Research Article

# Dissecting racial bias in an algorithm used to manage the health of populations

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Science  25 Oct 2019:
Vol. 366, Issue 6464, pp. 447-453
DOI: 10.1126/science.aax2342

### Tables

• Table 1 Descriptive statistics on our sample, by race.

BP, blood pressure; LDL, low-density lipoprotein.

 White Black n (patient-years) 88,080 11,929 n (patients) 43,539 6079 Demographics Age 51.3 48.6 Female (%) 62 69 Care management program Algorithm score (percentile) 50 52 Race composition of program (%) 81.8 18.2 Care utilization Actual cost $7540$8442 Hospitalizations 0.09 0.13 Hospital days 0.50 0.78 Emergency visits 0.19 0.35 Outpatient visits 4.94 4.31 Mean biomarker values HbA1c (%) 5.9 6.4 Systolic BP (mmHg) 126.6 130.3 Diastolic BP (mmHg) 75.5 75.7 Creatinine (mg/dl) 0.89 0.98 Hematocrit (%) 40.7 37.8 LDL (mg/dl) 103.4 103.0 Active chronic illnesses (comorbidities) Total number of active illnesses 1.20 1.90 Hypertension 0.29 0.44 Diabetes, uncomplicated 0.08 0.22 Arrythmia 0.09 0.08 Hypothyroid 0.09 0.05 Obesity 0.07 0.18 Pulmonary disease 0.07 0.11 Cancer 0.07 0.06 Depression 0.06 0.08 Anemia 0.05 0.10 Arthritis 0.04 0.04 Renal failure 0.03 0.07 Electrolyte disorder 0.03 0.05 Heart failure 0.03 0.05 Psychosis 0.03 0.05 Valvular disease 0.03 0.02 Stroke 0.02 0.03 Peripheral vascular disease 0.02 0.02 Diabetes, complicated 0.02 0.07 Heart attack 0.01 0.02 Liver disease 0.01 0.02
• Table 2 Performance of predictors trained on alternative labels.

For each new algorithm, we show the label on which it was trained (rows) and the concentration of a given outcome of interest (columns) at or above the 97th percentile of predicted risk. We also show the fraction of Black patients in each group.

 Algorithm training label Concentration in highest-risk patients (SE) Fraction of Black patients in group with highest risk (SE) Total costs Avoidable costs Active chronic conditions Total costs 0.165 (0.003) 0.187 (0.003) 0.105 (0.002) 0.141 (0.003) Avoidable costs 0.142 (0.003) 0.215 (0.003) 0.130 (0.003) 0.210 (0.003) Active chronic conditions 0.121 (0.003) 0.182 (0.003) 0.148 (0.003) 0.267 (0.003) Best-to-worst difference 0.044 0.033 0.043 0.126
• Table 3 Doctors’ decisions versus algorithmic predictions.

For those enrolled in the high-risk care management program (1.3% of our sample), we first show the fraction of the population that is Black, as well as the fraction of all costs and chronic conditions accounted for by these observations. We also show these quantities for four alternative program enrollment rules, which we simulate in our dataset (using the holdout set when we use our experimental predictors). We first calculate the program enrollment rate within each percentile bin of predicted risk from the original algorithm and either (i) randomly sample patients or (ii) sample those with the highest predicted number of active chronic conditions within a bin and assign them to the program. The resultant values are then compared with values obtained by simply assigning the aforementioned 1.3% of our sample with (iii) the highest predicted cost or (iv) the highest number of active chronic conditions to the program.

 Population Fraction Black (SE) Fraction of all costs (SE) Fraction of all active chronic conditions (SE) Observed program enrollment (1.3%) 0.192 (0.003) 0.029 (0.001) 0.033 (0.001) Simulated alternative enrollment rules Random, in predicted-cost bin 0.183 (0.003) 0.044 (0.002) 0.034 (0.001) Predicted health, in predicted-cost bin 0.269 (0.003) 0.044 (0.002) 0.064 (0.002) Highest predicted cost 0.172 (0.003) 0.100 (0.002) 0.047 (0.002) Worst predicted health 0.292 (0.004) 0.067 (0.002) 0.076 (0.002)

### Supplementary Materials

• Dissecting racial bias in an algorithm used to manage the health of populations

Ziad Obermeyer, Brian Powers, Christine Vogeli, Sendhil Mullainathan