Causal Inference and Alternative Explanations S.A. Murphy Univ. of Michigan May, 2004

Outline 1)Fundamental Problem of Causal Inference 2)Time Independent Treatments Example, Composition and Alternative Explanations, Ideal Trial 3)Time Dependent Treatments Example, Composition and Alternative Explanations, Ideal Trial

Fundamental Problem of Causal Inference

We have developed a new behavioral program for smokers. Is it better than standard care? Joe’s days abstinent if we provide the new behavioral program == Y 1 Joe’s days abstinent if we provide standard care==Y 0 If Y 1 > Y 0 then our answer is yes!

The fundamental problem of causal inference is that we can never observe both Y 1 and Y 0 and thus can not answer this question! We average Y 1 for people who appear like Joe and received new program. We average Y 0 for people who appear like Joe and received standard care. If average Y 1 > average Y 0 then our answer is yes!

Time Independent Treatments

Example: Does treatment improve abstinence one year later among smokers? Researchers compare smokers who receive standard care to smokers who receive the new behavioral program. Control for demographics, addiction severity, social network characteristics, stage of change.

Problem: Standard care smokers may differ from treated smokers in terms of unmeasured characteristics. There may be a compositional difference between smokers receiving standard care and smokers receiving the new behavioral program and this compositional difference may have led to observed differences in average days abstinent. Maybe difference in abstinence is due to difference in pretreatment motivational levels not difference in treatment?

Ideal Solution: Randomize subjects to new behavioral program or standard care

Example: Does the new behavioral program improve abstinence among smokers like Joe?

Example: Does the new behavioral program improve abstinence among smokers like Joe? But people who appear like Joe may differ from Joe in terms of unmeasured characteristics. Ideally we’d obtain the average effect of the new behavioral program for all smokers in our population who appear like Joe on measured characteristics: demographics, addiction severity, social network characteristics, stage of change

Randomize Treatment in our trial; control for measured demographics, pretreatment addiction severity, social network characteristics, stage of change Problem: People who appear like Joe in our trial may differ from people who appear like Joe in our population in terms of unmeasured characteristics. There may be a compositional difference between people like Joe in the population and people like Joe in our study.

Ideal Solution: Sample subjects from an explicitly defined population (Joe is a member of this population).

Time Dependent Treatments

Example: We want to evaluate a time varying treatment for smokers. Smokers are randomized to receive group therapy over 6 months or to standard care. In the treatment group, staff use clinical judgment that repeatedly assesses the smoker’s need for therapy and provides group therapy in response to this need. We would like to know if more group therapy translates into improved abstinence.

We compare smokers who are randomized to treatment and receive more group therapy to smokers who were randomized to treatment and who receive less group therapy. We control for demographics, addiction severity, social network characteristics, stage of change. We see a negative relationship between dose and days abstinent!

Problem: There may be unmeasured compositional differences between heavily treated and lightly treated smokers and these compositional differences may have led to observed differences in average abstinence rather than the dose of treatment. Perhaps smokers who show great need for treatment are getting the most treatment while smokers who show the least need for treatment are getting the least amount of group therapy.

X=measured characteristics U=unmeasured characteristics

Randomized Dose of Group Therapy X=measured characteristics U=unmeasured characteristics

For the Connoisseur!

Example: We want to inform clinical practice which would use measures of ongoing response in order to decide whether to provide more group therapy. Is it useful to provide more group therapy to those who show evidence of need? Regress days abstinent on measured characteristics X 1 and X 2 and on amounts of group therapy provided at times 1 and 2. Coefficient of group therapy at time 1 reflects more than the effect of group therapy at time 1 on days abstinent!

X=measured characteristics U=unmeasured characteristics

To assess the effect of and the usefulness of tailoring group therapy we need different kinds of regressions. This is what I do!