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01.12.2017 | Research article | Ausgabe 1/2017 Open Access

BMC Medical Research Methodology 1/2017

The alarming problems of confounding equivalence using logistic regression models in the perspective of causal diagrams

Zeitschrift:
BMC Medical Research Methodology > Ausgabe 1/2017
Autoren:
Yuanyuan Yu, Hongkai Li, Xiaoru Sun, Ping Su, Tingting Wang, Yi Liu, Zhongshang Yuan, Yanxun Liu, Fuzhong Xue
Wichtige Hinweise

Electronic supplementary material

The online version of this article (https://​doi.​org/​10.​1186/​s12874-017-0449-7) contains supplementary material, which is available to authorized users.

Abstract

Background

Confounders can produce spurious associations between exposure and outcome in observational studies. For majority of epidemiologists, adjusting for confounders using logistic regression model is their habitual method, though it has some problems in accuracy and precision. It is, therefore, important to highlight the problems of logistic regression and search the alternative method.

Methods

Four causal diagram models were defined to summarize confounding equivalence. Both theoretical proofs and simulation studies were performed to verify whether conditioning on different confounding equivalence sets had the same bias-reducing potential and then to select the optimum adjusting strategy, in which logistic regression model and inverse probability weighting based marginal structural model (IPW-based-MSM) were compared. The “do-calculus” was used to calculate the true causal effect of exposure on outcome, then the bias and standard error were used to evaluate the performances of different strategies.

Results

Adjusting for different sets of confounding equivalence, as judged by identical Markov boundaries, produced different bias-reducing potential in the logistic regression model. For the sets satisfied G-admissibility, adjusting for the set including all the confounders reduced the equivalent bias to the one containing the parent nodes of the outcome, while the bias after adjusting for the parent nodes of exposure was not equivalent to them. In addition, all causal effect estimations through logistic regression were biased, although the estimation after adjusting for the parent nodes of exposure was nearest to the true causal effect. However, conditioning on different confounding equivalence sets had the same bias-reducing potential under IPW-based-MSM. Compared with logistic regression, the IPW-based-MSM could obtain unbiased causal effect estimation when the adjusted confounders satisfied G-admissibility and the optimal strategy was to adjust for the parent nodes of outcome, which obtained the highest precision.

Conclusions

All adjustment strategies through logistic regression were biased for causal effect estimation, while IPW-based-MSM could always obtain unbiased estimation when the adjusted set satisfied G-admissibility. Thus, IPW-based-MSM was recommended to adjust for confounders set.
Zusatzmaterial
Additional file 2: Figure S1. Scenario 1 (Fig. 1a), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 ≈ A 3 when varied across the log transformed odds ratio effect of Z on X and X on Y. (PDF 25 kb)
Additional file 3: Figure S2. Scenario 2 (Fig. 1b), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 ≈ A 3 when varied across the log transformed odds ratio effect of Z on T and X on Y. (PDF 25 kb)
Additional file 4: Figure S3. Scenario 2 (Fig. 1b), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 ≈ A 3 when varied across the log transformed odds ratio effect of Z on X and W on X. (PDF 25 kb)
Additional file 5: Figure S4. Scenario 2 (Fig. 1b), simulation results of the bias and standard error of c-equivalence sets B 1 ≈ B 2 when varied across the log transformed odds ratio effect of Z on T and X on Y. (PDF 19 kb)
Additional file 6: Figure S5. Scenario 2 (Fig. 1b), simulation results of the bias and standard error of c-equivalence sets B 1 ≈ B 2 when varied across the log transformed odds ratio effect of Z on X and W on X. (PDF 19 kb)
Additional file 7: Figure S6 Scenario 3 (Fig. 1c), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 when varied across the log transformed odds ratio effect of Z on X and W on V. (PDF 19 kb)
Additional file 8: Figure S7. Scenario 3 (Fig. 1c), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 when varied across the log transformed odds ratio effect of T on Y, W on X and X on Y. (PDF 27 kb)
Additional file 9: Figure S8. Scenario 3 (Fig. 1c), simulation results of the bias and standard error of c-equivalence sets C 1 ≈ C 2 ≈ C 3 when varied across the log transformed odds ratio effect of Z on X and W on V. (PDF 25 kb)
Additional file 10: Figure S9. Scenario 3 (Fig. 1c), simulation results of the bias and standard error of c-equivalence sets C 1 ≈ C 2 ≈ C 3 when varied across the log transformed odds ratio effect of T on Y, W on X and X on Y. (PDF 35 kb)
Additional file 11: Figure S10 Scenario 4 (Figure 1d), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 ≈ A 3 when varied across the log transformed odds ratio effect of Z on X and X on Y. (PDF 25 kb)
Additional file 12: Figure S11. Scenario 4 (Fig. 1d), simulation results of the bias and standard error of c-equivalence sets A 1 ≈ A 2 ≈ A 3 when varied across the log transformed odds ratio effect of Z on W,T on W and W on Y. (PDF 35 kb)
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