Background
Methods
Prognostic models
Parameters | Possible methods for combining estimates of parameters after MI* |
---|---|
Covariate distribution | |
Mean Value | Rubin's rules |
Standard Deviation | Rubin's rules |
Correlation | Rubin's rules after Fisher's Z transformation |
Model parameters
| |
Regression coefficient | Rubin's rules |
Hazard ratio | Rubin's rules after logarithmic transformation |
Prognostic Index/linear predictor per patient | Rubin's rules |
Model fit and performance
| |
Testing significance of individual covariate in model | Rubin's rules using a Wald test for a single estimates (Table 2(A)) |
Testing significance of all fitted covariates in model | Rubin's rules using a Wald test for multivariate estimates (Table 2(B)) |
Likelihood ratio χ
2 test statistic | Rules for combining likelihood ratio statistics if parametric model (Table 2(D)) or χ
2 statistics if Cox model (Table 2(C)) |
Proportion of variance explained (e.g. R2 statistics) | Robust methods |
Discrimination (c-index) | Robust methods |
Prognostic Separation D statistic | Rubin's rules |
Calibration (Shrinkage estimate) | Robust methods |
Prediction
| |
Survival probabilities | Rubin's rules after complementary log-log transformation |
Percentiles of a survival distribution | Rubin's rules after logarithmic transformation |
Rules for MI inference
Combining parameter estimates
Hypothesis testing
Significance level based on a single combined estimate
Estimate |
F
| Test statistic | Degrees of freedom (df) | Relative increase in variance ( r ) |
---|---|---|---|---|
A) Scalar
|
F
1, v
|
, H0: Q = Q
0
|
v = (m - 1)(1 + r
-1)2
| |
B) Multivariate
| H0:Q = Q
0,
k = number of parameters | where a = k(m - 1) | ||
C)
χ
2
statistics
w
1,..., w
m
|
k = df associated with χ
2 tests | |||
D) Likelihood Ratio
χ
2
statistics
w
L1,..., w
Lm
|
k = number of parameters in fitted model |
where a = k(m - 1) |