Reading Response Discussions

Specify a hypothesis regarding a binary exposure, a continuous mediator, and a continuous outcome.  Specify how each variable affects its children (i.e., how the exposure influences the mediator) and the distribution of the random or unmeasured determinants of the child variables. 

 Research question: Does septic shock affect children’s length of stay in the PICU directly and/or is this relationship mediated by volume of fluid resuscitation received (ml/kg)?

 Septic shock (Y/N) --> fluid resuscitation volume (ml/kg) -->  PICU LOS

Using the software of your choice, generate a population with 10000 people under a causal structure consistent with this hypothesized causal structure. Use a conventional Baron-Kenny decomposition to estimate the direct and indirect effects of the exposure on the outcome. 

 x=septic shock

c=source of infection

m=fluid resuscitation volume

y=PICU LOS

Direct effect of x on y, not mediated by m is 1

Indirect effect of x on y, via m is 2*.25 = 0.5

Total effect of x on y is 1+.5=1.5 and there is no interaction between m and x and c=0

Controlled direct effect = CDE= Y(x=1,m)-Y(x=0,m)

Total Natural Direct Effect = total NDE = Y(x=1, m=1)- Y(x=0, m=1)

Pure Natural Direct Effect = pure NDE = Y(x=1, m=0)- Y(x=0, m=0)

Total Natural Indirect Effect = total NIE = Y(x=1, m=1)- Y(x=1, m=0)

Pure Natural Indirect Effect= pure NIE = Y(x=0, m=1)- Y(x=0, m=0)

Now introduce a confounder of the mediator and outcome (C) into your causal model.  Define the new causal models and simulate a new data set.  Use a conventional decomposition without control for the confounder first and then with control for the confounder to derive estimates of the direct and indirect effects of exposure on outcome. 

 Baron-Kenny decomposition to estimate the direct and indirect effects of the exposure on the outcome.

Total effect of x on y, including mediation by m, not controlling for C is 1.6

The effect of m on y is 2.1

Biased direct effect of x on y, not mediated by m, not controlling for C is -4

 Then, if control for c the direct effect of x on y, not mediated by m, controlling for C is 1

Indirect effect estimated w/o control for c is: 5.637

Indirect effect estimated w/ control for c is: .631, which is approximately what the above indirect effect of x on y (0.5) plus some random error

Total effect is: 1.64, which is approximately what the above total effect of x on y (1.5) plus some random error

Paramed gives the following, which is more similar to the above, true values:

CDE:Controlled direct effect= 1.0110056

NDE:natural direct effect = 1.0110515

NIE:natural indirect effect= .50238486

MTE:marginal total effect = 1.5134364

Create a new version of the mediator that represents a badly measured version of that variable, for example by taking the original variable and adding some random noise to it.  Now use that mediator to evaluate the direct and indirect effects. 

 Baron-Kenny decomposition to estimate the direct and indirect effects of the exposure on the outcome with the noisy mediator.

Total effect of x on y, including mediation by m, not controlling for C is 1.6

The effect of m on y is  1.959073

Biased direct effect of x on y, not mediated by m, not controlling for C is -3.340545 

Direct effect of x on y, not mediated by m, controlling for C is  1.115947

Now, because we have introduced error into the measurement of the mediator, the total effect doesn’t change but the effect of m on y increases, the biased direct of x on y decreases, and the direct effect of x on y increases slightly (therefore the indirect effect of x on y must decrease slightly).

Estimating the CDE

Direct Effect of x on y = 1.011006

 The average value of y if x is set to 0 and m is set to 0 = -.120016

The average value of y if x is set to 0 and m is set to 0 = .8909896

Estimated direct effect of x, setting m to 0, is: .8909896-(-.120016) = 1.011

The counterfactual value of y setting x to 0 = -.1909555

The counterfactual value of y setting x to 1  =  1.449322

Estimated total effect of x on y is: 1.449322 – (-.1909555) = 1.64

Paramed check gives almost identical answers

cde:controlled direct effect=  1.0110056

nde:natural direct effect =  1.011025  

nie:natural indirect effect= .16823403

mte:marginal total effect =  1.179259

Bonus

The counterfactual value of y setting x to 1 and m to the value it would take if x were set to 0= .8831828 

The counterfactual value of y setting x to 1 and m to the value it would take if x were set to 1)= 1.385568

The natural indirect effect of x on y, mediated by m is: 1.385568- .8831828  = .502

Do file is attached

1. Specify a hypothesis regarding a binary exposure, a continuous mediator, and a continuous outcome.  Specify how each variable affects its children (i.e., how the exposure influences the mediator) and the distribution of the random or unmeasured determinants of the child variables. 

Hypothesis: The effect of childhood poverty on income is mediated by years of education.

2. Using the software of your choice, generate a population with 10000 people under a causal structure consistent with this hypothesized causal structure. Use a conventional Baron-Kenny decomposition to estimate the direct and indirect effects of the exposure on the outcome.  

DATA GENERATING RULES
gen poverty = runiform()<0.20
gen eduyears = 0.75*poverty + rnormal()
gen income = 0.75*poverty + 2*eduyears + rnormal()

BASED ON THE DATA GENERATING RULES ABOVE…
Direct effect of poverty on income, not mediated through years of education = 0.75
Indirect effect of poverty on income, via years of education = 0.75*2 = 1.5
Total effect of poverty on income = 0.75+1.5 = 2.25

BARON-KENNY DECOMPOSITION RESULTS:
Direct effect: 0.723
Indirect effect: 1.536
Total effect: 2.259

3. Now introduce a confounder of the mediator and outcome (C) into your causal model.  Define the new causal models and simulate a new data set.  Use a conventional decomposition without control for the confounder first and then with control for the confounder to derive estimates of the direct and indirect effects of exposure on outcome.

NEW DATA GENERATING RULES
gen poverty = runiform()<0.20
gen eduqual = rnormal()
gen eduyears = 0.75*poverty + eduqual + rnormal()
gen income = 0.75*poverty + 2*eduyears + eduqual + rnormal()

BARON-KENNY DECOMPOSITION RESULTS:
Indirect effect without controlling for confounder: 1.838
Indirect effect with controlling for confounder: 1.467
Total effect: 2.196 

CONFIRMING RESULTS WITH PARAMED
Controlled direct effect: 0.754
Natural direct effect: 0.755
Natural indirect effect: 1.46
Marginal total effect: 2.22

CONFIRMING RESULTS WITH MEDEFF
ACME: 1.487
Direct effect: 0.730
Total effect: 2.217

4. Create a new version of the mediator that represents a badly measured version of that variable, for example by taking the original variable and adding some random noise to it.  Now use that mediator to evaluate the direct and indirect effects.

NEW DATA GENERATING RULES
gen bias = rnormal()*0.8
gen eduyears_biased = eduyears + bias 

BARON-KENNY DECOMPOSITION RESULTS:
Direct effect: 1.305
Indirect effect: 0.892
Total effect: 2.196

5. Now try estimating the CDE:

Controlled direct effect of x, setting M=0: 0.818
Estimated total effect of x on y: 2.253 

CONFIRMING RESULTS WITH PARAMED
Controlled direct effect: 0.818
Natural direct effect: 0.818
Natural indirect effect: 0.25
Marginal total effect: 1.07

6. BONUS: Go back to the original data (prior to estimating the CDE) and estimate the natural indirect effect of X on Y, mediated by M.
Natural indirect effect of x on y, mediated by m: 1.442

Specify a hypothesis regarding a binary exposure, a continuous mediator, and a continuous outcome.  Specify how each variable affects its children (i.e., how the exposure influences the mediator) and the distribution of the random or unmeasured determinants of the child variables. 

Population: Ugandan Adults

Exposure: Kaposi sarcoma (KS) (y/n)

Outcome Quality of life

Mediator: Number of Kaposi sarcoma lesions

KS itself may have a decreasing effect of quality of life.  Kaposi sarcoma commonly presents with cutaneous lesions, we wonder what effect (if any) the number of cutaneous lesions itself may have an effect on quality of life. 

Using the software of your choice, generate a population with 10000 people under a causal structure consistent with this hypothesized causal structure. Use a conventional Baron-Kenny decomposition to estimate the direct and indirect effects of the exposure on the outcome.  

Data generation:

Data arbitrarily follows data from a case-control study (Ziegler. Risk factors for Kaposi’s sarcoma in HIV-positive subjects in Uganda. AIDS. 11(13):1619-1626.)  We use a KS+ proportion of 40%.  Direct of KS on QOL is 5.  Indirect effect of KS on QOL through number of lesions by .05 per lesion.

[QOL = 5*KS + .05*number of lesiosn + rnormal()]

gen ks  = runiform()<.4

gen ksnum = .5*ks + runiform()

gen qol = 5*ks + .05*ksnum + runiform()

Baron-Kenny Decompensation results:

Direct Effect: 5.018

Indirect Effect: .501

Total Effect: 5.519

Now introduce a confounder of the mediator and outcome (C) into your causal model.  Define the new causal models and simulate a new data set.  Use a conventional decomposition without control for the confounder first and then with control for the confounder to derive estimates of the direct and indirect effects of exposure on outcome. 

Confounder: nevirapine therapy (y/n)

gen ks  = runiform()<.4

gen art = runiform

gen ksnum = .5*ks + art + runiform()

gen qol = 5*ks + .05*ksnum + art + runiform()

Baron-Kenny Decompensation results:

Indirect Effect without control: -.01

Indirect Effect with control .016

Total Effect: 5.026

paramed:

Controlled direct effect: 5.022

Natural direct effect: 5.013

Natural indirect effect: .014

Marginal total effect: 5.027

Create a new version of the mediator that represents a badly measured version of that variable, for example by taking the original variable and adding some random noise to it.  Now use that mediator to evaluate the direct and indirect effects. 

Baron-Kenny Decompensation results:

Direct Effect with confounder: 5.022

Indirect Effect with confounder: .001

Total Effect: 5.027

Now try estimating the CDE:

Controlled direct effect: 4.977

Estimated total effect of KS on QOL: 5.021

Please see code and responses attached. 

I think I finally figured this out... attached. 

This was my skip week.