^{ 1}Department of Biostatistics, University of Copenhagen, Copenhagen, Denmark
^{ 2}Center for Statistical Science, Peking University, Copenhagen, Denmark
^{ 3}Department of Cardiology, University Hospital Bispebjerg, Copenhagen, Denmark
^{ 4}Department of Cardiology, Rigshospitalet, Copenhagen, Denmark
©2017, Korean Society of Epidemiology
This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
•Y_{i} (a, m) is the outcome achieved for person i if, possibly contrary to fact, exposure had been set to a and mediator to m.
•M_{i} (a) is the mediator achieved for person i if, possibly contrary to fact, exposure had been set to a.
- Using the original data alone, fit a parametric survival model to the outcome conditioned on confounders, exposure, and mediator. This could, for instance, be a Weibull based parametric time-to-event model.
- Construct a new data set by repeating each observation in the original data set twice and including an additional variable a^{*}, which is equal to the original exposure for the first replication and equal to the opposite of the actual exposure for the second replication. In addition, add an identification variable to indicate which data rows originate from the same subject.
- Use the predict functionality, possibly along with the Weibull distribution function, to impute possible survival times for the rows where A ≠ A^{*}. In the imputations, the value of the exposure is set to a^{*}, while mediators and confounders are set to their observed values; that is, impute values for the survival times Y_{i}(a^{*}, M (a)).
- Fit a Cox model to the extended data set including A, A^{*}, and C, but not the mediator. The coefficient of A will be the natural indirect log-HR and the coefficient of a^{*} will be the natural direct log-HR.
- Repeat steps 3 and 4 ten times and combine the obtained log- HRs as with ordinary multiple imputation; that is, take the average of the log-HR estimates.
- CIs for the natural effect estimates, as well as derived quantities such as mediated proportions, can be obtained by bootstrapping, which involves repeating steps 1-5 a total of 1,000 times, each time creating a new data set by random sampling with replacement from the original data set.
fitAux ← glm (BinaryMort ~ dhrkag3 + asatreat30 + adptreat30
+ statintreat30 + betatreat30 + i_alder + factor (sex)
+ factor (indkgrp) + factor (uddankat) + boralene + factor (fi_aar)
+ mi + card + cochf + puled + shock + cervas + mal + diabet
+ arf + crf + anemi + pneumoni + sepsis + klap + bleed
+ Antihyp_12mb + Lipidlow_12mb + ASA_12mb + VitKant_12mb
+ Diureti_loop_12mb + COPD_12mb + tidl_reva, data=workData, family=“binomial”)
extendedData ← neImpute(fitAux, nMed=4)
fit NEM_binaryOutcome ← neModel (BinaryMort ~ dhrkag30 + dhrkag31
+ i_alder + factor (sex) + factor (indkgrp) + factor (uddankat)
+ boralene + factor (fi_aar) + mi + card + cochf + puled + shock
+ cervas + mal + diabet + arf + crf + anemi + pneumoni + sepsis
+ klap + bleed + Antihyp_12mb + Lipidlow_12mb + ASA_12mb
+ VitKant_12mb + Diureti_loop_12mb + COPD_12mb + tidl_reva, expData=extendedData, family=“binomial”, se=“robust”
Conservative | Early invasive | p-value | |
---|---|---|---|
n | 26,858 | 22,782 | |
Mean age (yr) | 69.0 | 63.0 | <0.001 |
Male (%) | 59.4 | 70.7 | <0.001 |
HR |
95% CI |
||
---|---|---|---|
Lower limit | Upper limit | ||
Effect^{1} | |||
Natural indirect | 0.90 | 0.88 | 0.92 |
Natural direct | 0.77 | 0.76 | 0.79 |
Total | 0.70 | 0.69 | 0.70 |
Mediated proportion | 0.30 | 0.25 | 0.34 |
OR |
95% CI |
||
---|---|---|---|
Lower limit | Upper limit | ||
Effect | |||
Natural indirect | 0.84 | 0.78 | 0.89 |
Natural direct | 0.66 | 0.62 | 0.70 |
Total | 0.55 | 0.51 | 0.60 |
Mediated proportion | 0.30 | 0.22 | 0.38 |
Conservative | Early invasive | p-value | |
---|---|---|---|
n | 26,858 | 22,782 | |
Mean age (yr) | 69.0 | 63.0 | <0.001 |
Male (%) | 59.4 | 70.7 | <0.001 |
HR | 95% CI |
||
---|---|---|---|
Lower limit | Upper limit | ||
Effect^{1} | |||
Natural indirect | 0.90 | 0.88 | 0.92 |
Natural direct | 0.77 | 0.76 | 0.79 |
Total | 0.70 | 0.69 | 0.70 |
Mediated proportion | 0.30 | 0.25 | 0.34 |
OR | 95% CI |
||
---|---|---|---|
Lower limit | Upper limit | ||
Effect | |||
Natural indirect | 0.84 | 0.78 | 0.89 |
Natural direct | 0.66 | 0.62 | 0.70 |
Total | 0.55 | 0.51 | 0.60 |
Mediated proportion | 0.30 | 0.22 | 0.38 |
Variable (in R notation) | Estimate | SE | p-value |
---|---|---|---|
(Intercept) | 13.302 | 0.101 | 0.000 |
dhrkag3TEMP | 0.250 | 0.024 | 0.000 |
asa_treat30 | 0.080 | 0.015 | 0.000 |
adp_treat30 | 0.095 | 0.011 | 0.000 |
statin_treat30 | 0.204 | 0.013 | 0.000 |
beta_treat30 | 0.098 | 0.012 | 0.000 |
i_alder | -0.064 | 0.001 | 0.000 |
factor(sex)2 | 0.232 | 0.021 | 0.000 |
factor(indkgrp)2 | 0.159 | 0.028 | 0.000 |
factor(indkgrp)3 | 0.316 | 0.038 | 0.000 |
factor(uddankat)2 | 0.030 | 0.022 | 0.165 |
factor(uddankat)3 | 0.146 | 0.034 | 0.000 |
boralene | -0.155 | 0.021 | 0.000 |
factor(fi_aar)2006 | 0.003 | 0.029 | 0.918 |
factor(fi_aar)2007 | -0.027 | 0.032 | 0.399 |
factor(fi_aar)2008 | -0.146 | 0.038 | 0.000 |
factor(fi_aar)2009 | -0.209 | 0.042 | 0.000 |
factor(fi_aar)2010 | -0.173 | 0.048 | 0.000 |
factor(fi_aar)2011 | -0.280 | 0.055 | 0.000 |
mi | -0.598 | 0.032 | 0.000 |
card | -0.026 | 0.027 | 0.339 |
cochf | -0.283 | 0.026 | 0.000 |
puled | -0.234 | 0.077 | 0.003 |
shock | -0.107 | 0.170 | 0.530 |
cervas | -0.341 | 0.034 | 0.000 |
mal | -0.985 | 0.039 | 0.000 |
diabet | -0.388 | 0.036 | 0.000 |
arf | -0.405 | 0.066 | 0.000 |
crf | -0.395 | 0.051 | 0.000 |
anemi | -0.285 | 0.040 | 0.000 |
pneumoni | -0.380 | 0.028 | 0.000 |
sepsis | -0.155 | 0.074 | 0.036 |
klap | -0.260 | 0.037 | 0.000 |
bleed | -0.102 | 0.048 | 0.034 |
Antihyp_12mb | -0.021 | 0.022 | 0.352 |
Lipidlow_12mb | 0.093 | 0.024 | 0.000 |
ASA_12mb | -0.101 | 0.022 | 0.000 |
VitKant_12mb | -0.048 | 0.037 | 0.188 |
Diureti_loop_12mb | -0.442 | 0.023 | 0.000 |
COPD_12mb | -0.362 | 0.023 | 0.000 |
tidl_reva | 0.278 | 0.064 | 0.000 |
Log(scale) | -0.022 | 0.009 | 0.012 |
Description | R variable names | log-HR | SE | p-value |
---|---|---|---|---|
Indirect | dhrkag3 | -0.10 | 0.01 | 0.00 |
Direct | dhrkag3STAR | -0.26 | 0.01 | 0.00 |
Age | i_alder | 0.07 | 0.00 | 0.00 |
Gender (female) | sex2 | -0.21 | 0.01 | 0.00 |
Income (middle) | factor(indkgrp)2 | -0.16 | 0.02 | 0.00 |
Income (high) | factor(indkgrp)3 | -0.32 | 0.03 | 0.00 |
Education (middle) | factor(uddankat)2 | -0.05 | 0.01 | 0.00 |
Education (high) | factor(uddankat)3 | -0.12 | 0.02 | 0.00 |
Live alone | boralene | 0.17 | 0.01 | 0.00 |
Year (2006) | factor(fi_aar)2006 | -0.03 | 0.02 | 0.19 |
Year (2007) | factor(fi_aar)2007 | 0.00 | 0.02 | 0.92 |
Year (2008) | factor(fi_aar)2008 | 0.14 | 0.03 | 0.00 |
Year (2009) | factor(fi_aar)2009 | 0.20 | 0.03 | 0.00 |
Year (2010) | factor(fi_aar)2010 | 0.16 | 0.03 | 0.00 |
Year (2011) | factor(fi_aar)2011 | 0.25 | 0.03 | 0.00 |
Myocardial infarction | mi | 0.49 | 0.02 | 0.00 |
Cardiac arrhythmia | card | 0.05 | 0.02 | 0.01 |
chronic obstructive pulmonary disease | cochf | 0.30 | 0.02 | 0.00 |
Pulmonary oedema | puled | 0.30 | 0.06 | 0.00 |
Cardiogenic shock | shock | 0.22 | 0.11 | 0.05 |
Cerebrovascular disease | cervas | 0.37 | 0.02 | 0.00 |
Diabetes with complications | diabet | 0.36 | 0.03 | 0.00 |
acute renal failure | arf | 0.44 | 0.05 | 0.00 |
Chronic renal failure | crf | 0.44 | 0.04 | 0.00 |
Anaemia | anemi | 0.34 | 0.03 | 0.00 |
Pneumonia | pneumoni | 0.46 | 0.02 | 0.00 |
Sepsis | sepsis | 0.20 | 0.05 | 0.00 |
Valvular heart disease | klap | 0.26 | 0.03 | 0.00 |
Prior in-hospital bleeding | bleed | 0.17 | 0.03 | 0.00 |
Use of antihyp. medication last 12M | Antihyp_12mb | 0.06 | 0.01 | 0.00 |
Use of lipid-lowering drugs last 12M | Lipidlow_12mb | -0.04 | 0.02 | 0.02 |
Asprin | ASA_12mb | 0.16 | 0.01 | 0.00 |
Use of vitamin K antagonists last 12M | VitKant_12mb | 0.09 | 0.02 | 0.00 |
Use of glucose-lowering drugs lst 12M?? | Diureti_loop_12mb | 0.50 | 0.02 | 0.00 |
Use of loop diuretics or COPD last 12M | COPD_12mb | 0.39 | 0.02 | 0.00 |
Prior revascularization | tidl_reva | -0.24 | 0.04 | 0.00 |
HR, hazard ratio; CI, confidence interval.
The effects are HRs for all-cause mortality except for the mediated proportion. These results are based on a natural effects Cox model conditional on all recorded baseline confounders.
OR, odds ratio; CI, confidence interval.