cs.CVAug 26, 2026
SaveFRAME: Separating sampling variation from performance disparities in medical image analysis
Organizations: Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany · Lab for AI in Medicine, RWTH Aachen University, Aachen, Germany · Department of Diagnostic and Interventional Radiology, University Hospital RWTH Aachen, Aachen, Germany
Abstract
Fairness audits of medical imaging models commonly report the largest performance difference between demographic subgroups and treat any positive value as evidence of bias. Yet a perfectly fair model also produces a positive difference, which grows as subgroups shrink. Some mitigation methods remove demographic information from models because they assume that it produces the difference. Here we introduce Fair-model Reference And Mechanism Evaluation (FRAME). Its first step compares each reported difference with the difference expected from a perfectly fair model at the same subgroup counts. Its second step tests whether candidate causes of any excess over this fair-model reference change the difference when they are injected into model features. We evaluated 36 encoders on nine datasets in three modalities and audited 89 published differences across six modalities. For 10 frozen encoders and 13 chest radiograph findings, the reference is a median 41% of the race difference and 22% of the age difference. It is exceeded by 40 of 53 published differences in sensitivity or false positive rate and by one of 36 in the area under the receiver operating characteristic curve (AUROC). Adding race information to the features of two encoders does not change the race difference significantly. At matched disease performance, mitigation reduces the race difference by less than its spread across three pretraining seeds (medians 0.005 and 0.012) and the age difference by more (0.008 and 0.006). Image-text pretraining raises the worst-group AUROC for race by a median 0.049 over self-supervised pretraining. Reporting the fair-model reference beside every new and published subgroup difference could direct mitigation to the differences above it.
Figures & tables
Figure 1: FRAME and the audit of a reported subgroup difference. The top row shows four statements that lead from a measured difference to a fairness intervention. A label under a statement names the FRAME step that evaluates it. a , The object being audited. The example image is a test radiograph from NIH ChestX-ray14 that is positive for cardiomegaly, shown at the stored size of pixels. Classifier performance is evaluated separately in each subgroup. The bars show the cases positive for cardiomegaly in each of the five race subgroups of the pooled test split, 16,346 in total. Each count is printed beside its bar. The reported difference is the maximum minus the minimum of the per-subgroup values. b , The first step. It takes the overall performance of the model and the same subgroup counts. The overall performance is marked A on a scale from chance to perfect. The step simulates models with the same true performance in every subgroup. The distribution of their maximum minus minimum defines the fair-model reference, which replaces zero as the comparison value for the reported difference. The blue tail beyond the reported difference is the exceedance level. c , The second step. It tests the excess, which is the part of the difference above the reference. Each candidate cause is injected into the cached features of a released encoder at graded strengths. The demographic-signal injection adds a demographic direction with no disease signal. The disease-signal removal projects disease signal out of every group except the largest. A solid arrow marks a flow, and a dashed arrow marks a comparison. FRAME, Fair-model Reference And Mechanism Evaluation.
| Source or subgroup | Images | Train | Validation | Test | Test patients |
|---|---|---|---|---|---|
| Chest radiography, six sites | |||||
| MIMIC-CXR [ 31 ] | 243,345 | 180,300 | 18,409 | 44,636 | 11,179 |
| CheXpert [ 29 ] | 157,865 | 115,449 | 13,098 | 29,318 | 9,810 |
| NIH ChestX-ray14 [ 62 ] | 112,120 | 77,870 | 8,654 | 25,596 | 2,797 |
| PadChest [ 11 ] | 110,525 | 79,697 | 8,783 | 22,045 | 13,438 |
| VinDr-CXR [ 44 ] | 18,000 | 15,000 | 0 | 3,000 | 3,000 |
Table 1: Imaging cohorts and their subgroup composition. Counts are images after curation. The train, validation, and test columns follow the released or assigned split, and the last column reports the number of patients in the test split. Subgroup rows list the harmonized groups evaluated in the fairness analysis. Images with a missing value for an attribute are listed as not recorded and are excluded from the analysis of that attribute. The chest radiograph race category Other combines every radiograph from the four sites without a race field with the radiographs at MIMIC-CXR and CheXpert whose race is recorded as another category or is missing. Age bands are in years. VinDr-CXR and VinDr-PCXR release no patient identifier. Each of their images counts as one patient. Dermatology images are split individually for DDI and Fitzpatrick17k, which provide no patient identifier, and by lesion for ISIC 2019. The patient column counts images for DDI and Fitzpatrick17k and lesions for ISIC 2019. A patient whose test images fall in more than one subgroup of an attribute is counted in each. The patient counts of the subgroups can therefore sum to more than the total. Each fundus record is one image from one patient. DDI, Diverse Dermatology Images.
| Model | Pretraining objective | Domain | Dimension | Role |
| Publicly released encoders and the untrained control | ||||
| RAD-DINO [ 48 ] | Self-supervised | CXR | 768 | Panel, injections, finetuning |
| BiomedCLIP [ 68 ] | Image-text | Biomedical | 512 | Panel |
| TorchXRayVision DenseNet-121 [ 14 ] | Label-supervised | CXR | 1,024 | Panel, injections |
| DINOv3 ViT-L [ 57 ] | Self-supervised | General | 1,024 | Panel |
| DINOv3 ViT-B [ 57 ] | Self-supervised | General | 768 | Panel |
Table 2: The encoder panel and the controlled pretraining design. Outside the finetuning experiment, every model is run locally as a frozen feature extractor on images stored at pixels. The dimension column lists the width of the global embedding for each model. The panel includes domain-specific medical encoders, general-purpose vision encoders at three widths, and an untrained ViT-S/16 from timm. The controlled block lists the 22 encoders trained in this study for 50 epochs on the MIMIC-CXR training split, each initialized from the DINOv3 checkpoint of the same size. The run count is the product of the varying factors named in the objective and model columns. The six seed runs repeat the three objectives at ViT-S under two further seeds. Untrained ViT-S is the ViT-S/16 of timm with randomly initialized weights. CXR, chest radiograph; ViT, vision transformer.
Figure 2: The observed subgroup performance difference against the difference expected from a perfectly fair model. Every panel uses the 130 combinations of 10 frozen encoders and 13 findings on the pooled chest radiograph test split of 125,992 images from 41,621 patients. The age analyses use the 121,800 test images with a recorded age. Blue denotes race and red denotes age. A filled marker marks a combination that exceeds its reference at an FDR of 0.05. Gray dashed lines mark the identity and the 100% line. Only c has a box plot. a , b , The observed difference against its fair-model reference for race in a and age in b , with one point per combination ( each) on identical axes. c , The reference as a share of the observed difference, with one point per combination ( per attribute). The box marks the 25th, 50th, and 75th percentiles, and the whiskers extend to the most extreme share within 1.5 times the interquartile range. The median is printed beside the box. d , The reference against positive cases in the smallest evaluable subgroup, with one point per combination ( per attribute) and a logarithmic horizontal axis. e , Per finding, the number of the 10 encoders whose difference exceeds the reference, with race to the left and age to the right. f , Per finding, the median observed race difference (dot) and the median reference (diamond) over the 10 encoders. g , Positive cases in the smallest evaluable subgroup on a logarithmic axis, with one point per finding ( per attribute) and a line at the median. Exceedance is tested one-sided against the 2,000 simulated fair models, under FDR control within each attribute. Spearman is the rank correlation over the 130 combinations. FDR, false discovery rate.
Figure 3: Observed subgroup differences in dermatology and funduscopy against their fair-model references. Blue is dermatology and red is funduscopy throughout. Every panel uses the nine combinations of encoder and task evaluated in each modality. In dermatology, skin type is evaluated on the 1,486 labeled test images of DDI and Fitzpatrick17k. Sex and age are evaluated on the 7,533 and 7,513 labeled test images of ISIC 2019. In funduscopy, every attribute is evaluated on the 3,000 test images from 3,000 patients. The two modalities have 63 combinations of encoder, task, and attribute, nine in each of the seven groups of modality and attribute. In a , b , e , and f , the value of a group is the median over its nine combinations. No panel has an error bar. a , The median reference and the median observed difference of each group, joined by an arrow. The number of combinations exceeding their reference is printed beside each group. b , The seven groups, where marker area increases with the median observed difference and a solid fill marks a group in which at least one combination exceeds its reference. The same count is printed beside each marker. c , Every combination against its reference ( ), with the dashed identity line. A filled marker marks a combination that exceeds its reference at an FDR of 0.05. d , The number of the nine combinations of each group that exceed their reference. A gray bar marks the nine. e , The median unmitigated difference and the median achievable difference of Eq. 5 . f , The median reference against the positive cases in the smallest evaluable subgroup, with one point per group and a logarithmic horizontal axis. Exceedance is tested one-sided against 2,000 simulated fair models, under FDR control within each attribute. DDI, Diverse Dermatology Images; FDR, false discovery rate.
Figure 4: Published subgroup performance differences compared with the fair-model reference. Every panel uses the 89 audited claims from nine studies, 10 datasets, and six imaging modalities. Only f has an error bar. a , The reported difference of each claim against its reference ( ), with the identity line. b , The reference share per statistic and modality, for the 87 claims with a nonzero reported difference. The axis is logarithmic and has a dashed line at 100%. Points mark the claims, a violin marks their kernel density, and a heavy line marks their median. The number of claims that exceed their reference is printed beside each group of 4 to 21 claims. c , The number of claims per study (1 to 24), with those that exceed their reference in color. d , The reference against the cases in the smallest subgroup, with one point per claim on logarithmic axes. e , Per modality with rate claims (4 to 21 claims), the median reference share against the median smallest subgroup. A line joins the modalities in order of subgroup size. f , The largest reported difference in each of the 10 datasets (point) and its reference (diamond). A reference is the mean difference of 2,000 simulated fair models at the counts of its claim. The line marks its 95% interval, from the 2.5th to the 97.5th percentile of those models. Each label ends with the number of cases in the smallest subgroup. g , The source of the subgroup counts of the 89 claims. Printed counts include those computed as a printed total minus a printed count. Derived counts are products of a printed total and a printed share. Exceedance is tested one-sided against the simulated fair models under FDR control at 0.05 within each metric. AUROC, area under the receiver operating characteristic curve; CT, computed tomography; DR, diabetic retinopathy; FDR, false discovery rate; FPR, false positive rate; PDAC, pancreatic ductal adenocarcinoma; TPR, true positive rate.
Figure 5: The subgroup performance difference and the disease AUROC on chest radiographs under mitigation, pretraining, and finetuning. In a – c , g , and h , a change is paired against the unmitigated model on each of 130 combinations of encoder and finding per attribute. In a , g , and h , a change is the mitigated minus the unmitigated value, so a reduction is negative. The seed spread is the range of the difference across three pretraining seeds, over 39 combinations of objective and finding. Only d and h have error bars or boxes. a , The median change of each method. Dashed lines mark minus the median seed spread of each attribute. b , One bubble per method at its median reductions. Bubble area increases with the absolute median change in the FPR difference. c , The cumulative share of combinations by the largest reduction of any method at matched disease performance, with a dot at the median on the 0.5 line. d , The pretraining contrasts over 52 comparisons per objective contrast, 78 for balancing, and 26 per report condition. The marker is the median paired change, and the line extends from its 25th to its 75th percentile. The number of significant comparisons is printed beside each contrast. A filled marker indicates a nonzero count. e , The four unfreezing levels over 26 combinations of two encoders and 13 findings, with a line per combination and a thick median line. f , Per attribute, kernel densities of the seed spread and of the reduction of c , with a line at each median. g , Every method on all four measures. The median race change is printed in each cell and encoded by its color. h , The change in the race AUROC difference, pooled over the methods of each family (260 to 390 changes). Boxes mark the 25th, 50th, and 75th percentiles, whiskers extend to the most extreme change within 1.5 times the interquartile range, and points mark the changes beyond them. Four Platt changes above 0.17 are drawn as one triangle at the edge. Significance is tested by a paired cluster bootstrap over patients with 1,000 resamples, under FDR control at 0.05 within each family. AUROC, area under the receiver operating characteristic curve; DRO, distributionally robust optimization; FDR, false discovery rate; FPR, false positive rate; INLP, iterative nullspace projection.
Figure 6: Worst-group AUROC, equity-scaled AUROC, and the subgroup performance difference on chest radiographs across pretraining objectives and unfreezing levels. Blue is race, red is age, and dark gray is sex. Panels a – c and h use the 52 paired comparisons per attribute on natural pretraining data. Panels d – f use four unfreezing levels over 26 combinations of two finetuned encoders and 13 findings. Only b and g have error bars. a , The paired gain in worst-group AUROC from image-text over self-supervised pretraining, as a kernel density per attribute with a point per comparison and a line at the median. b , The median gain in worst-group AUROC against each baseline objective, with a line from the 25th to the 75th percentile of the 52 comparisons. c , The number of significant comparisons among the 52 on each measure. A gray bar marks the 52. d , The equity-scaled AUROC at each level, as a kernel density per attribute with a mark at the median. e , The subgroup difference on the same runs, with a point per combination and a line at the median. f , The median overall disease AUROC at the first and last levels and its change between successive levels. g , One worked comparison, on cardiomegaly with the ViT-B backbone over 40,204 test patients. The point marks the estimate on the full test split. Over 1,000 patient-cluster bootstrap resamples, the thick band marks one standard deviation on each side, and the thin line marks the 95% confidence interval, from the 2.5th to the 97.5th percentile. h , The worst-group AUROC of every comparison, image-text against self-supervised pretraining, with the identity line. Significance is tested by a paired cluster bootstrap over patients with 1,000 resamples, under FDR control at 0.05 within each family. AUROC, area under the receiver operating characteristic curve; FDR, false discovery rate.
Figure 7: Demographic decodability and the two injection operators. Every panel shows race on chest radiographs. Panels a – c use the 130 combinations of 10 frozen encoders and 13 findings. Panels d – h show the injections into the cached features of RAD-DINO on three findings. In d – g , a value is the mean over the three findings. In d – h , mid blue circles show the demographic-signal injection and dark blue diamonds show the disease-signal removal. In b and h , an open marker marks a nonsignificant correlation at an FDR of 0.05. Dark gray marks the overall disease AUROC. No panel has an error bar. a , The median observed and achievable differences of each encoder over its 13 findings against its median linear decodability ( encoders). The band marks the range of the 10 median observed differences. b , Spearman correlation of each measure with the achievable difference, above the cross-fitted out-of-sample of three feature sets. c , The two erasure methods against the unmitigated model, as medians over the 130 combinations, with the median paired change in the box. d , The race difference against linear race decodability across injection strengths, starting from the shared uninjected model. Marker size increases with strength. e , f , Every quantity at every strength. Each entry shows its value, and its color encodes the change from the uninjected model on one scale for both operators. g , The race difference at the largest strength of each grid. The bar marks the mean, and a point marks each finding. h , Spearman correlation of each quantity with strength, over 12 combinations of strength and finding for the injection and 18 for the removal. Every correlation is permutation tested under FDR control, over the 130 combinations in b and within each operator in h . AUROC, area under the receiver operating characteristic curve; FDR, false discovery rate.
Supplementary Fig. 1: The synthetic collinearity model and the prediction of the achievable difference. No panel has an error bar. a – c , The model of Eq. S1 at the six values of the collinearity between the disease direction and the demographic direction, where a collinearity of 1 is evaluated as 0.999. Each value is the mean over five seeds of 4,000 samples each. a , The observed difference (dark blue circles) and the achievable difference of Eq. 5 over LEACE, reweighing, and the per-group threshold shift (mid blue diamonds). The lower band shows the achievable difference, and the upper band shows the part of the observed difference removed by the most effective of the three methods. b , The geometric overlap and the erasure cost on the left axis and linear demographic decodability on the right axis. c , The achievable difference as a share of the observed difference. d – f , The 130 combinations of encoder and finding of the frozen chest radiograph panel, evaluated for race. d , The achievable difference of every combination as a point, grouped by encoder in the upper track (10 groups of 13) and by finding in the lower track (13 groups of 10) on one scale. The bar marks the median of each group. e , The median of linear decodability, the geometric overlap, and the erasure cost over the 13 findings of each encoder, standardized across the 10 encoders. f , Out-of-sample of a predictor of the achievable difference by five-fold cross-fitting over the 130 combinations, with one bar per feature set. A filled bar marks a predictor that is significant at an FDR of 0.05 against 1,000 shuffles of the achievable difference. The rightmost bar shows the leave-one-encoder-out result. g , The chest radiograph predictor applied to the nine combinations of dermatology (blue) and of funduscopy (red). Each p-value comes from 1,000 shuffles of the achievable difference. h , The achievable difference of each combination in each modality (130, 9, and 9 points), for race on chest radiographs, skin type in dermatology, and race in funduscopy, with a line at the median. Correlations in a and b are permutation tested over the 30 combinations of level and seed under FDR control at 0.05. AUROC, area under the receiver operating characteristic curve; FDR, false discovery rate.
Supplementary Fig. 2: Subgroup performance differences with the acquisition view held fixed, and with acquisition view and site treated as attributes. Every panel uses the 26 combinations of two encoders and 13 findings on the pooled chest radiograph test split of 125,992 images from 41,621 patients. For view as an attribute, the VinDr-CXR images without a recorded view are a third level in 10 findings. Blue marks the acquisition view, pale blue marks the site, dark blue marks race, and red marks age. In a , d , f , and g , a value is the median over the 26 combinations. No panel has an error bar. The change in b and c is the within-view difference minus the pooled difference. a , The median race and age difference with views pooled and within each view (bars) and the median fair-model reference (diamonds). b , The change against the pooled difference, with one point per combination and view (26 per attribute and view). Circles mark AP and triangles mark PA. c , The same change per finding as the median over the two encoders, which is printed in each cell. d , Each attribute from its median reference to its median observed difference, with the p-value of its paired test. e , The cumulative distribution of the difference for each attribute. A dashed line marks a share of 0.5. f , The median difference on AUROC, sensitivity, FPR, and the expected calibration error. A line joins the smallest and the largest attribute median on each measure. g , The median fair-model reference in each condition. Every p-value comes from a two-sided Wilcoxon signed-rank test over the paired combinations, under FDR control at 0.05 within its family. AP, anteroposterior; AUROC, area under the receiver operating characteristic curve; FDR, false discovery rate; FPR, false positive rate; PA, posteroanterior.
| Attribute | Category | Recorded | Not recorded | Total |
| Race | White | 42,477 | 0 | 42,477 |
| Race | Black | 8,446 | 0 | 8,446 |
| Race | Asian | 4,368 | 0 | 4,368 |
| Race | Hispanic or Latino | 2,180 | 0 | 2,180 |
| Race | Other | 16,483 | 52,038 | 68,521 |
| Insurance | Medicare | 35,014 | 0 | 35,014 |
Supplementary Table 1: Composition of the two pooled chest radiograph attributes whose residual category contains every image from the sites without the field. Counts are radiographs in the pooled test split of 125,992 images. The recorded column counts images from the two sites that record the field, which are MIMIC-CXR and CheXpert. The not recorded column counts images from the four sites without the field, which are NIH ChestX-ray14, PadChest, VinDr-CXR, and VinDr-PCXR. Every image from a site without the field is assigned to the Other category. Other is the only category that contains images from sites with and without the field.
| Finding | Evaluable | Positive | Prevalence (%) |
|---|---|---|---|
| Atelectasis | 610,323 | 92,977 | 15 |
| Cardiomegaly | 635,437 | 82,311 | 13 |
| Consolidation | 616,837 | 27,617 | 4 |
| Edema | 499,085 | 74,846 | 15 |
| Enlarged cardiomediastinum | 382,768 | 15,444 | 4 |
| Fracture | 418,170 | 11,280 | 3 |
Supplementary Table 2: Per-finding evaluable and positive counts over the chest radiograph pool. The evaluable column counts the images whose label for that finding is positive, negative, or uncertain. Because a blank label excludes an image from that finding only, the evaluable count differs across findings. The positive column counts the images with a positive label, and prevalence is the positive count as a share of the evaluable count. Counts are over all 650,207 pooled radiographs and not over the test split.
| Attribute | Linear head | Nonlinear head | Median paired change | Largest change |
|---|---|---|---|---|
| Race | 0.075 (0.057–0.103) | 0.072 (0.056–0.102) | 0.088 | |
| Age | 0.067 (0.047–0.094) | 0.074 (0.056–0.097) | 0.061 | |
| Insurance | 0.062 (0.047–0.076) | 0.064 (0.049–0.083) | 0.028 | |
| Sex | 0.012 (0.007–0.018) | 0.012 (0.007–0.024) | 0.055 |
Supplementary Table 3: Subgroup performance differences for four sensitive attributes under the linear and the nonlinear disease head. Values are differences in the area under the receiver operating characteristic curve on the 0 to 1 scale. They are measured on the controlled encoders pretrained on the natural data composition at seed 0, over 78 combinations of objective, backbone, and finding per attribute. The two head columns report the median and the interquartile range of the difference under each head. The paired columns compare the two heads within each combination, and the largest change column reports the largest absolute change over the 78 pairs. The main text reports the race and age differences. The sex and insurance differences are reported here only. Insurance has no fair-model reference and no significance test.
| Dataset | Task | Attribute | Condition | Metric | Groups | Counts | Reported | Reference | |
|---|---|---|---|---|---|---|---|---|---|
| Seyyed-Kalantari et al. [ 55 ] (chest radiograph) | |||||||||
| MIMIC-CXR | No finding | Race sex | N/A | FPR | 4 (1,152) | R | 0.122 | 0.017 [0.005, 0.035] | 0.001 † |
| Glocker et al. [ 23 ] (chest radiograph) | |||||||||
| CheXpert | No finding | Race | N/A | AUROC | 3 (2,746) | R | 0.010 | 0.017 [0.003, 0.038] | 0.864 |
| CheXpert | No finding | Race | N/A | FPR | 3 (2,434) | R | 0.030 | 0.010 [0.002, 0.023] | 0.006 † |
| CheXpert | No finding | Race | N/A | TPR | 3 (312) | R | 0.050 | 0.029 [0.005, 0.065] | 0.149 |
Supplementary Table 4: Published subgroup performance differences against the fair-model reference, for 89 claims from nine studies. Each row is one reported difference, audited with step one of FRAME from the values and subgroup counts printed by that study and with none of our models. Rows are grouped by study, with its modality beside its name. The condition column names the experimental condition and gives the training dataset in parentheses where the study varied it. A study that reports one condition has N/A in this column. The groups column reports the number of subgroups and, in parentheses, the number of cases in the smallest subgroup. These cases are the positives for TPR, the negatives for FPR, and the positives and negatives for AUROC. The counts column records the source of the denominators: R, printed in the article or a printed total minus a printed count; D, the product of a printed total and a printed share; P, reconstructed from the stated pool composition and split fraction. The reported difference keeps the precision of the article, with at least three decimals. The reference is the mean difference of 2,000 simulated fair models at those counts, with its 2.5th and 97.5th percentiles in brackets. The column reports the one-sided exceedance level, corrected across the claims sharing a metric under FDR control at . A dagger marks a difference that exceeds its reference. AUROC, area under the receiver operating characteristic curve; CT, computed tomography; CXP, CheXpert; DR, diabetic retinopathy; ERM, empirical risk minimization; FDR, false discovery rate; FPR, false positive rate; FRAME, Fair-model Reference And Mechanism Evaluation; IDC, invasive ductal carcinoma; ILC, invasive lobular carcinoma; LUAD, lung adenocarcinoma; LUSC, lung squamous cell carcinoma; MXR, MIMIC-CXR; N/A, not applicable; PDAC, pancreatic ductal adenocarcinoma; TC, Tyrer-Cuzick; TPR, true positive rate.
| Method | Race | Age | ||||
|---|---|---|---|---|---|---|
| Median | IQR | Median | IQR | |||
| Group-balanced resampling | 130 | 0.003 | 0.004 to 0.009 | 130 | 0.001 | 0.002 to 0.005 |
| Reweighing | 130 | 0.002 | 0.002 to 0.005 | 130 | 0.002 | 0.001 to 0.005 |
| Group DRO | 130 | 0.004 | 0.010 to 0.017 | 130 | 0.000 | 0.010 to 0.010 |
| Adversarial removal | 130 | 0.005 | 0.013 to 0.023 | 130 | 0.005 | 0.007 to 0.026 |
| Exponentiated gradient | 130 | 0.003 | 0.005 to 0.010 | 130 | 0.007 | 0.001 to 0.013 |
Supplementary Table 5: Every mitigation method, over all combinations on the chest radiograph pool. is the number of combinations of encoder and finding for each attribute. The change is the unmitigated AUROC difference minus the mitigated value on the same combination. A positive value is a reduction. Values are the median and the interquartile range of that paired change. AUROC, area under the receiver operating characteristic curve; DRO, distributionally robust optimization; IQR, interquartile range; INLP, iterative nullspace projection; LEACE, least-squares concept erasure.
| Finding | Race | Age | ||||||
|---|---|---|---|---|---|---|---|---|
| Observed | Reference | Share | Observed | Reference | Share | |||
| Support devices | 396 | 0.058 | 0.015 | 26 | 3,258 | 0.048 | 0.007 | 15 |
| Cardiomegaly | 392 | 0.079 | 0.019 | 23 | 1,601 | 0.115 | 0.010 | 8 |
| Lung opacity | 384 | 0.080 | 0.019 | 24 | 2,290 | 0.154 | 0.009 | 6 |
| Pleural effusion | 339 | 0.084 | 0.015 | 18 | 1,890 | 0.069 | 0.007 | 10 |
| Atelectasis | 291 | 0.093 | 0.023 | 24 | 1,953 | 0.093 | 0.010 | 11 |
Supplementary Table 6: The frozen chest radiograph panel by finding. Findings are ordered by the number of positive cases in the smallest evaluable race subgroup, given in the column. Each value is the median over the 10 encoders of a difference in the area under the receiver operating characteristic curve, on the pooled test split of 125,992 radiographs from 41,621 patients. The reference is the mean of the sampling distribution of the same statistic under exact fairness, over 2,000 simulated fair models at the per-subgroup counts of that finding. The share column reports the median of the 10 per-encoder ratios of the reference to the observed difference. The share column is not the ratio of the observed and reference medians in the same row.
| Modality | Attribute | Observed | Reference | Exceeding | Achievable |
| Dermatology | Age | 0.068 | 0.023 | 9 | 0.055 |
| Dermatology | Skin type | 0.072 | 0.037 | 0 | 0.052 |
| Dermatology | Sex | 0.006 | 0.007 | 0 | 0.004 |
| Fundus | Age | 0.087 | 0.050 | 2 | 0.069 |
| Fundus | Race | 0.067 | 0.038 | 1 | 0.061 |
| Fundus | Ethnicity | 0.063 | 0.038 | 0 | 0.041 |
Supplementary Table 7: The fair-model reference and the mitigation methods in dermatology and funduscopy. Each row is one attribute in one modality over nine combinations of encoder and task. In dermatology, skin type is evaluated on the Diverse Dermatology Images set and Fitzpatrick17k. Sex and age are evaluated on ISIC 2019, the only source that records them. The observed column reports the median subgroup performance difference over those nine combinations. The reference column reports the median difference expected from a perfectly fair model at the same subgroup sizes. Both columns are AUROC differences on the 0 to 1 scale. The exceeding column gives the number of the nine combinations whose observed difference is significantly larger than its reference. Exceedance is tested one-sided against 2,000 simulated fair models, under FDR control at 0.05. The achievable column reports the median of the lowest difference among the unmitigated model and the nine mitigation methods whose disease AUROC is at most 0.010 below that of the unmitigated model. Skin type is the Fitzpatrick scale grouped from six levels into three. AUROC, area under the receiver operating characteristic curve; FDR, false discovery rate.
| Contrast | Attribute | Worst-group AUROC | Equity-scaled AUROC | |||
|---|---|---|---|---|---|---|
| Gain | Significant | Gain | Significant | |||
| Image-text vs self-supervised | Race | 52 | 0.049 | 35 | 0.049 | 32 |
| Image-text vs self-supervised | Age | 52 | 0.054 | 50 | 0.047 | 44 |
| Image-text vs self-supervised | Sex | 52 | 0.044 | 49 | 0.042 | 49 |
| Image-text vs supervised | Race | 52 | 0.046 | 34 | 0.046 | 34 |
| Image-text vs supervised | Age | 52 | 0.050 | 51 | 0.047 | 47 |
Supplementary Table 8: The controlled pretraining design, one row per contrast and attribute. is the number of paired comparisons. Each comparison pairs two runs with different pretraining objectives at the same backbone, seed, and number of epochs on the natural pretraining data. The 52 comparisons cover the 13 findings with ViT-S at seeds 0, 1, and 2 and with ViT-B at seed 0. The three ViT-S seeds share their test patients. The FDR family of each attribute contains the three objective contrasts, their comparisons on the race-balanced data, and the tests of every other measure. The self-supervised runs also use a wider crop range and color jitter. In the image-text runs, the weights are updated after every batch of 256 images. In the self-supervised and label-supervised runs, they are updated after every two batches, and the learning rate ends at 59% of its peak. Supervised means label-supervised pretraining. The gain is the median paired difference in the worst-group AUROC and in the equity-scaled AUROC. The count beside each gain is the number of significant comparisons under a paired cluster bootstrap over patients, with FDR control at . AUROC, area under the receiver operating characteristic curve; FDR, false discovery rate.