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Hybrid integrated diode lasers have so far been realized using silicon, polymer, and silicon nitride (Si3N4) waveguide platforms for extending on-chip tunable light engines from the infrared throughout the visible range. Here we demonstrate the first hybrid integrated laser using the aluminum oxide (Al2O3) deep-UV capable waveguide platform. By permanently coupling low-loss Al2O3 frequency-tunable Vernier feedback circuits with GaN double-pass amplifiers in a hermetically sealed housing, we demonstrate the first extended cavity diode laser (ECDL) in the near UV. The laser shows a maximum fiber-coupled output power of 0.74 mW, corresponding to about 3.5 mW on chip, and tunes more than 4.4 nm in wavelength from 408.1 nm to 403.7 nm. Integrating stable, single-mode and tunable lasers into a deep-UV platform opens a new path for chip-integrated photonic applications.

Additional file 2. Derivation of the metrics measuring overall performance of models predicting treatment effect.

Additional file 8. Calibration plots of pairwise treatment effect of simulated data from patients receiving metformin intervention. This Figure depicts observed versus predicted pairwise treatment effect by smoothed calibration curves (blue line) and quantiles of predicted pairwise treatment effect (black dots) of simulated data from the metformin versus placebo treatment. Observed pairwise treatment effect was obtained by matching patients based on patient characteristics. Smoothed calibration curves were obtained by local regression of the observed pairwise treatment effect of matched patient pairs on predicted pairwise treatment effect of matched patient pairs. For prediction of individualized treatment effect, we used a treatment effect modelling approach for the “optimal model” (panel A) and three “perturbed models” that overestimate average treatment effect (panel B), risk heterogeneity (panel C), and treatment effect heterogeneity (panel D). The average treatment effect is 6.6, 11.9, 6.6 (after a correction of with -0.085), and 6.6 (after a correction of with -0.16), respectively.

Additional file 6. The probability of the potential outcome of diabetes under metformin treatment versus under control treatment predicted by the “optimal model”, and three “perturbed models” that overestimate average treatment effect, risk heterogeneity, and treatment effect heterogeneity.

Additional file 7. Calibration plots of pairwise treatment effect of simulated data from patients receiving lifestyle intervention or metformin. This Figure depicts observed versus predicted pairwise treatment effect by smoothed calibration curves (blue line) and quantiles of predicted pairwise treatment effect (black dots) of simulated data from the lifestyle intervention or metformin versus placebo treatment. Observed pairwise treatment effect was obtained by matching patients based on patient characteristics. Smoothed calibration curves were obtained by local regression of the observed pairwise treatment effect of matched patient pairs on predicted pairwise treatment effect of matched patient pairs. For prediction of individualized treatment effect, we used the “perturbed model” that underestimates average treatment effect for lifestyle intervention (panel A) and metformin treatment (panel B). The average treatment effect is 7.1 and 3.5, respectively.

Additional file 4. Parameter settings of Ridge regression and causal forest.

Additional file 3. Characteristics of patients in the Diabetes Prevention Program receiving lifestyle intervention, metformin, or placebo treatment.

Additional file 1. Sensitivity analysis of matching method.

Additional file 9. Calibration plot of pairwise treatment effect of training and test data of lifestyle intervention. This Figure depicts observed versus predicted pairwise treatment effect by smoothed calibration curves (blue line with 95% confidence interval displayed by grey shaded area) and quarters of predicted pairwise treatment effect (black dots) of lifestyle intervention versus placebo treatment. Observed pairwise treatment effect was obtained by matching patients based on patient characteristics. Smoothed calibration curves were obtained by local regression of the observed pairwise treatment effect of matched patient pairs on predicted pairwise treatment effect of matched patient pairs. For prediction of treatment effect, we used: a risk modelling approach (panel A; B), a treatment effect modelling approach (panel C; D), and a causal forest (panel E; F). The models are trained on 70 percent of the data (panel A; C; E) and evaluated on the other 30 percent of the data (B; D; F). Confidence intervals around the metric values were obtained using 100 bootstrap samples.

Additional file 5. The probability of the potential outcome of diabetes under lifestyle intervention versus under control treatment predicted by the “optimal model”, and three “perturbed models” that overestimate average treatment effect, risk heterogeneity, and treatment effect heterogeneity.