Questions: Difference-in-Differences in Biostatistics

Question 1

A state implements a smoking ban in restaurants in 2015. A researcher compares lung cancer rates in that state before and after 2015 and finds a decline. Why is this simple pre-post comparison insufficient to identify the causal effect of the ban?

• A. Lung cancer rates may have been declining anyway due to national trends in smoking cessation — the pre-post change confounds the policy effect with the secular trend
• B. The sample size is too small for one state
• C. Lung cancer takes decades to develop, so effects would not be visible by 2015
• D. Pre-post comparisons are never valid in health research

Answer: (A)

A simple pre-post comparison cannot distinguish the policy effect from other things changing over time (secular trends, other health policies, demographic shifts). DiD addresses this by using states without the ban as a control group. If the control states' lung cancer rates declined by 5% and the ban state's declined by 12%, the DiD estimate attributes the additional 7% decline to the ban. This requires the parallel trends assumption — both states would have declined by the same amount without the ban.

Question 2

In a DiD analysis of Medicaid expansion on emergency department visits, the parallel trends assumption requires that treatment and control states had the same level of ED visits before expansion.

• T. True
• F. False

Answer: False

Parallel trends requires the same CHANGE (slope/trend), not the same level. Treatment states may have higher ED visit rates than control states at all time points — what matters is that the trends were moving in the same direction and at the same rate before the intervention. If treatment states' ED visits were declining at 2% per year and control states' were also declining at 2% per year before expansion, parallel trends is supported. This is assessed by examining pre-intervention trends visually and with statistical tests, though the assumption about the post-intervention counterfactual trend is ultimately untestable.

Question 3

A researcher presents a DiD analysis but has only one pre-intervention time point and one post-intervention time point. Why does having multiple pre-intervention time points strengthen the analysis?

Model answer: Multiple pre-intervention time points allow you to visually and statistically assess whether treatment and control groups had parallel trends before the intervention. With only one pre-period, you can compute the DiD estimate but cannot verify the parallel trends assumption — you are taking it on faith that the groups would have continued on parallel paths. With multiple pre-periods, you can plot the outcome trajectories and test whether they diverge before the intervention (which would indicate the assumption fails). Pre-intervention trend divergence would undermine the entire causal interpretation.

Event-study plots — showing the treatment-control difference at each time point relative to the intervention — are the standard diagnostic. If the pre-intervention differences fluctuate around zero (no pre-trend), the parallel trends assumption is supported. If they show a systematic trend before the intervention, the DiD estimate is unreliable because the groups were already diverging before the policy change.