TABLE 4.
Comparison of biases for predicted doses and infection risks by censoring degree and method for handling censored dataa
| Estimation and censored data method | Bias for indicated degree of censoring |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Low |
Medium |
High |
Severe |
Real-life example |
||||||
| Mean (SD) | Min, max | Mean (SD) | Min, max | Mean (SD) | Min, max | Mean (SD) | Min, max | Mean (SD) | Min, max | |
| Estimated dose (viral particles) | ||||||||||
| Substitution LOD/ | 0.32 (0.0071) | 0.27, 0.33 | 1.13 (0.015) | 1.02, 1.14 | 2.09 (0.018) | 1.98, 2.11 | 2.90 (0.022) | 2.80, 2.93 | 3.12 (0.022) | 3.02, 3.15 |
| MLE | −14.74 (10.65) | −65.12, 2.87 | −6.72 (8.97) | −57.19, 19.31 | 2.56 (10.17) | −27.8, 115.92 | 92.45 (1105.51) | −12.88, 2.75 × 10−4 | 2.94 × 108 (8.64 × 109) | 0.00, 2.73 × 1011 |
| KM | 0.46 (0.010) | 0.40, 0.51 | 1.63 (0.038) | 1.51, 1.88 | 3.09 (0.12) | 2.91, 3.76 | 4.70 (0.67) | 4.06, 9.51 | 8.36 (7.20) | 4.39, 94.10 |
| MI method 1 | 0.25 (0.039) | 0.12, 0.37 | 0.68 (0.095) | 0.40, 1.00 | 0.77 (0.14) | 0.38, 1.32 | 0.42 (0.19) | 0.03, 1.86 | 0.25 (0.33) | −0.058, 3.14 |
| MI method 2 | 0.23 (0.043) | 0.12, 0.35 | 0.80 (0.078) | 0.54, 1.03 | 1.48 (0.11) | 1.15, 1.80 | 2.04 (0.13) | 1.62, 2.44 | 2.20 (0.13) | 1.72, 2.67 |
| Estimated infection risk | ||||||||||
| Substitution LOD/ | 9.93 × 10−4 (6.61 × 10−5) | 7.05 × 10−4, 1.13 × 10−3 | 3.66 × 10−3 (2.13 × 10−4) | 2.69 × 10−3, 4.05 × 10−3 | 7.23 × 10−3 (2.92 × 10−4) | 6.14 × 10−3, 7.72 × 10−3 | 1.05 × 10−2 (2.48 × 10−4) | 8.53 × 10−3, 1.084 × 10−2 | 1.15 × 10−2 (1.55 × 10−4) | 1.03 × 10−2, 1.17 × 10−2 |
| MLE | −4.55 × 10−2 (3.091 × 10−2) | −1.85 × 10−1, 9.39 × 10−3 | −2.14 × 10−2 (2.75 × 10−2) | −1.54 × 10−1, 5.56 × 10−2 | 8.11 × 10−3 (3.072 × 10−2) | −9.19 × 10−2, 2.89 × 10−1 | 6.37 × 10−2 (1.49 × 10−1) | −4.41 × 10−2, 9.46 × 10−1 | 1.77 × 10−1 (3.36 × 10−1) | 8.68 × 10−4, 9.93 × 10−1 |
| KM | 1.43 × 10−3 (9.46 × 10−5) | 1.05 × 10−3, 1.69 × 10−3 | 5.28 × 10−3 (3.26 × 10−4) | 3.86 × 10−3, 6.41 × 10−3 | 1.065 × 10−2 (5.77 × 10−4) | 8.70 × 10−3, 1.33 × 10−2 | 1.70 × 10−2 (2.38 × 10−3) | 1.24 × 10−2, 3.46 × 10−2 | 3.02 × 10−2 (2.39 × 10−2) | 1.60 × 10−2, 2.88 × 10−1 |
| MI method 1 | 7.78 × 10−4 (1.41 × 10−4) | 3.54 × 10−4, 1.22 × 10−3 | 2.23 × 10−3 (3.81 × 10−4) | 1.15 × 10−3, 3.52 × 10−3 | 2.68 × 10−3 (5.54 × 10−4) | 1.26 × 10−3, 4.81 × 10−3 | 1.55 × 10−3 (7.29 × 10−4) | 1.14 × 10−4, 6.91 × 10−3 | 9.48 × 10−4 (1.23 × 10−3) | −2.14 × 10−4, 1.17 × 10−2 |
| MI method 2 | 6.99 × 10−4 (1.40 × 10−4) | 2.50 × 10−4, 1.10 × 10−3 | 2.58 × 10−3 (2.84 × 10−4) | 1.70 × 10−3, 3.51 × 10−3 | 5.10 × 10−3 (4.22 × 10−4) | 3.21 × 10−3, 6.55 × 10−3 | 7.44 × 10−3 (4.98 × 10−4) | 5.79 × 10−3, 8.98 × 10−3 | 8.16 × 10−3 (4.95 × 10−4) | 6.41 × 10−3, 9.78 × 10−3 |
a
Data sets comprised simulated data sets with low (10%), medium (35%), high (65%), and severe (90%) degrees of censoring and a real-life censoring example (97%); censored data methods included substitution LOD/, MLE, KM, MI method 1, and MI method 2. Bold values indicate those that were the closest to the known values for that degree of censoring. Min, minimum; max, maximum.