Analytic Methods and Issues in CER from Observational Data
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UCSF researcher, Charles McCulloch, PhD, presents. View more related presentations and resources at http://accelerate.ucsf.edu/research/cer
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Analytic Methods and Issues in CER from Observational Data
- 1. Analytic Methods and Issues in CER from Observational Data CER Symposium, January 2012 Charles E. McCulloch Division of Biostatistics University of California, San Francisco
- 9. Example Treatment effect 1.4 (95% CI 0.6, 2.3)
- 11. Issues with regression adjustment (true model)
- 12. Issues with regression adjustment (fit interaction) Treatment effect 3.2 (95% CI -.6, 7.1) Previously: 1.4 (95% CI 0.6, 2.3)
- 17. Counterfactuals Outcome under Patient Group Ctl Trt Difference 1 Trt 4 8 4 2 Ctl 0 3 3 3 Trt 4 3 -1 4 Trt 3 4 1 … Ave in popl’n 1.02 = Ave Causal Effect Outcome under Patient Group Ctl Trt Difference 1 Trt 4 8 4 2 Ctl 0 3 3 3 Trt 4 3 -1 4 Trt 3 4 1 … Ave in popl’n 1.02 = Average Causal Effect
- 31. Regression estimation Predicted causal effect for a trt subject ACE estimated to be 1.2 (CI 0.4, 2.1) Predicted causal effect for a ctl subject
Notes de l'éditeur
- Explain carefully: Y axis is delta BDI. Red is treatment group, blue is control. Change in BDI values for blue and red are well interspersed. So average values are about the same. No treatment effect? Perhaps there is confounding by age. Older participants are less likely to adopt the internet intervention (very few red dots on right of graph). And older participants do better in either treatment group. And, for a given age the treatment group seems to do better. In the older age range, we have very few comparators. This lack of overlap makes it almost impossible to understand the relationship between age and delta BDI (among the older ages) in the treatment group. So difficult to model.
- We fit a regression model. Being careful, neither nonlinearity in the relationship nor interactions are even close to statistically significant, so we stick with the basic model, which is what many people would fit solely. Stat sign treatment effect. Can interpret causally if we believe the only differences between the groups are their ages and model is correct.
- Lack of overlap is a serious concern because it is difficult to determine if differences are causal or due to the incorrect model. Can see the lack of overlap here, but wouldn’t be able to in a more realistic example with many predictors.
- Here is the true model from which I generated the (made-up) data. Observations: I fit the wrong model There is little or no treatment effect in the older age group Since most of the data for comparison is in the younger age group (where the treatment effect is larger), I overestimated the average effect across all ages. Note: data generating model was 4+(age-30)*3.5/40 for treatment and 2+(age-30)*6/40 for control. So average causal effect at a given age is the difference, or 3.875-age*0.0625. and the ACE is 3.875-\\bar(age)*0.0625 or 3.875-45.65*0.0625 = 1.02.
- What!? Treatment effect is now estimated to be 3.2! And not statistically significant. What is going on? When you enter the interaction, the treatment effect is the estimated (extrapolated) value at age=0. Need to center variables so a value of 0 is a value of interest.
- Statistically significant treatment effect.
- I learned this in 1978 …. From a book written in 1959 …. Quoting a result from a 1923 paper by Jerzy Neyman.
- Entries in table are change in BDI. So the first patient was in the Trt group and improved by 8 points. But if they had been in the Ctl group, they would also have improved, by only by 4 points. Patient 3 improved by 3 points. But if they had been in the Ctl group they would have done better and improved by 4 points. Notes: Causal effect need not be the same in each patient. Need not even be the same direction. Could be different in different subgroups of the population, e.g., women, or those who would choose the treatment.
- Statisticians have enough bad press without such technical definitions.
- Generic – treatment and control. Marginal – because it is the average effect. Structural – because it is causal.
- Assume likelihood of choosing the intervention only depends on whether age<50 or not.
- Doesn’t tell you how to adjust.
- Perhaps effect isn’t as big among the elderly?
- If you want an estimate of ACE in a subgroup, use weights for that subgroup.
- No longer stat significant. Counting one person ten times introduces significant amounts of variability. Small errors in that one observation get magnified.
- The filled circles represent the (model-based) predicted value for a participant in the treatment or control groups. The open circles represent the (model-based) predicted potential outcome for the participants. So, for example, a participant in the treatment group has a predicted potential outcome in the control group. And vice versa. Now have an estimate of the individual causal effect, which you can average to get ACE. Can either compare predicted potential outcome with predicted value or with the real value.
- This used to be restricted to numerical, approximately cont outcomes, but modern software allows a wide variety of outcome and predictor types.
- Cigarette tax may influence smoking, but no direct effect on birthweight. Issues: cigarette tax may not strongly predict smoking. Could cigarette tax be associated with other omitted variables? Suppose localities with high cigarette taxes also have strong maternal educational programs? These could lead to reduced smoking and (through other pathways, e.g., nutrition) better outcomes.
- Issue: cigarette tax may not strongly predict smoking.