| Background:In observational studies,assessing causal effects of exposure on health/disease outcomes are important for identifying risk factors and developing effective intervention policies.Longitudinal data are widely used in many fields such as medicine,sociology,economics,epidemiology,and psychology.Based on the chronological order,longitudinal data has obvious advantages in the study of causality.Randomized control trial,as representative of experimental studies,is always the gold standard for causal inference.In observational studies,it is difficult to randomize exposure factors.Therefore,the most commonly used statistical methods,such as the traditional regression model(linear regression,logistic regression,poisson regression),mixed effects models,generalized estimating equations are correlation analysis method which often ignore unobserved confounding factors.Furthermore,ignoring unobserved confounding will lead to biased causal effect estimations.Epidemiologists have proposed a variety of statistical methods to control for unobserved confounders.Theoretically,quasi-experimental methods such as Instrumental variables,Difference-in-difference,Regression discontinuity design and Negative control can eliminate unobserved confounding factors and accurately estimate causal effects.However,these methods have some limitations in applications.For example,since environmental factors are almost always produced alongside other environmental factors,it is difficult to find instrumental variables that satisfy the assumption of "horizontal pleiotropy".The lagged causal effect of pre-outcome on post-outcome will lead to the parallel trend assumption of the difference-in-difference model violated,and the negative control exposure or outcome invalid,further result in biased causal effect estimation.For Regression discontinuity design,the sample around discontinuity will not be random if the individuals can precisely change their behavior and obtain their preferred status.In addition,the Crosslag panel models can be used to estimate the bidirectional association between exposure and health/disease outcome.However,association analysis is not causality theoretically.Therefore,a series of new causal inference methods are urgently needed in observational studies.Such methods,which could make full use of "time-difference" information in longitudinal data,can control the time-depending confounding factors,and estimate causal effects accurately.Method:Based on the causal diagram theory,taking advantage of the "time-difference"information in the longitudinal time,we propose three novel methods to control the unobserved time-varying confounding factors,and estimate causal effects accurately only using the exposure and outcome variables themselves.①When the longitudinal data including exposures at three times and outcome at a single time,we propose the Negative Control Exposure based on Time-series study,NCE-TS,in the situation of no bidirectional causality between exposure and outcome and no lagged causal effect of pre-exposure on post-exposure(or pre-outcome on post-outcome).②When the longitudinal data including outcomes at three times and exposure at a single time,we propose the Negative Control Outcome Regression,NCOR,in the situation of no bidirectional causality between exposure and outcome and permitted lagged causal effect of pre-outcome on post-outcome.③When the longitudinal data including exposure and outcome at least three times,we propose the CrossLag Weighted Regression,CLWR,in the situation of bidirectional causality between exposure and outcome and permitted lagged causal effect of pre-exposure on post-exposure(and pre-outcome on postoutcome).A systematic theoretical derivation,statistical simulations and application studies are used to verified the scientificity and feasibility of NCE-TS,NCOR,CLWR models.(1)Theoretical proof:For NCE-TS,NCOR,CLWR models,the proof is divided into three steps.①Calculate the true causal effect of interested based on do-calcus,including the true causal effect of exposure on outcome,true lagged causal effect of pre-exposure on post-exposure and real lagged causal effect of pre-outcome on post-outcome.② Calculate the estimations of these models based on model assumptions and causal diagram.③Prove that the estimations are the unbiased causal effect estimate.(2)Simulation study:The simulation study is divided into three aspects to verify the scientificity and validity of these models(NCE-TS,NCOR,CLWR models).①The biases and standard errors are used to evaluate the precision and accuracy of causal effect estimation.②The type I error rates and statistical power are used to assess the statistical test ability of these model(NCE-TS,NCOR,CLWR models).③The stability of the model is tested through sensitivity analysis by relaxing the assumptions.(3)Application study:①Two challenging applications are used to verify the validity of NCE-TS model.One is to explore the potential causal relationship between ambient average temperature and cancer cumulative risk(50 males and 54 females)using a step-adjusted confounder approach based on global environment-cancer incidence cohort.Another one is to explore the potential causal relationship between green space and death due to stroke in stroke patients based on death cohort of stroke patients in Pingyi,Shandong province.② For NCOR model,we investigate the causal relationship between green space and blood pressure in hypertensive patients and the lagged causal effect of pre-blood pressure on post-blood pressure based on the hypertension patients’ cohort in Huangdao,Shandong province.③ For the CLWR model,we estimate the bidirectional causal relationship between fasting blood glucose and systolic blood pressure in diabetes patients and the lagged causal effect pre-fasting blood glucose on post-fasting blood glucose(pre-systolic blood pressure on post-systolic blood pressure)based on the Shandong Provincial health and medical big data platform.Results:Taking advantages of exposure and outcome variables themselves,the NCE-TS,NCOR,and CLWR models are constructed to control unobserved confounders and estimate the causal effects.The main results are as follows:(1)NCE-TS model:In longitudinal data,Xt-h is the exposure at time t-h,Yt is the outcome at time t,taking advantage of exposure Xt+h at time t+h,the NCE-TS model can be used to control the time-depending confounders Ut-h,Ut,Ut+h.1)Theoretical result:Construct yt=β0+β1xt-h+β2xt+h+ε when the outcome is continuous.Then calculate the regression coefficient β1 and β2.The φXt-h→Yt=β1-β2 further can be constructed.The theoretical result indicates that φXt-h→Yt,is the unbiased causal effect estimation and φXt-h→Yt follows the normal distribution.Construct φ’Xt-h→Yt=κxt-h-κxt+h when the outcome is categorical.When the Xt-h and Xt+h are binary variables.The κxt-h and κxt+h can be expressed as κxt-h=P(yt|Xt-h=1,Xt+h=1)-P(yt|Xt-h=0,Xt+h=1)andκxt+h=P(yt|Xt-h=1,Xt+h=1)-P(yt|Xt-h=1,Xt+h=0).The theoretical result showsφ’Xt-h→Yt is unbiased causal effect estimation.2)Simulation results:①Accuracy and precision:The simulation results show that NCE-TS model can completely eliminate the unobserved confounders and obtain unbiased causal effect estimation regardless of the outcome is a continuous variable or a categorical variable.While traditional linear regression model(crude association)and the linear regression model adjusting for the proxy of unobserved confounders(crude association conditional on the proxy of unobserved confounders)cannot effectively control the unobserved confounders.Compared with other models,the NCE-TS model has a relatively large standard error,but it is acceptable.② Statistical test:The hypothesis test results show that the type I error rates are stable around the given test level(0.05)when the null hypothesis is true,and the statistical power is high enough when the sample size reaches 600.③Sensitivity analysis,the estimations of NCE-TS model are biased after relaxing the model assumptions.And the biases of NCE-TS model is less than other models.3)Application results:① The traditional regression models show that ambient average temperature is negatively correlated with the cumulative risk of most cancers.The number of negative associations is reduced significantly when adjusting for the absolute value of longitude,latitude,and altitude via linear regression adjusting for potential confounders.Furthermore,the number of negative associations further decreases after adjusting for the proxy of unobserved confounders.Finally,none of site-specific cancers show negative causal associations with air temperatures statistically significantly when eliminating all unobserved confounders by employing NCE-TS.② All three models including crude association,crude association conditional on the proxy of unobserved confounders and NCE-TS model indicate that the green space and stroke patients’ mortality show negative association with statistical significances until exposure period reaches 6 months.However,compared with the other two models,the NCE-TS model has a relatively large estimated value.The proposed NCE-TS model is implemented in an R package called NCETS,freely available on GitHub(https://github.com/yuyy-shandong/NCETS).(2)NCOR model:In longitudinal data,Xt is the exposure at time t,Yt-h,Yt and Yt+h are the outcomes at time t-h,t and t+h.Taking advantage of Yt-h at time t-h,we propose NCOR model to control time-depending unobserved confounder,Ut-h,Ut,Ut+h and estimate the causal effect.1)Theoretical result:Based on J studies,construct the weighted regression βt+h=κ0+κ1βt+κ2βt-h+ε.Where βt+h,βt and βt-h are regression coefficients of Yt+h,Yt and Yt-h on Xt based on J studies.The theoretical result shows κ0 is the unbiased causal effect estimations of Xt on Yt+h and κ1 is unbiased causal effect estimations of Yt on Yt+h.2)Simulation results:① Accuracy and precision:NCOR model can obtain unbiased causal effect estimates of exposure on outcome and the lagged causal effect estimation of pre-outcome on post-outcome,while other models,such as Difference-inDifference,Adjusts for the Lagged Dependent Variables,Double Proxy variable model and meta-analysis of these models cannot accurately estimate the causal effect.In addition,the standard errors of NCOR model is minimum.② Statistical test:The hypothesis test results show that the type I error rates are stable around the given test level(0.05)when the null hypothesis is true,and the statistical power is high enough when the number of studies reaches 10.The type I error rates of NCOR model will inflated when estimating the lagged causal effect of pre-outcome on post-outcome and the statistical power is high enough when the number of studies reaches 20.③ Sensitivity analysis,the estimations of NCOR model is biased after relaxing the model assumptions.And the biases of NCOR model is less than other models.3)Application results:Difference-in-difference,Adjusts for the Lagged Dependent Variables,Double Proxy variable model show that there is a correlation between green space and blood pressure of hypertensive patients in most interval months.In addition,the number of associations with significantly further decreases using meta-analysis.Finally,NCOR model shows that there is no obvious causal correlation between green space and blood pressure of hypertensive patients.In addition,NCOR model,Adjusts for the Lagged Dependent Variables,and it’s meta-analysis illustrate that pre-blood pressure is the risk factor for post-blood pressure.The proposed NCOR model is implemented in an R package called NCOR2022,freely available on GitHub(https://github.com/yuyy-shandong/NCOR2022).(3)CLWR model:The longitudinal data includes exposures(Xt1,Xt2 and Xt3),outcomes(Yt1,Yt2 and Yt3)at time t1,t2,t3.Taking advantage of Xt1 and Yt1 at time t1,we propose CLWR model to control time-depending unobserved confounder,Ut-h,Ut,Ut+h and estimate the causal effect.1)Theoretical result:Based on J studies,construct the weighted regression Where γXt3|Yt1,γYt2|Yt1 and γXt2|Ytl are the regression coefficients of Xt3,Yt2 and Xt2 on Yt1,respectively.γYt3|Xt1,γXt2|Xt1 and γYt2|Xt1 are the regression coefficients of Yt3,Xt2 and Yt2 on Xt1,respectively.The theoretical results show κXt2→Yt3,κYt2→Yt3,κYt2→Xt3 an κXt2→Xt3 are the unbiased causal effect estimation Xt2→Yt3,Yt2→Xt3,Xt2→Xt3 and Yt2→Yt3.2)Simulation results:① Accuracy and precision:Simulation results show that CLWR model can obtain unbiased estimates of the above four causal effects,while other models,CrossLag Panel model and it’s meta-analysis model cannot accurately estimate the causal effects.The CLWR model has the smallest standard errors in all models.②Statistical test:In addition,hypothesis testing shows that the type I error rates for the above four causal effect are stable around the given test level(0.05).When the number of studies is greater than 25,the statistical power is high enough.③ Sensitivity analysis,the estimations of CLWR model is biased after relaxing the model assumptions.And the biases of CLWR model is less than other models.3)Application results:The CrossLag Panel model shows that the pre-systolic blood pressure is the risk factor of the post-systolic blood pressure.Meta-analysis based on CrossLag panel model shows that he pre-systolic blood pressure is the risk factor of the post-systolic blood pressure in a shorter interval time.Finally,the CLWR model shows that pre-systolic blood pressure is the risk factor of the post-systolic blood when the interval time is less than around 20 months,and the effect gradually decreases with the time interval longer.The fasting blood glucose shows similary results.In addition,the CrossLag regression model shows a bidirectional relationship between systolic blood pressure and fasting blood glucose,while CLWR model shows no obvious bidirectional causal relationship between systolic blood pressure and fasting blood glucose.The proposed CLWR model is implemented in an R package called CLWR,freely available on GitHub(https://github.com/yuyy-shandong/CLWR).Conclusion:Based on causal diagram,taking advantage of the "time-difference"information in the longitudinal time,the NCE-TS,NCOR,and CLWR models are constructed to control unobserved confounders and estimate the causal effect only using exposures and outcomes themselves.1)Based on unidirectional and temporal causality of exposure to health/disease outcomes,both theoretical and simulation studies show that the NCE-TS model could completely eliminate unobserved confounders and obtain unbiased and robust estimates of causal effects,regardless of outcome is a continuous or a categorical variable.2)Based on the unidirectional effect of exposure on health/disease outcomes,and permitted lagged causal effect of pre-outcome on post-outcome.Both theoretical and simulation studies show that NCOR model can accurately identify and estimate the causal effect of exposure factors on health/disease outcomes and lagged causal effect of pre-outcome on postoutcome.3)Based on bidirectional causal effect between exposure and health/disease outcome,theoretical and simulation studies show that CLWR model can be used to identify and estimate the bidirectional causal effect between exposure and health/disease outcome,lagged causal effect of pre-exposure on post-exposure and pre-outcome on post-outcome.4)The NCE-TS model suggests that the negative correlation between temperature and cancer risk in the association analysis may be a spurious association which is caused by unobserved confounders.In addition,the NCE-TS model shows that living in areas with higher levels of green vegetation for more than 6 months is associated with a lower risk of death from stroke.NCOR model suggests that the negative correlation between green space and blood pressure in previous studies may be spurious association caused by unobserved confounders.In addition,pre-blood pressure is a risk factor for post-blood pressure.Furthermore,CLWR model shows that pre-systolic blood pressure is the risk factor for post-systolic blood pressure,and pre-fasting blood glucose is a risk factor for post-fasting blood glucose,and there is no obvious bidirectional causal relationship between systolic blood pressure and fasting blood glucose. |
