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

-1.491ms

p=0.711 | CI [-9.42, +6.43]

Jakavi slope change

-0.078ms

p=0.775 | CI [-0.61, +0.46]

Beta-blocker level shift

In range

19.070ms

p<0.001 | CI [+11.67, +26.47]

Beta-blocker slope change

-0.028ms

p=0.916 | CI [-0.55, +0.49]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+7.3327	2.1377	[+3.1235, +11.5418]	p<0.001 *
Baseline trend (b1)	+0.0804	0.0551	[-0.0280, +0.1889]	p=0.145
Jakavi level shift (b2)	-1.4911	4.0243	[-9.4151, +6.4328]	p=0.711
Jakavi slope change (b3)	-0.0780	0.2720	[-0.6136, +0.4576]	p=0.775
Beta-blocker level shift (b4)	+19.0701	3.7605	[+11.6656, +26.4746]	p<0.001 *
Beta-blocker slope change (b5)	-0.0280	0.2654	[-0.5506, +0.4946]	p=0.916

AR(1) Rho

0.216

Durbin-Watson

1.569

Ideal: 2.0

Ljung-Box p

0.001

Fail (autocorrelation remains)

R-squared

0.500

Adj: 0.490 | N=270

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METRIC LOWEST_HEART_RATE

Lowest Heart Rate (bpm)

Jakavi level shift

1.858bpm

p=0.615 | CI [-5.41, +9.13]

Jakavi slope change

0.157bpm

p=0.528 | CI [-0.33, +0.65]

Beta-blocker level shift

In range

-10.202bpm

p=0.002 | CI [-16.50, -3.91]

Beta-blocker slope change

-0.020bpm

p=0.936 | CI [-0.50, +0.46]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+82.5589	1.6577	[+79.2943, +85.8234]	p<0.001 *
Baseline trend (b1)	-0.1708	0.0424	[-0.2542, -0.0874]	p<0.001 *
Jakavi level shift (b2)	+1.8585	3.6933	[-5.4149, +9.1318]	p=0.615
Jakavi slope change (b3)	+0.1573	0.2492	[-0.3335, +0.6482]	p=0.528
Beta-blocker level shift (b4)	-10.2022	3.1966	[-16.4974, -3.9071]	p=0.002 *
Beta-blocker slope change (b5)	-0.0197	0.2456	[-0.5034, +0.4639]	p=0.936

AR(1) Rho

0.050

Durbin-Watson

1.894

Ideal: 2.0

Ljung-Box p

0.078

Pass (white noise)

R-squared

0.608

Adj: 0.600 | N=261

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METRIC AVERAGE_HEART_RATE

Average Heart Rate (bpm)

Jakavi level shift

2.245bpm

p=0.582 | CI [-5.78, +10.26]

Jakavi slope change

0.258bpm

p=0.349 | CI [-0.28, +0.80]

Beta-blocker level shift

In range

-9.844bpm

p=0.006 | CI [-16.81, -2.88]

Beta-blocker slope change

-0.092bpm

p=0.734 | CI [-0.63, +0.44]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+92.0789	1.8689	[+88.3983, +95.7594]	p<0.001 *
Baseline trend (b1)	-0.2056	0.0476	[-0.2994, -0.1118]	p<0.001 *
Jakavi level shift (b2)	+2.2446	4.0722	[-5.7750, +10.2643]	p=0.582
Jakavi slope change (b3)	+0.2583	0.2754	[-0.2841, +0.8007]	p=0.349
Beta-blocker level shift (b4)	-9.8436	3.5353	[-16.8059, -2.8813]	p=0.006 *
Beta-blocker slope change (b5)	-0.0921	0.2709	[-0.6255, +0.4413]	p=0.734

AR(1) Rho

0.129

Durbin-Watson

1.742

Ideal: 2.0

Ljung-Box p

0.047

Fail (autocorrelation remains)

R-squared

0.544

Adj: 0.535 | N=261

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METRIC SLEEP_EFFICIENCY

Sleep Efficiency (%)

Jakavi level shift

2.321%

p=0.431 | CI [-3.47, +8.12]

Jakavi slope change

-0.236%

p=0.235 | CI [-0.63, +0.15]

Beta-blocker level shift

3.901%

p=0.126 | CI [-1.10, +8.91]

Beta-blocker slope change

0.216%

p=0.272 | CI [-0.17, +0.60]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+77.4044	1.3004	[+74.8435, +79.9652]	p<0.001 *
Baseline trend (b1)	+0.0389	0.0333	[-0.0266, +0.1044]	p=0.244
Jakavi level shift (b2)	+2.3211	2.9426	[-3.4739, +8.1160]	p=0.431
Jakavi slope change (b3)	-0.2359	0.1983	[-0.6263, +0.1546]	p=0.235
Beta-blocker level shift (b4)	+3.9014	2.5415	[-1.1037, +8.9065]	p=0.126
Beta-blocker slope change (b5)	+0.2156	0.1957	[-0.1697, +0.6009]	p=0.272

AR(1) Rho

-0.022

Durbin-Watson

2.038

Ideal: 2.0

Ljung-Box p

0.854

Pass (white noise)

R-squared

0.169

Adj: 0.152 | N=261

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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	184	supported	+15.21 ms *	p<0.001	-0.186 ms/day	p=0.607	0.412
-2d	2026-04-06	183	supported	+16.46 ms *	p<0.001	-0.128 ms/day	p=0.697	0.437
-1d	2026-04-07	182	supported	+18.39 ms *	p<0.001	-0.038 ms/day	p=0.898	0.469
+0d (actual)	2026-04-08	181	supported	+19.07 ms *	p<0.001	-0.028 ms/day	p=0.916	0.500
+1d	2026-04-09	180	supported	+20.53 ms *	p<0.001	+0.022 ms/day	p=0.929	0.525
+2d	2026-04-10	179	supported	+18.86 ms *	p<0.001	-0.092 ms/day	p=0.685	0.531
+3d	2026-04-11	178	supported	+16.87 ms *	p<0.001	-0.208 ms/day	p=0.328	0.532

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	181	supported	-7.10 bpm	p=0.063	+0.150 bpm/day	p=0.659	0.563
-2d	2026-04-06	180	supported	-7.87 bpm *	p=0.029	+0.101 bpm/day	p=0.741	0.575
-1d	2026-04-07	179	supported	-11.69 bpm *	p<0.001	-0.138 bpm/day	p=0.614	0.592
+0d (actual)	2026-04-08	178	supported	-10.20 bpm *	p=0.002	-0.020 bpm/day	p=0.936	0.608
+1d	2026-04-09	177	supported	-13.62 bpm *	p<0.001	-0.201 bpm/day	p=0.373	0.621
+2d	2026-04-10	177	supported	-13.82 bpm *	p<0.001	-0.201 bpm/day	p=0.373	0.621
+3d	2026-04-11	176	supported	-10.68 bpm *	p<0.001	-0.002 bpm/day	p=0.991	0.624

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	181	supported	-6.27 bpm	p=0.133	+0.099 bpm/day	p=0.789	0.498
-2d	2026-04-06	180	supported	-5.88 bpm	p=0.139	+0.130 bpm/day	p=0.698	0.506
-1d	2026-04-07	179	supported	-11.78 bpm *	p=0.002	-0.242 bpm/day	p=0.422	0.526
+0d (actual)	2026-04-08	178	supported	-9.84 bpm *	p=0.006	-0.092 bpm/day	p=0.734	0.544
+1d	2026-04-09	177	supported	-15.22 bpm *	p<0.001	-0.379 bpm/day	p=0.126	0.562
+2d	2026-04-10	177	supported	-15.60 bpm *	p<0.001	-0.379 bpm/day	p=0.126	0.562
+3d	2026-04-11	176	supported	-11.08 bpm *	p=0.001	-0.097 bpm/day	p=0.668	0.562

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	181	supported	+0.62 %	p=0.831	+0.034 %/day	p=0.894	0.157
-2d	2026-04-06	180	supported	+3.69 %	p=0.182	+0.242 %/day	p=0.302	0.163
-1d	2026-04-07	179	supported	+3.29 %	p=0.215	+0.195 %/day	p=0.363	0.164
+0d (actual)	2026-04-08	178	supported	+3.90 %	p=0.126	+0.216 %/day	p=0.272	0.169
+1d	2026-04-09	177	supported	+6.46 % *	p=0.009	+0.346 %/day	p=0.056	0.182
+2d	2026-04-10	177	supported	+6.80 % *	p=0.010	+0.346 %/day	p=0.056	0.182
+3d	2026-04-11	176	supported	+4.31 %	p=0.086	+0.184 %/day	p=0.269	0.173