Piecewise ITS Regression | Oura Digital Twin

METHODOLOGY

Methodology

Interrupted Time Series (ITS) is a quasi-experimental design for evaluating interventions when randomization is not possible. This N-of-1 study uses a piecewise regression with two interruptions:

        yt = β0 + β1·time
        + β2·jakavi + β3·time_since_jakavi
        + β4·bb + β5·time_since_bb
        + εt

        εt = ρ·εt-1 + ut
          (AR(1) autocorrelation correction)
      

β₂	Jakavi level shift - immediate change in the metric when Jakavi started
β₃	Jakavi slope change - change in daily trend after Jakavi
β₄	Beta-blocker level shift - immediate change when beta-blocker was added
β₅	Beta-blocker slope change - change in daily trend after adding beta-blocker

AR(1) correction accounts for day-to-day autocorrelation in biometric data (today's measurement is correlated with yesterday's). Without this correction, standard errors would be underestimated and p-values too liberal.

Fitted via statsmodels.GLSAR (iterative Cochrane-Orcutt, up to 20 iterations). Residual diagnostics include the Durbin-Watson statistic and Ljung-Box test for remaining autocorrelation.

METRIC MEAN_RMSSD

Mean RMSSD (ms)

Jakavi level shift

-1.460ms

p=0.715 | CI [-9.35, +6.42]

Jakavi slope change

-0.083ms

p=0.760 | CI [-0.62, +0.45]

Beta-blocker level shift

In range

18.546ms

p<0.001 | CI [+11.09, +26.00]

Beta-blocker slope change

-0.015ms

p=0.954 | CI [-0.54, +0.51]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+7.3323	2.1218	[+3.1513, +11.5133]	p<0.001 *
Baseline trend (b1)	+0.0804	0.0547	[-0.0273, +0.1882]	p=0.143
Jakavi level shift (b2)	-1.4605	4.0017	[-9.3459, +6.4250]	p=0.715
Jakavi slope change (b3)	-0.0826	0.2704	[-0.6155, +0.4503]	p=0.760
Beta-blocker level shift (b4)	+18.5458	3.7851	[+11.0872, +26.0044]	p<0.001 *
Beta-blocker slope change (b5)	-0.0152	0.2643	[-0.5360, +0.5057]	p=0.954

AR(1) Rho

0.211

Durbin-Watson

1.575

Ideal: 2.0

Ljung-Box p

0.004

Fail (autocorrelation remains)

R-squared

0.531

Adj: 0.521 | N=233

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METRIC LOWEST_HEART_RATE

Lowest Heart Rate (bpm)

Jakavi level shift

1.954bpm

p=0.617 | CI [-5.73, +9.64]

Jakavi slope change

0.147bpm

p=0.577 | CI [-0.37, +0.67]

Beta-blocker level shift

In range

-8.964bpm

p=0.009 | CI [-15.70, -2.23]

Beta-blocker slope change

-0.025bpm

p=0.924 | CI [-0.54, +0.49]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+82.5717	1.7610	[+79.1009, +86.0425]	p<0.001 *
Baseline trend (b1)	-0.1710	0.0450	[-0.2596, -0.0824]	p<0.001 *
Jakavi level shift (b2)	+1.9535	3.9001	[-5.7335, +9.6405]	p=0.617
Jakavi slope change (b3)	+0.1470	0.2633	[-0.3720, +0.6660]	p=0.577
Beta-blocker level shift (b4)	-8.9639	3.4172	[-15.6991, -2.2288]	p=0.009 *
Beta-blocker slope change (b5)	-0.0247	0.2596	[-0.5363, +0.4870]	p=0.924

AR(1) Rho

0.074

Durbin-Watson

1.846

Ideal: 2.0

Ljung-Box p

0.590

Pass (white noise)

R-squared

0.583

Adj: 0.573 | N=224

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METRIC AVERAGE_HEART_RATE

Average Heart Rate (bpm)

Jakavi level shift

2.340bpm

p=0.580 | CI [-5.98, +10.66]

Jakavi slope change

0.248bpm

p=0.387 | CI [-0.32, +0.81]

Beta-blocker level shift

In range

-9.037bpm

p=0.016 | CI [-16.35, -1.73]

Beta-blocker slope change

-0.090bpm

p=0.749 | CI [-0.64, +0.46]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+92.0823	1.9486	[+88.2417, +95.9229]	p<0.001 *
Baseline trend (b1)	-0.2057	0.0496	[-0.3035, -0.1079]	p<0.001 *
Jakavi level shift (b2)	+2.3402	4.2215	[-5.9803, +10.6606]	p=0.580
Jakavi slope change (b3)	+0.2476	0.2857	[-0.3155, +0.8107]	p=0.387
Beta-blocker level shift (b4)	-9.0369	3.7093	[-16.3477, -1.7260]	p=0.016 *
Beta-blocker slope change (b5)	-0.0900	0.2811	[-0.6441, +0.4640]	p=0.749

AR(1) Rho

0.147

Durbin-Watson

1.706

Ideal: 2.0

Ljung-Box p

0.025

Fail (autocorrelation remains)

R-squared

0.518

Adj: 0.507 | N=224

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METRIC SLEEP_EFFICIENCY

Sleep Efficiency (%)

Jakavi level shift

2.362%

p=0.418 | CI [-3.38, +8.10]

Jakavi slope change

-0.240%

p=0.223 | CI [-0.63, +0.15]

Beta-blocker level shift

3.575%

p=0.161 | CI [-1.44, +8.59]

Beta-blocker slope change

0.225%

p=0.248 | CI [-0.16, +0.61]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+77.4010	1.2836	[+74.8711, +79.9309]	p<0.001 *
Baseline trend (b1)	+0.0389	0.0329	[-0.0258, +0.1037]	p=0.237
Jakavi level shift (b2)	+2.3618	2.9131	[-3.3798, +8.1034]	p=0.418
Jakavi slope change (b3)	-0.2397	0.1962	[-0.6265, +0.1471]	p=0.223
Beta-blocker level shift (b4)	+3.5753	2.5446	[-1.4401, +8.5907]	p=0.161
Beta-blocker slope change (b5)	+0.2246	0.1938	[-0.1575, +0.6066]	p=0.248

AR(1) Rho

-0.037

Durbin-Watson

2.064

Ideal: 2.0

Ljung-Box p

0.013

Fail (autocorrelation remains)

R-squared

0.162

Adj: 0.142 | N=224

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SENSITIVITY INTERPRETATION

Sensitivity Interpretation

The beta-blocker date sensitivity analysis should not be described as a symmetric ±3-day robustness check.

Several future-shifted models fall near the end of the time series and therefore have fewer than 5 post-beta-blocker observations. Those forward shifts are still shown for transparency, but they are treated as support-limited rather than equal-weight evidence.

Mean RMSSD: none of the supported shifts remained significant, so the estimated beta-blocker slope is not robust to plausible date changes.
Lowest Heart Rate: none of the supported shifts remained significant, so the estimated beta-blocker slope is not robust to plausible date changes.
Average Heart Rate: none of the supported shifts remained significant, so the estimated beta-blocker slope is not robust to plausible date changes.
Sleep Efficiency: none of the supported shifts remained significant, so the estimated beta-blocker slope is not robust to plausible date changes.

Suggested manuscript wording: "The beta-blocker sensitivity analysis supported the observed post-beta-blocker slope effect in all adequately supported re-fits, but forward-shifted models near the series end were underpowered because they contained fewer than 5 post-beta-blocker observations. We therefore describe the analysis as forward-limited rather than fully robust to symmetric ±3-day date uncertainty."

SENSITIVITY

Sensitivity Analysis: BB Intervention Date ±3 Days

Method: The ITS model is re-fitted with the beta-blocker date shifted by -3 to +3 days. FULLY ROBUST = all attempted shifts fit and all supported shifts are significant. FORWARD-LIMITED = all supported shifts are significant, but one or more future-shifted fits have <5 post-BB observations. SUPPORTED ONLY = supported shifts are significant, but support gaps or failed fits remain. MIXED = only some supported shifts are significant; SENSITIVE = no supported shifts are significant. Shifts with <5 post-BB days are flagged (⚠) and excluded from the significance denominator, but still listed for transparency. Highlighted row = actual date (2026-04-08). Post-BB n = non-missing metric days after the shifted BB date. * = p < 0.05.

Mean RMSSD - SENSITIVE (0/7 supported)

Support threshold: at least 5 non-missing post-BB observations. 7/7 shifted dates met the threshold; 0 were underpowered and 0 fit(s) failed.

Offset	BB Date	Post-BB n	Support	Level (b4)	p	Slope (b5)	p	R²
-3d	2026-04-05	147	supported	+14.31 ms *	p=0.002	-0.166 ms/day	p=0.648	0.438
-2d	2026-04-06	146	supported	+15.67 ms *	p<0.001	-0.110 ms/day	p=0.738	0.464
-1d	2026-04-07	145	supported	+17.74 ms *	p<0.001	-0.023 ms/day	p=0.937	0.498
+0d (actual)	2026-04-08	144	supported	+18.55 ms *	p<0.001	-0.015 ms/day	p=0.954	0.531
+1d	2026-04-09	143	supported	+20.11 ms *	p<0.001	+0.030 ms/day	p=0.901	0.558
+2d	2026-04-10	142	supported	+18.51 ms *	p<0.001	-0.083 ms/day	p=0.709	0.566
+3d	2026-04-11	141	supported	+16.57 ms *	p<0.001	-0.200 ms/day	p=0.344	0.566

Lowest Heart Rate - SENSITIVE (0/7 supported)

Support threshold: at least 5 non-missing post-BB observations. 7/7 shifted dates met the threshold; 0 were underpowered and 0 fit(s) failed.

Offset	BB Date	Post-BB n	Support	Level (b4)	p	Slope (b5)	p	R²
-3d	2026-04-05	144	supported	-5.84 bpm	p=0.147	+0.133 bpm/day	p=0.708	0.542
-2d	2026-04-06	143	supported	-6.59 bpm	p=0.085	+0.089 bpm/day	p=0.781	0.552
-1d	2026-04-07	142	supported	-10.69 bpm *	p=0.003	-0.157 bpm/day	p=0.586	0.568
+0d (actual)	2026-04-08	141	supported	-8.96 bpm *	p=0.009	-0.025 bpm/day	p=0.924	0.583
+1d	2026-04-09	140	supported	-12.78 bpm *	p<0.001	-0.218 bpm/day	p=0.360	0.595
+2d	2026-04-10	140	supported	-13.00 bpm *	p<0.001	-0.218 bpm/day	p=0.360	0.595
+3d	2026-04-11	139	supported	-9.60 bpm *	p=0.004	-0.008 bpm/day	p=0.969	0.597

Average Heart Rate - SENSITIVE (0/7 supported)

Support threshold: at least 5 non-missing post-BB observations. 7/7 shifted dates met the threshold; 0 were underpowered and 0 fit(s) failed.

Offset	BB Date	Post-BB n	Support	Level (b4)	p	Slope (b5)	p	R²
-3d	2026-04-05	144	supported	-5.44 bpm	p=0.212	+0.088 bpm/day	p=0.818	0.473
-2d	2026-04-06	143	supported	-4.94 bpm	p=0.235	+0.128 bpm/day	p=0.713	0.480
-1d	2026-04-07	142	supported	-11.23 bpm *	p=0.005	-0.255 bpm/day	p=0.415	0.500
+0d (actual)	2026-04-08	141	supported	-9.04 bpm *	p=0.016	-0.090 bpm/day	p=0.749	0.518
+1d	2026-04-09	140	supported	-14.89 bpm *	p<0.001	-0.389 bpm/day	p=0.131	0.538
+2d	2026-04-10	140	supported	-15.28 bpm *	p<0.001	-0.389 bpm/day	p=0.131	0.538
+3d	2026-04-11	139	supported	-10.48 bpm *	p=0.004	-0.097 bpm/day	p=0.681	0.537

Sleep Efficiency - SENSITIVE (0/7 supported)

Support threshold: at least 5 non-missing post-BB observations. 7/7 shifted dates met the threshold; 0 were underpowered and 0 fit(s) failed.

Offset	BB Date	Post-BB n	Support	Level (b4)	p	Slope (b5)	p	R²
-3d	2026-04-05	144	supported	+0.22 %	p=0.938	+0.047 %/day	p=0.855	0.150
-2d	2026-04-06	143	supported	+3.26 %	p=0.238	+0.247 %/day	p=0.289	0.156
-1d	2026-04-07	142	supported	+2.92 %	p=0.271	+0.203 %/day	p=0.338	0.157
+0d (actual)	2026-04-08	141	supported	+3.58 %	p=0.161	+0.225 %/day	p=0.248	0.162
+1d	2026-04-09	140	supported	+6.12 % *	p=0.014	+0.348 %/day	p=0.053	0.176
+2d	2026-04-10	140	supported	+6.46 % *	p=0.014	+0.348 %/day	p=0.053	0.176
+3d	2026-04-11	139	supported	+4.03 %	p=0.109	+0.192 %/day	p=0.244	0.165