Methods for inferring short- and long-term effects of exposures on outcomes, using longitudinal data on both measures

Transcription

1 Methods for inferring short- and long-term effects of exposures on outcomes, using longitudinal data on both measures Ruth Keogh, Stijn Vansteelandt, Rhian Daniel Department of Medical Statistics London School of Hygiene and Tropical Medicine MRC BSU Centenary Conference 2014

2 Motivation

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6 Aims of this work Compare methods for addressing causal questions using data of this type most of the causal inference literature has focused on a single outcome Suggest a sensible strategy for analysis Aimed at an epidemiological audience

7 Three questions 1. What is the causal effect of X t on Y t? We refer to this as a short term effect. 2. Do there exist any longer term effects? Is there any effect of X t 1 which is not mediated through X t? 3. What is the effect of X t 1 on Y t? We may be interested in the direct effect or total effect

8 Three questions 1. What is the causal effect of X t on Y t? We refer to this as a short term effect. 2. Do there exist any longer term effects? Is there any effect of X t 1 which is not mediated through X t? 3. What is the effect of X t 1 on Y t? We may be interested in the direct effect or total effect

9 Three questions 1. What is the causal effect of X t on Y t? We refer to this as a short term effect. 2. Do there exist any longer term effects? Is there any effect of X t 1 which is not mediated through X t? 3. What is the effect of X t 1 on Y t? We may be interested in the direct effect or total effect

10 Three questions 1. What is the causal effect of X t on Y t? We refer to this as a short term effect. 2. Do there exist any longer term effects? Is there any effect of X t 1 which is not mediated through X t? 3. What is the effect of X t 1 on Y t? We may be interested in the direct effect or total effect

11 Estimating short-term effects Two approaches Sequential conditional mean models Marginal structural models and inverse probability weighting Both fitted using Generalized Estimating Equations (GEEs) We focus on a binary exposure X t and continuous outcome Y t

12 Sequential conditional mean models Sequential conditional mean model E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 The causal short term effect, β X1, can be estimated using generalized estimating equations (GEEs)

13 Sequential conditional mean models Sequential conditional mean model E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 The causal short term effect, β X1, can be estimated using generalized estimating equations (GEEs)

14 Counterfactuals and Marginal Structural Models Counterfactuals Y X t =1 t and Y X t =0 t Short term causal effect E(Y X t =1 t ) E(Y X t =0 t ). Marginal structural model E(Y X t =x t ) = ω 0 + ω 1 x

15 Counterfactuals and Marginal Structural Models Counterfactuals Y X t =1 t and Y X t =0 t Short term causal effect E(Y X t =1 t ) E(Y X t =0 t ). Marginal structural model E(Y X t =x t ) = ω 0 + ω 1 x

16 Counterfactuals and Marginal Structural Models Counterfactuals Y X t =1 t and Y X t =0 t Short term causal effect E(Y X t =1 t ) E(Y X t =0 t ). Marginal structural model E(Y X t =x t ) = ω 0 + ω 1 x

17 Inverse probability weighting Marginal structural model E(Y X t =x t ) = ω 0 + ω 1 x The causal short term effect, ω 1, can be estimate using weighted generalized estimating equations (GEEs) Individual weights { Pr(Xt = x X t 1, L t,ȳt 1) } 1

18 Inverse probability weighting Marginal structural model E(Y X t =x t ) = ω 0 + ω 1 x The causal short term effect, ω 1, can be estimate using weighted generalized estimating equations (GEEs) Individual weights { Pr(Xt = x X t 1, L t,ȳt 1) } 1

19 Estimating short term effects: comparison of methods Sequential conditional mean model E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 Marginal structural model E(Y X t =x t ) = ω 0 + ω 1 x

20 Estimating short term effects: comparison of methods Method Independence Unstructured Seq cond mean model (0.100) (0.098) MSM and IPW (0.236) (4.331)

21 Estimating short term effects: comments We do not need to resort to MSMs/IPW to estimate short term causal effects MSMs/IPW is inefficient relative to using sequential conditional mean models MSMs/IPW does not easily extend to continuous exposures We have looked at adjustment for propensity scores in the sequential conditional mean model approach Sequential conditional mean model with propensity score E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 + β PS PS t

22 Estimating short term effects: comments We do not need to resort to MSMs/IPW to estimate short term causal effects MSMs/IPW is inefficient relative to using sequential conditional mean models MSMs/IPW does not easily extend to continuous exposures We have looked at adjustment for propensity scores in the sequential conditional mean model approach Sequential conditional mean model with propensity score E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 + β PS PS t

23 Estimating short term effects: comments We do not need to resort to MSMs/IPW to estimate short term causal effects MSMs/IPW is inefficient relative to using sequential conditional mean models MSMs/IPW does not easily extend to continuous exposures We have looked at adjustment for propensity scores in the sequential conditional mean model approach Sequential conditional mean model with propensity score E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 + β PS PS t

24 Estimating short term effects: comments We do not need to resort to MSMs/IPW to estimate short term causal effects MSMs/IPW is inefficient relative to using sequential conditional mean models MSMs/IPW does not easily extend to continuous exposures We have looked at adjustment for propensity scores in the sequential conditional mean model approach Sequential conditional mean model with propensity score E(Y t X t, L t,ȳt 1) = β 0 + β X1 X t + β X2 X t 1 + β T L L t + β Y Y t 1 + β PS PS t

25 Three questions 1. What is the causal effect of X t on Y t? We refer to this as a short term effect. 2. Do there exist any longer term effects? Is there any effect of X t 1 which is not mediated through X t? 3. What is the effect of X t 1 on Y t? We may be interested in the direct effect or total effect

26 A new test for long term effects Proposed test - basic idea 1. Predict Y t under a situation where the arrow from X t to Y t is eliminated 2. Perform a test of whether X t depends on future predicted Y.

27 A new test for long term effects Proposed test - basic idea 1. Predict Y t under a situation where the arrow from X t to Y t is eliminated 2. Perform a test of whether X t depends on future predicted Y.

28 A new test for long term effects Step 1: Predict Y t if the arrow from X t to Y t is eliminated. Fit a model for Y t X t, L t,ȳt 1 Obtain the predicted outcome, Ŷt, when X t = 0 Step 2: Perform a test of whether X t depends on future predicted Y Fitting a model for X t 1 X t 2, L t 1,Ȳt 2,Ŷt

29 A new test for long term effects Step 1: Predict Y t if the arrow from X t to Y t is eliminated. Fit a model for Y t X t, L t,ȳt 1 Obtain the predicted outcome, Ŷt, when X t = 0 Step 2: Perform a test of whether X t depends on future predicted Y Fitting a model for X t 1 X t 2, L t 1,Ȳt 2,Ŷt

30 A new test for long term effects Step 2: Perform a test of whether X t depends on future predicted Y logit Pr(X t 1 = 1 X t 2, L t 1,Ȳt 2,Ŷt ) = θ 0 + θ 1 X t 2 + θ 2 L t 1 + θ 3 Y t 2 + θ 4 Ŷ t Comments The test of θ 4 = 0 should take into account the uncertainty in the predicted value Ŷt This can be done using bootstrapping According to our simulation studies the test performs as it should in a range of situations

31 A new test for long term effects Step 2: Perform a test of whether X t depends on future predicted Y logit Pr(X t 1 = 1 X t 2, L t 1,Ȳt 2,Ŷt ) = θ 0 + θ 1 X t 2 + θ 2 L t 1 + θ 3 Y t 2 + θ 4 Ŷ t Comments The test of θ 4 = 0 should take into account the uncertainty in the predicted value Ŷt This can be done using bootstrapping According to our simulation studies the test performs as it should in a range of situations

32 Three questions 1. What is the causal effect of X t on Y t? We refer to this as a short term effect. 2. Do there exist any longer term effects? Is there any effect of X t 1 which is not mediated through X t? 3. What is the effect of X t 1 on Y t? We may be interested in the direct effect or total effect

33 Estimating long term effects Sequential conditional mean models We can estimate the total effect of X t 1 on Y t but not the direct effect Marginal structural models and inverse probability weighting We can estimate both the total effect and the direct effect of X t 1 on Y t

34 Estimating long term effects Sequential conditional mean models We can estimate the total effect of X t 1 on Y t but not the direct effect Marginal structural models and inverse probability weighting We can estimate both the total effect and the direct effect of X t 1 on Y t

35 Summary comments MSMs/IPW are inefficient for estimation of short term effects When the outcome is binary the two approach no longer estimate the same effect do you want the marginal or conditional effect? We have devised a new test which can be used to establish whether long term effects exist Long term effects can be estimated using both approaches, but it depends on whether you want the total or direct effect Future work: use sequential conditional mean models to estimate direct effects

36 Summary comments MSMs/IPW are inefficient for estimation of short term effects When the outcome is binary the two approach no longer estimate the same effect do you want the marginal or conditional effect? We have devised a new test which can be used to establish whether long term effects exist Long term effects can be estimated using both approaches, but it depends on whether you want the total or direct effect Future work: use sequential conditional mean models to estimate direct effects

37 Summary comments MSMs/IPW are inefficient for estimation of short term effects When the outcome is binary the two approach no longer estimate the same effect do you want the marginal or conditional effect? We have devised a new test which can be used to establish whether long term effects exist Long term effects can be estimated using both approaches, but it depends on whether you want the total or direct effect Future work: use sequential conditional mean models to estimate direct effects

38 Summary comments MSMs/IPW are inefficient for estimation of short term effects When the outcome is binary the two approach no longer estimate the same effect do you want the marginal or conditional effect? We have devised a new test which can be used to establish whether long term effects exist Long term effects can be estimated using both approaches, but it depends on whether you want the total or direct effect Future work: use sequential conditional mean models to estimate direct effects

39 Summary comments MSMs/IPW are inefficient for estimation of short term effects When the outcome is binary the two approach no longer estimate the same effect do you want the marginal or conditional effect? We have devised a new test which can be used to establish whether long term effects exist Long term effects can be estimated using both approaches, but it depends on whether you want the total or direct effect Future work: use sequential conditional mean models to estimate direct effects

40 Thank you