Background
Methods
Statistical methods for assessing CoPs
The prentice criteria
The meta-analytic framework
Statistical solutions for high vaccine efficacy
Flexible models for prentice criteria framework
The meta-analytic approach using penalised likelihood
logistf
and bayesglm
R packages respectively [30, 31]. In a second step, we evaluated the performance of both methods as part of a meta-analysis in the context of high VE, by running simulations.Results
Flexible models for the prentice criteria framework
logit model 4 |
\(\hat {VE}\)
| p(S)<α | p(Z)<α | p(S)<α & p(Z)≥α |
---|---|---|---|---|
Linear | 0.41 | 1.00 | 0.05 | 0.95 |
Non-linear | 0.41 | 1.00 | 0.05 | 0.95 |
Scaled logit | 0.41 | 1.00 | 0.03 | 0.96 |
Linear | 0.75 | 1.00 | 0.10 | 0.90 |
Non-linear | 0.75 | 1.00 | 0.04 | 0.96 |
Scaled logit | 0.75 | 1.00 | 0.04 | 0.96 |
Linear | 0.86 | 1.00 | 0.22 | 0.78 |
Non-linear | 0.86 | 1.00 | 0.05 | 0.95 |
Scaled logit | 0.86 | 1.00 | 0.04 | 0.96 |
Linear | 0.96 | 1.00 | 0.34 | 0.66 |
Non-linear | 0.96 | 1.00 | 0.04 | 0.96 |
Scaled logit | 0.96 | 0.99 | 0.03 | 0.96 |
The meta-analytic approach using penalised likelihood
n
C
|
n
V
| Logistic | Firth | WIP | |||
---|---|---|---|---|---|---|---|
\(\hat \beta \)
|
\(\hat Var(\hat \beta)\)
|
\(\hat \beta \)
|
\(\hat Var(\hat \beta)\)
|
\(\hat \beta \)
|
\(\hat Var(\hat \beta)\)
| ||
0 | 0 | 0.00 | 2.33e+09 | 0.00 | 1.15 | 0.00 | 1.28 |
1 | 0 | -9.18 | 7.85e+06 | -0.60 | 0.79 | -0.59 | 0.65 |
2 | 0 | -9.59 | 7.85e+06 | -0.91 | 0.72 | -0.90 | 0.58 |
3 | 0 | -9.36 | 2.89e+06 | -1.14 | 0.69 | -1.15 | 0.57 |
4 | 0 | -9.58 | 2.89e+06 | -1.34 | 0.68 | -1.37 | 0.58 |
5 | 0 | -9.78 | 2.89e+06 | -1.52 | 0.68 | -1.59 | 0.61 |
6 | 0 | -9.99 | 2.89e+06 | -1.71 | 0.68 | -1.80 | 0.64 |
7 | 0 | -10.21 | 2.89e+06 | -1.90 | 0.69 | -2.04 | 0.69 |
8 | 0 | -10.98 | 7.85e+06 | -2.13 | 0.72 | -2.33 | 0.77 |
9 | 0 | -11.38 | 7.85e+06 | -2.45 | 0.79 | -2.73 | 0.92 |
10 | 0 | -25.57 | 2.33e+09 | -3.04 | 1.15 | -3.84 | 1.91 |
1 | 1 | 0.00 | 5.60e-01 | 0.00 | 0.42 | 0.00 | 0.35 |
3 | 1 | -0.67 | 4.00e-01 | -0.54 | 0.33 | -0.49 | 0.26 |
9 | 2 | -1.79 | 4.30e-01 | -1.53 | 0.35 | -1.51 | 0.30 |
2 | 3 | 0.27 | 2.80e-01 | 0.23 | 0.26 | 0.21 | 0.21 |
Model |
V
E
| mean (R2) | median(R2) | Std (R2) | 95%ll | 95%ul | MSE (R2) |
---|---|---|---|---|---|---|---|
Logistic | 0.75 | 0.59 | 0.61 | 0.16 | 0.24 | 0.84 | 0.12 |
Firth | 0.75 | 0.72 | 0.73 | 0.09 | 0.54 | 0.86 | 0.04 |
WIP | 0.75 | 0.71 | 0.72 | 0.09 | 0.51 | 0.85 | 0.05 |
Logistic | 0.82 | 0.52 | 0.54 | 0.22 | 0.03 | 0.85 | 0.19 |
Firth | 0.82 | 0.73 | 0.75 | 0.09 | 0.52 | 0.87 | 0.04 |
WIP | 0.82 | 0.71 | 0.72 | 0.10 | 0.48 | 0.87 | 0.05 |
Logistic | 0.9 | 0.46 | 0.49 | 0.26 | 0.01 | 0.86 | 0.26 |
Firth | 0.9 | 0.72 | 0.74 | 0.10 | 0.48 | 0.88 | 0.04 |
WIP | 0.9 | 0.70 | 0.71 | 0.11 | 0.45 | 0.87 | 0.05 |