Published on: Wednesday, August 23, 2023

Doctor is convicted of running pill mill based on 13 counts of unlawfully dispensing schedule II controlled substances (one count for each unlawful prescription). At trial, the government put on evidence of many prescriptions beyond the ones in the indictment. That evidence came from the government’s statistician and its medical expert. The statistician identified 1,142 patients who had gotten a prescription from the doctor in the last two years and drew a random sample of 300 patients to extrapolate from them to the total universe of patients, concluding that the doctor had prescribed more than 30,000 controlled substance prescriptions. But the statistician said nothing about how many were illegal. The government’s medical expert reviewed 24 patient files from the statistician’s random sample and concluded that 18 of 24 were illegal.  

At sentencing, the government tried to include all of the doctor’s schedule II controlled substances (converted drug weight of 106,000 kilos and base offense level 38), while the doctor argued that drug weight should be limited to the 13 patients in the indictment plus the 18 whom the government’s medical expert had had identified (converted drug weight of 7,500 kilos and base offense level 32). The district court “steered a middle path,” revising the government’s calculation to hold the doctor responsible for 30,000 kilos, citing “general trial evidence” and the backdrop of “widespread illegal prescribing….”

In United States v. Titus, No. 22-1516 (3rd Cr. Aug. 22, 2023), the Third Circuit vacated the sentence as too speculative:

Yet the evidence did not support a reliable extrapolation. The District Court used the medical expert’s review of twenty-four files to infer the illegality of thousands of other prescriptions. In the court’s view, that sample size was not “statistically valid.” JA 2336. Yet it extrapolated anyway. And without much explanation from the District Court, Titus had no chance to “respond meaningfully, or for that matter, at all.” United States v. Nappi, 243 F.3d 758, 766 (3d Cir. 2001).

Plus, the government never showed that the sample was large enough to be reliably representative of the remaining thousands of prescriptions. (Though statistical evidence can help to show that a sample size is large enough to support reliable inferences, we do not hold that such evidence is always necessary.) Nor did it document proper extrapolation methods. And it never explained how extrapolating from this sample could prove the huge drug weight by a preponderance of the evidence. So the sentencing court failed to “ensure that the Government carrie[d] [its] burden [of proof] by presenting reliable and specific evidence.” United States v. Roman, 121 F.3d 136, 141 (3d Cir. 1997) (internal quotation marks omitted).


The government may not use a small sample size to justify a much larger criminal punishment without explaining how that evidence satisfies its burden of proof. And courts must tread cautiously too. At a minimum, any extrapolation must be shown to be reliable, and defendants must have a fair chance to challenge its reliability. Because Titus’s sentencing fell short, we will vacate his sentence and remand.