| TP | FN | FP | TN | |
|---|---|---|---|---|
| Ahn | 19 | 0 | NA | NA |
| Bock | 5 | 5 | 2 | 17 |
| Chung | 5 | 0 | 48 | 114 |
| Cordoba | 21 | 1 | NA | NA |
| Espinosa | 5 | 0 | NA | NA |
| Haliloglu | 3 | 0 | 1 | 73 |
| Langer | 57 | 17 | NA | NA |
| Liberman | 6 | 0 | NA | NA |
| Nishanova | 26 | 4 | NA | NA |
| Obenauer | 2 | 2 | 0 | 23 |
| Oh | 9 | 0 | NA | NA |
| Qian | 50 | 1 | 63 | 92 |
| Reyes | 32 | 1 | NA | NA |
| Robbins | 4 | 0 | 17 | 101 |
| Taskin | 47 | 0 | NA | NA |
| Taylor | 21 | 0 | NA | NA |
| Yang | 21 | 0 | NA | NA |
| Myers | 33 | 0 | NA | NA |
| Taron | 19 | 0 | NA | NA |
| Son | 6 | 0 | 6 | 23 |
| Jafari | 31 | 0 | NA | NA |
| Wang | 110 | 18 | NA | NA |
Multiple imputations of missing data in meta-analysis of diagnostic accuracy
\[ \def\TPi{\mbox{TP}_i} \def\FNi{\mbox{FN}_i} \def\FPi{\mbox{FP}_i} \def\TNi{\mbox{TN}_i} \]
Set-up and notation
Suppose there are \(m\) studies to evaluate the diagnostic accuracy of some test. For the \(i\)th study, let
- \(\TPi\): number of true positives
- \(\FNi\): number of false negatives
- \(\FPi\): number of false positives
- \(\TNi\): number of true negatives
These are the data we wish to collect for each \(i=1,\ldots, m\). Write \(N_i=\TPi+\FNi\), the number of cases; \(\bar N_i=\FPi + \TNi\), the number of non-cases; and \(n_i = N_i + \bar N_i\), the total sample size.
Let \(p_i\) denote the sensitivity, \(q_i\) the specificity, and \(\pi_i\) the prevalence of cases in the \(i\)th study. If there is no missing data, we can easily estimate them by \(\hat p_i=\TPi/N_i\), \(\hat q_i=\TNi/\bar N_i\), and \(\hat\pi_i=N_i/n_i\), respectively. We can also feed the entire data \((\TPi, \FNi, \FPi, \TNi)\) \((i=1,\ldots, m)\) into any standard software, e.g., mada (Sousa-Pinto 2022), for meta-analysis.
Methods
A motivating example
Consider the scenario where there are no non-cases in some study \(i\), so \(\FNi\), \(\TNi=\)NA. An example:
We aim to fill in the missing values fof \(\FNi\) and \(\TNi\) by multiple imputations (MI).
References
Sousa-Pinto, Philipp Doebler with contributions from Bernardo. 2022. “Mada: Meta-Analysis of Diagnostic Accuracy.” https://CRAN.R-project.org/package=mada.