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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

A dataset of 200 health insurance claims has 40 records with missing income. Among the 160 complete records, mean claim is Rs 30,000. Among the 40 incomplete records, it is known from a sample audit that mean claim is Rs 50,000. If the analyst uses only the complete records (complete case analysis), what is the bias in the estimated mean claim for the full dataset of 200 records, assuming the audit figures are exact?

The complete case analysis understates the mean by Rs 4,000. The true mean is (160 x 30,000 + 40 x 50,000)/200 = Rs 34,000, while the complete records give Rs 30,000, because the missing records have higher claims.

  1. ARs 4,000 overstatement
  2. BRs 4,000 understatementCorrect
  3. CRs 10,000 understatement
  4. DRs 20,000 understatement
  5. Rs 2,000 understatement

Explanation

True mean = (160x30,000 + 40x50,000)/200 = (4,800,000 + 2,000,000)/200 = 34,000. Complete case estimate is 30,000. Bias = 30,000 - 34,000 = -4,000, an understatement. Rs 10,000 wrongly uses half the gap between groups' means, and Rs 20,000 ignores weights.

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