The fundamental problem of causal inference - that we never observe counterfactuals - prevents us from identifying how many might be negatively affected by a proposed intervention. If, in an A/B test, half of users click (or buy, or watch, or renew, etc.), whether exposed to the standard experience A or a new one B,

The fundamental problem of causal inference -- that we never observe counterfactuals -- prevents us from identifying how many might be negatively affected by a proposed intervention. If, in an A/B test, half of users click (or buy, or watch, or renew, etc.), whether exposed to the standard experience A or a new one B, hypothetically it could be because the change affects no one, because the change positively affects half the user population to go from no-click to click while negatively affecting the other half, or something in between. While unknowable, this impact is clearly of material importance to the decision to implement a change or not, whether due to fairness, long-term, systemic, or operational considerations. We therefore derive the tightest-possible (i.e., sharp) bounds on the fraction negatively affected (and other related estimands) given data with only factual observations, whether experimental or observational. Naturally, the more we can stratify individuals by observable covariates, the tighter the sharp bounds. Since these bounds involve unknown functions that must be learned from data, we develop a robust inference algorithm that is efficient almost regardless of how and how fast these functions are learned, remains consistent when some are mislearned, and still gives valid conservative bounds when most are mislearned. Our methodology altogether therefore strongly supports credible conclusions: it avoids spuriously point-identifying this unknowable impact, focusing on the best bounds instead, and it permits exceedingly robust inference on these. We demonstrate our method in simulation studies and in a case study of career counseling for the unemployed.

The global statistics for breast cancer are staggering: 1 in 8 women worldwide will be diagnosed at some point during their lifetime. Women who are diagnosed early have a 95 percent chance of living at least five years after diagnosis and it's estimated early breast cancer diagnosis could save 400,000 lives globally each year, according to the World Health Organization. Fine needle aspiration (FNA) is currently the least invasive technique to biopsy breast lumps, or masses. FNAs are less painful, less expensive to do, result in less complications for patients, and make results available more quickly than the current traditional core or open biopsies. FNAs are currently less reliable in conclusively diagnosing breast cancer than more invasive and painful techniques.