Overview of variables in the data setIn this study, we separated the large number of mouse records identified from the Janus database into two groups—cancer and non-cancer—according to diagnoses made at the time of death. The purpose was to model these outcomes as competing risks and investigate how neutron dose, fractionation, age and sex of the mice influenced the hazard and incidence functions for these two disease categories. The list of non-cancer diagnoses is detailed in Table S1 and Fig. S1 from the supplementary material, with hemothorax/ascites, pneumonitis, pneumonia, anemia, and hydronephrosis being the five most prevalent conditions.For a comprehensive understanding of the study parameters, summary statistics for key variables are provided in Table 1 for non-cancerous mice and for cancerous mice. Variable meanings are also provided there in the Table 1 caption. As expected, the variables related to experimental conditions (dose, number of fractions, duration of fraction, treatment age) had similar distributions for the cancer and non-cancer mouse groups. However, the median age at death was considerably lower for non-cancerous mice (815 days) than for cancerous mice (915 days). Due to the large size of the data set, this difference in age at death distributions is highly statistically significant by Wilcoxon rank sum test with continuity correction (W = 21,971,395, p-value < 2.2 × 10–16). A more detailed look at these age at death distributions by disease category is illustrated in Fig. 1. A visual analysis of the figure reveals that cancer is the predominant cause of mortality with its distribution peaking around the middle age range of the cohort. In contrast, non-cancer deaths are less frequent and display a distribution that suggests a relatively earlier onset of mortality, but a wide range. The overlap of the distributions indicates a range of ages where both cancer and non-cancer deaths occur, while also highlighting the differing frequency and age distribution patterns between the two event types. This figure underscores the importance of distinguishing between cancer and non-cancer outcomes when considering the lifespan and mortality risks in populations exposed to radiation.
Table 1 Summary table of variables in the both the cancer and non-cancer data sets.Figure 1Frequency distribution of age at death for two distinct event types among the mice: cancer (red) and non-cancer (blue) mortalities in histogram form, as function of Age at Death in days. The frequency distribution is separated into unexposed and exposed. White numbers within the histogram bars indicate the corresponding numbers of mouse deaths.Cause-specific cumulative hazard and cumulative incidence functions for cancer and non-cancerThe data set was analyzed using the RSF machine learning method for competing risks, and the results were visualized through the Cause-Specific Cumulative Hazard Function (CSCHF) and the Cumulative Incidence Function (CIF) plots, as described above. The CSCHF and CIF generated by the RSF model are shown in Fig. 2. The ‘Time (d)’ axis represents the mouse age in days from birth. The ‘mean’ CSCHF and CIF values represent the average of the CSCHF or CIF predictions for a given data point over all the trees in the random forest. This averaging is done over all the trees in a single run of the random forest algorithm, ensuring that the displayed curves reflect the ensemble prediction for the whole dataset, not individual mice. The black curves denote cancer mortality, while the red curves represent non-cancer mortality. These results clearly show that cancer was the dominant cause of death in the selected mouse population. However, the non-cancer disease hazard continued to increase up to the oldest mouse ages. Over a large portion of the age range (roughly between 600 and 1200 days), the hazards for both cancer and non-cancer diseases followed a sigmoid pattern, appearing roughly linear in this specific region. The plots shown in Figs. 1 and 2 lump together mouse groups exposed to different neutron doses and fractionation regimens, but they give a good overall idea of the age dependences of cancer and non-cancer deaths in the population.Figure 2Cause-Specific Cumulative Hazard Function (CSCHF) and Cumulative Incidence Function (CIF) plots for cancer (red) and non-cancer (blue) diseases. These functions were generated by the RSF model fit to the training data.Concordance scoresThe concordance scores for the RSF model fitted to this data set are as follows. On the training dataset, the model achieved concordance scores of 0.659 for cancer outcomes and 0.602 for non-cancer outcomes. These scores indicate that the model has some (although far from perfect) predictive capability, with higher accuracy in distinguishing cancer-related outcomes compared to non-cancer ones. When applied to the testing dataset, the model achieved concordance scores of 0.649 for cancer and 0.552 for non-cancer outcomes. These results suggest that the model performed better for cancer than for non-cancer, likely because there were much more cancer events in the data set so the fit was more heavily influenced by them. For cancer, there is almost no reduction in concordance values between training and testing data, suggesting that the model is both stable and generalizable for cancer. For non-cancer there was some reduction in concordance on testing data compared to training, which is also likely due to the smaller number of non-cancer instances within our dataset. However, while the reduction in concordance score was 0.05, it is important to recognize that this reduction is substantial because a further reduction of similar magnitude would approach a score indicative of random chance (0.5). This underscores the need to interpret the performance difference between training and testing data cautiously.Variable importance scores (VIMP)VIMP scores for this analysis are shown in Table 2. The variables called “Experiment” represent binary (0 or 1) indicators for the different Janus neutron exposure experiments included in the analysis. The different Janus neutron exposure experiments varied in their objectives and methodologies, including differences in dose rates, fractionation schedules, total doses, and exposure durations. For instance, some experiments tested single doses while others explored fractionated doses given over weeks or months. Specific experiments focused on comparing high-dose-rate exposures to low-dose-rate exposures, investigating the effects of age at the time of exposure, and examining the efficacy of radioprotective agents. These variations allowed for a comprehensive evaluation of the biological effects of neutron radiation under different conditions. The specific meanings of the listed ‘Experiment’ variables are as follows:
Experiment 2 (JM-2): This was the first and largest experiment, testing the additivity of small increments of neutron dose delivered in different patterns over 24 weeks. It involved five different exposure patterns, including single high-dose-rate exposures and fractionated low-dose-rate exposures, to evaluate their effects on life shortening and neoplastic disease incidence.
Experiment 3 (JM-3): This was a straightforward single-dose study with seven replications, including a small dose-rate comparison where one group received a single dose of 240 cGy of neutrons over 20 min and another over 8 h.
Experiment 4 (JM-4 K): This experiment used a 24-week once-weekly exposure procedure with different total doses to test dose-rate and protraction factors, involving multiple replications to evaluate life shortening and neoplastic disease incidence.
Experiment 8 (JM-8): This was the only duration-of-life exposure experiment in the JM series, comparing protraction factors between 24- and 60-week once-weekly exposure paradigms, with varying weekly dose levels for both γ-rays and neutrons.
Table 2 Variable importance (VIMP) scores for both cancer and non-cancer, and their lower and upper 95% confidence intervals (CI).By providing this additional context, readers can better understand the significance of these experiment variables and their contributions to the model’s predictions.For cancer mortality, dose emerges as the most influential variable, with a VIMP value of 0.207 (CI 0.184–0.223), underscoring the significant role that neutron radiation dosage plays in predicting cancer outcomes. Following dose, number of fractions holds a VIMP value of 0.095 (CI 0.076–0.123), indicating its substantial, though lesser, influence compared to the dosage. Variables ‘Treatment Age’, ‘Experiment 2’, and ‘Experiment 8’ also contribute to the model’s predictions with VIMP values of 0.047 (CI 0.032–0.063), 0.038 (CI 0.027–0.048), and 0.035 (CI 0.018–0.067), respectively. While these VIMP values are lower compared to the dominant variable ‘Dose’, they still indicate that these variables have a meaningful, albeit smaller, impact on the model’s accuracy. VIMP values around 0.03 suggest that the variables provide some predictive power and should not be disregarded, especially in the context of complex interactions within the model. Notably, ‘Sex’, ‘Experiment 3’, and ‘Experiment 4’ show minimal VIMP values, suggesting their relatively limited impact on cancer mortality predictions within this model. In the context of non-cancer mortality, dose still remains a pivotal feature with a VIMP value of 0.131 (CI 0.092–0.172). However, the VIMP values for ‘Sex’, ‘Treatment Age’, and ‘Duration of Fraction’, 0.012 (CI − 0.007 to 0.031), 0.024 (CI − 0.006 to 0.057), and − 0.004 (CI − 0.026 to 0.023), respectively, indicate that these features contribute minimally to the prediction of non-cancer outcomes.Overall, we can see that dose was the predominant factor in both models, as expected. Interestingly, number of fractions, duration of fraction, and treatment age appeared to be important for cancer, but not important for non-cancer outcome predictions. There also appeared to be more contribution of differences between experiments for cancer than for non-cancer. Sex did not appear very important for either outcome.SHAP value analysis for cancer and non-cancer mortalityThe application of SHAP values to our competing risks model provides a granular understanding of feature importance, quantifying the impact of each predictor on the model’s output for each mouse. SHAP values, rooted in cooperative game theory, offer an interpretable measure of the contribution of each variable to the prediction of both cancer and non-cancer mortality risks in the cohort of B6CF1 mice. The aggregated median SHAP values for different variables in the RSF model are listed in Table 3, with variables listed in alphabetical order. As expected, the SHAP analysis highlights ‘Dose’ as the most impactful predictor for both cancer and non-cancer mortality, with other features exerting varying smaller effects, which are not completely consistent between cancer and non-cancer outcomes.
Table 3 Summary of SHAP value contributions for different features, for cancer and non-cancer diseases.Visualizations of how the SHAP values of each continuous feature changed as function of the feature values for cancer and non-cancer diseases are provided in Fig. 3. These SHAP value graphs provide a visual representation of the impact each feature has on the model’s prediction for cancer and non-cancer outcomes. For dose, the SHAP values expectedly illustrate a positive relationship with the predicted hazard of both cancer and non-cancer outcomes (Fig. 3). The increasing SHAP values with higher doses indicate that as the dose increases, so does the risk of both cancer and non-cancer mortality, aligning with the established understanding of dose–response relationships in radiation exposure. However, the SHAP value trends with dose differed in shape for cancer and non-cancer outcomes. For cancer they show a non-linear trend with dose, with the effect plateauing and then slightly decreasing at higher doses, possibly indicating a saturation point beyond which additional dose increments do not correspond to a proportionally higher risk. In contrast, non-cancer SHAP trends with dose appeared to continue to increase (linearly or even with upward curvature) even at the highest tested doses, with no sign of saturation. This difference in dose response shapes may represent a difference in biological effects of neutrons on cancer vs non-cancer diseases, but the saturation for the cancer response may also be due to the fact that at the highest doses the majority of mice developed cancer, so not much further increase was possible.Figure 3Visualizations of how the SHAP values of each continuous feature change as function of the feature values for cancer (red) and non-cancer (blue) diseases. To better visualize on comparing the shapes, rather than the magnitudes, of the SHAP value dependences for cancer vs non-cancer, all SHAP values were normalized by dividing by the absolute value of the mean of SHAP values for each feature.For age at treatment (i.e. at the start of irradiation), the SHAP values for non-cancer and cancer both tended towards decreases at older ages, with more scattering for non-cancer. Complexity in the trends could reflect the interplay between age-related disease susceptibility and the decreasing probability of disease manifestation as mice reach advanced ages.For non-cancer, the number of fractions variable exhibited relatively small and unclear effects on the predicted hazard, with the SHAP values clustering around zero, implying a limited influence of these treatment-related factors on non-cancer mortality. Conversely, for cancer outcomes, number of fractions showed a trend where initially the risk increases with the number of fractions, then reaches a peak around 100 fractions and decreases at higher fraction numbers.These trends, especially for cancer, may be consistent with the concept of an inverse dose rate or protraction effect30, where increased number of fractions in the intermediate range and/or increased fraction duration were associated with higher SHAP values compared with single-fraction exposures. The subsequent decrease in SHAP values at the highest fraction numbers might indicate a saturation effect, where additional fractions do not correspond to increased risk. For non-cancer events, this peak is not visible, suggesting that the inverse dose rate effect does not apply in the same way or is not present for non-cancer outcomes.The duration of fraction feature seemed to have little effect on either cancer or non-cancer SHAP values. Regarding categorical (binary) features, the analysis indicated a reduction in SHAP values for males compared to females for both disease outcomes. This suggests that being male is associated with a lower hazard of both cancer and non-cancer mortality compared to being female, within the context of this study population. The binary indicator variables for various experiments also contributed, suggesting that there was some variability between mouse cohorts.Pearson’s and Spearman correlation analyses were used to investigate to what extent the SHAP value contributions of the different variables to the RSF model were independent, or correlated with each other (Figs. S2–S3 from the supplementary material). The correlations were generally not very strong, suggesting largely independent contributions. The only exception was the correlation between SHAP values for dose and number of fractions, particularly for the cancer outcome, which may indicate some redundancy in the SHAP contributions of these variables.CSCHF summaries for different dose binsIn addition to the SHAP analysis, we also visualized the model predictions by plotting the distributions of CSCHF at 900, 1000 or 1100 days for each disease for different dose bins (0–0.5 Gy, 0.5–1 Gy, and so on). These results are shown in Fig. 4. The trends in this visualization are generally consistent with those from the SHAP analysis (Fig. 3), indicating clear increases in predicted hazards for both diseases with increasing neutron dose, and a lot of variability in hazard values between different mice even in the same dose bracket.Figure 4Cumulative hazard function error bar plots for cancer (left) and non-cancer (right) diseases by dose bin at time points 900, 1000, and 1100 days.