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Objectives: We aim to estimate geographic variability in total numbers of infections and infection fatality ratios (IFR; the number of deaths caused by an infection per 1,000 infected people) when the availability and quality of data on disease burden are limited during an epidemic. Methods: We develop a noncentral hypergeometric framework that accounts for differential probabilities of positive tests and reflects the fact that symptomatic people are more likely to seek testing. We demonstrate the robustness, accuracy, and precision of this framework, and apply it to the United States (U.S.) COVID-19 pandemic to estimate county-level SARS-CoV-2 IFRs. Results: The estimators for the numbers of infections and IFRs showed high accuracy and precision; for instance, when applied to simulated validation data sets, across counties, Pearson correlation coefficients between estimator means and true values were 0.996 and 0.928, respectively, and they showed strong robustness to model misspecification. Applying the county-level estimators to the real, unsimulated COVID-19 data spanning April 1, 2020 to September 30, 2020 from across the U.S., we found that IFRs varied from 0 to 44.69, with a standard deviation of 3.55 and a median of 2.14. Conclusions: The proposed estimation framework can be used to identify geographic variation in IFRs across settings.