==================================================| 100%
print(x)
#> Number of bootstraps: 100
#> Confidence intervals are based on percentile bootstrap confidence intervals
#>
#> Exposure: X
#> Tables:
#>
#> Time: 1
#> X estimate lower upper
#> 1 0 0.3426359 0.2685875 0.4126004
#> 2 1 0.3306066 0.2719930 0.3968803
#>
#> Time: 1.1
#> X estimate lower upper
#> 1 0 0.3193937 0.2478319 0.3800825
#> 2 1 0.3140225 0.2554192 0.3785019
#>
#> Time: 1.2
#> X estimate lower upper
#> 1 0 0.2910216 0.2229411 0.3537408
#> 2 1 0.2929892 0.2427978 0.3563471
#>
#> Time: 1.3
#> X estimate lower upper
#> 1 0 0.2784148 0.2174233 0.3452300
#> 2 1 0.2844500 0.2347156 0.3465131
#>
#> Time: 1.4
#> X estimate lower upper
#> 1 0 0.2722029 0.2119961 0.3390574
#> 2 1 0.2801398 0.2333808 0.3414379
#>
#> Time: 1.5
#> X estimate lower upper
#> 1 0 0.2537637 0.1902978 0.3208143
#> 2 1 0.2670585 0.2136579 0.3222557
#>
#> Time: 1.6
#> X estimate lower upper
#> 1 0 0.2473441 0.1836796 0.3202737
#> 2 1 0.2625318 0.2112083 0.3187268
#>
#> Time: 1.7
#> X estimate lower upper
#> 1 0 0.2284202 0.1650471 0.2935825
#> 2 1 0.2487069 0.1926763 0.3090800
#>
#> Time: 1.8
#> X estimate lower upper
#> 1 0 0.2284202 0.1650471 0.2935825
#> 2 1 0.2487069 0.1926763 0.3090800
#>
#> Time: 1.9
#> X estimate lower upper
#> 1 0 0.2155678 0.1545570 0.2795913
#> 2 1 0.2385031 0.1879035 0.2981300
#>
#> Time: 2
#> X estimate lower upper
#> 1 0 0.2083187 0.1540708 0.2697798
#> 2 1 0.2328579 0.1835953 0.2894313
#>
#> Time: 2.1
#> X estimate lower upper
#> 1 0 0.2010004 0.1422739 0.2664994
#> 2 1 0.2271435 0.1820213 0.2827236
#>
#> Time: 2.2
#> X estimate lower upper
#> 1 0 0.2010004 0.1422739 0.2664994
#> 2 1 0.2271435 0.1820213 0.2827236
#>
#> Time: 2.3
#> X estimate lower upper
#> 1 0 0.1931929 0.1335466 0.2582027
#> 2 1 0.2210044 0.1767496 0.2766781
#>
#> Time: 2.4
#> X estimate lower upper
#> 1 0 0.1931929 0.1335466 0.2582027
#> 2 1 0.2210044 0.1767496 0.2766781
#>
#> Time: 2.5
#> X estimate lower upper
#> 1 0 0.1648695 0.1077254 0.2294345
#> 2 1 0.1993885 0.1465611 0.2613009
#>
#> Time: 2.6
#> X estimate lower upper
#> 1 0 0.1557581 0.1009572 0.2232631
#> 2 1 0.1920041 0.1396859 0.2496035
#>
#> Time: 2.7
#> X estimate lower upper
#> 1 0 0.1557581 0.1009572 0.2232631
#> 2 1 0.1920041 0.1396859 0.2496035
#>
#> Time: 2.8
#> X estimate lower upper
#> 1 0 0.1557581 0.1009572 0.2232631
#> 2 1 0.1920041 0.1396859 0.2496035
#>
#> Time: 2.9
#> X estimate lower upper
#> 1 0 0.1557581 0.1009572 0.2232631
#> 2 1 0.1920041 0.1396859 0.2496035
#>
#> Time: 3
#> X estimate lower upper
#> 1 0 0.1455376 0.09859477 0.2099133
#> 2 1 0.1838344 0.13550757 0.2463232
#>
#> Time: 3.1
#> X estimate lower upper
#> 1 0 0.1344841 0.08736479 0.1989949
#> 2 1 0.1752849 0.13259212 0.2324468
#>
#> Time: 3.2
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.3
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.4
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.5
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.6
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.7
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.8
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 3.9
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.1
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.2
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.3
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.4
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.5
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.6
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.7
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.8
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 4.9
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#> Time: 5
#> X estimate lower upper
#> 1 0 0.1239428 0.08002961 0.1812128
#> 2 1 0.1662973 0.12094475 0.2177145
#>
#>
#> Reference level: = 0
#> Contrast: difference
#> Time: 1
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.000000
#> 2 1 -0.01202936 -0.08167224 0.063079
#>
#> Time: 1.1
#> X estimate lower upper
#> 1 0 0.000000000 0.00000000 0.00000000
#> 2 1 -0.005371227 -0.07540159 0.07050428
#>
#> Time: 1.2
#> X estimate lower upper
#> 1 0 0.000000000 0.00000000 0.00000000
#> 2 1 0.001967654 -0.06990685 0.07668053
#>
#> Time: 1.3
#> X estimate lower upper
#> 1 0 0.000000000 0.0000000 0.0000000
#> 2 1 0.006035151 -0.0652183 0.0817649
#>
#> Time: 1.4
#> X estimate lower upper
#> 1 0 0.000000000 0.00000000 0.00000000
#> 2 1 0.007936927 -0.06470686 0.08250201
#>
#> Time: 1.5
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.000000
#> 2 1 0.01329481 -0.05696887 0.086919
#>
#> Time: 1.6
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.01518772 -0.05696887 0.08771999
#>
#> Time: 1.7
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.02028668 -0.04978553 0.09089055
#>
#> Time: 1.8
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.02028668 -0.04978553 0.09089055
#>
#> Time: 1.9
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.0000000
#> 2 1 0.02293534 -0.04767694 0.0918496
#>
#> Time: 2
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.02453919 -0.04613972 0.09298423
#>
#> Time: 2.1
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.02614307 -0.04472088 0.09315902
#>
#> Time: 2.2
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.02614307 -0.04472088 0.09315902
#>
#> Time: 2.3
#> X estimate lower upper
#> 1 0 0.0000000 0.00000000 0.00000000
#> 2 1 0.0278115 -0.04234635 0.09415061
#>
#> Time: 2.4
#> X estimate lower upper
#> 1 0 0.0000000 0.00000000 0.00000000
#> 2 1 0.0278115 -0.04234635 0.09415061
#>
#> Time: 2.5
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.03451898 -0.03573643 0.09685651
#>
#> Time: 2.6
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.03624594 -0.03573643 0.09685959
#>
#> Time: 2.7
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.03624594 -0.03573643 0.09685959
#>
#> Time: 2.8
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.03624594 -0.03573643 0.09685959
#>
#> Time: 2.9
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.03624594 -0.03573643 0.09685959
#>
#> Time: 3
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.03829678 -0.03307009 0.09632176
#>
#> Time: 3.1
#> X estimate lower upper
#> 1 0 0.0000000 0.00000000 0.00000000
#> 2 1 0.0408008 -0.02680682 0.09743773
#>
#> Time: 3.2
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.3
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.4
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.5
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.6
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.7
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.8
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 3.9
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.1
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.2
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.3
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.4
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.5
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.6
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.7
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.8
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 4.9
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#> Time: 5
#> X estimate lower upper
#> 1 0 0.00000000 0.00000000 0.00000000
#> 2 1 0.04235446 -0.02413252 0.09619845
#>
#>