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

-1.330ms

p=0.725 | CI [-8.77, +6.11]

Jakavi slope change

-0.103ms

p=0.687 | CI [-0.60, +0.40]

Beta-blocker level shift

In range

19.746ms

p<0.001 | CI [+12.44, +27.05]

Beta-blocker slope change

-0.010ms

p=0.969 | CI [-0.51, +0.49]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+7.3311	1.9664	[+3.4492, +11.2130]	p<0.001 *
Baseline trend (b1)	+0.0805	0.0508	[-0.0197, +0.1808]	p=0.115
Jakavi level shift (b2)	-1.3298	3.7698	[-8.7717, +6.1122]	p=0.725
Jakavi slope change (b3)	-0.1027	0.2542	[-0.6045, +0.3990]	p=0.687
Beta-blocker level shift (b4)	+19.7463	3.7019	[+12.4384, +27.0543]	p<0.001 *
Beta-blocker slope change (b5)	-0.0099	0.2510	[-0.5054, +0.4855]	p=0.969

AR(1) Rho

0.159

Durbin-Watson

1.673

Ideal: 2.0

Ljung-Box p

0.025

Fail (autocorrelation remains)

R-squared

0.605

Adj: 0.593 | N=176

Loading chart...

METRIC LOWEST_HEART_RATE

Lowest Heart Rate (bpm)

Jakavi level shift

1.560bpm

p=0.647 | CI [-5.15, +8.27]

Jakavi slope change

0.189bpm

p=0.410 | CI [-0.26, +0.64]

Beta-blocker level shift

In range

-8.232bpm

p=0.008 | CI [-14.33, -2.14]

Beta-blocker slope change

-0.111bpm

p=0.626 | CI [-0.56, +0.34]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+82.5197	1.5006	[+79.5562, +85.4832]	p<0.001 *
Baseline trend (b1)	-0.1699	0.0384	[-0.2458, -0.0941]	p<0.001 *
Jakavi level shift (b2)	+1.5597	3.3996	[-5.1542, +8.2736]	p=0.647
Jakavi slope change (b3)	+0.1892	0.2290	[-0.2631, +0.6416]	p=0.410
Beta-blocker level shift (b4)	-8.2321	3.0864	[-14.3274, -2.1367]	p=0.008 *
Beta-blocker slope change (b5)	-0.1112	0.2274	[-0.5603, +0.3379]	p=0.626

AR(1) Rho

-0.028

Durbin-Watson

2.045

Ideal: 2.0

Ljung-Box p

0.625

Pass (white noise)

R-squared

0.654

Adj: 0.644 | N=167

Loading chart...

METRIC AVERAGE_HEART_RATE

Average Heart Rate (bpm)

Jakavi level shift

2.033bpm

p=0.588 | CI [-5.37, +9.44]

Jakavi slope change

0.282bpm

p=0.267 | CI [-0.22, +0.78]

Beta-blocker level shift

In range

-8.333bpm

p=0.016 | CI [-15.08, -1.59]

Beta-blocker slope change

-0.163bpm

p=0.517 | CI [-0.66, +0.33]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+92.0729	1.7050	[+88.7057, +95.4402]	p<0.001 *
Baseline trend (b1)	-0.2055	0.0435	[-0.2914, -0.1196]	p<0.001 *
Jakavi level shift (b2)	+2.0332	3.7506	[-5.3738, +9.4403]	p=0.588
Jakavi slope change (b3)	+0.2820	0.2534	[-0.2184, +0.7825]	p=0.267
Beta-blocker level shift (b4)	-8.3335	3.4140	[-15.0757, -1.5912]	p=0.016 *
Beta-blocker slope change (b5)	-0.1631	0.2512	[-0.6592, +0.3331]	p=0.517

AR(1) Rho

0.098

Durbin-Watson

1.804

Ideal: 2.0

Ljung-Box p

0.103

Pass (white noise)

R-squared

0.581

Adj: 0.568 | N=167

Loading chart...

METRIC SLEEP_EFFICIENCY

Sleep Efficiency (%)

Jakavi level shift

2.547%

p=0.322 | CI [-2.52, +7.61]

Jakavi slope change

-0.257%

p=0.138 | CI [-0.60, +0.08]

Beta-blocker level shift

4.359%

p=0.063 | CI [-0.23, +8.95]

Beta-blocker slope change

0.230%

p=0.182 | CI [-0.11, +0.57]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+77.3854	1.1162	[+75.1809, +79.5898]	p<0.001 *
Baseline trend (b1)	+0.0391	0.0286	[-0.0174, +0.0956]	p=0.174
Jakavi level shift (b2)	+2.5472	2.5652	[-2.5188, +7.6132]	p=0.322
Jakavi slope change (b3)	-0.2573	0.1726	[-0.5982, +0.0836]	p=0.138
Beta-blocker level shift (b4)	+4.3591	2.3261	[-0.2346, +8.9529]	p=0.063
Beta-blocker slope change (b5)	+0.2297	0.1715	[-0.1089, +0.5684]	p=0.182

AR(1) Rho

-0.115

Durbin-Watson

2.221

Ideal: 2.0

Ljung-Box p

0.122

Pass (white noise)

R-squared

0.157

Adj: 0.131 | N=167

Loading chart...

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: supported shifts showed mixed significance, so the estimated beta-blocker slope is sensitive 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	90	supported	+14.00 ms *	p=0.003	-0.136 ms/day	p=0.710	0.475
-2d	2026-04-06	89	supported	+15.79 ms *	p<0.001	-0.089 ms/day	p=0.786	0.509
-1d	2026-04-07	88	supported	+18.35 ms *	p<0.001	-0.015 ms/day	p=0.959	0.556
+0d (actual)	2026-04-08	87	supported	+19.75 ms *	p<0.001	-0.010 ms/day	p=0.969	0.605
+1d	2026-04-09	86	supported	+21.60 ms *	p<0.001	+0.011 ms/day	p=0.961	0.644
+2d	2026-04-10	85	supported	+20.44 ms *	p<0.001	-0.101 ms/day	p=0.623	0.659
+3d	2026-04-11	84	supported	+18.89 ms *	p<0.001	-0.214 ms/day	p=0.263	0.665

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	87	supported	-4.19 bpm	p=0.255	+0.049 bpm/day	p=0.876	0.610
-2d	2026-04-06	86	supported	-5.24 bpm	p=0.133	-0.001 bpm/day	p=0.997	0.620
-1d	2026-04-07	85	supported	-9.04 bpm *	p=0.007	-0.195 bpm/day	p=0.446	0.636
+0d (actual)	2026-04-08	84	supported	-8.23 bpm *	p=0.008	-0.111 bpm/day	p=0.626	0.654
+1d	2026-04-09	83	supported	-11.47 bpm *	p<0.001	-0.237 bpm/day	p=0.256	0.668
+2d	2026-04-10	83	supported	-11.71 bpm *	p<0.001	-0.237 bpm/day	p=0.256	0.668
+3d	2026-04-11	82	supported	-9.05 bpm *	p=0.003	-0.069 bpm/day	p=0.716	0.669

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	87	supported	-3.82 bpm	p=0.347	+0.016 bpm/day	p=0.964	0.525
-2d	2026-04-06	86	supported	-3.54 bpm	p=0.362	+0.046 bpm/day	p=0.884	0.532
-1d	2026-04-07	85	supported	-9.93 bpm *	p=0.007	-0.294 bpm/day	p=0.300	0.555
+0d (actual)	2026-04-08	84	supported	-8.33 bpm *	p=0.016	-0.163 bpm/day	p=0.517	0.581
+1d	2026-04-09	83	supported	-14.05 bpm *	p<0.001	-0.403 bpm/day	p=0.079	0.605
+2d	2026-04-10	83	supported	-14.46 bpm *	p<0.001	-0.403 bpm/day	p=0.079	0.605
+3d	2026-04-11	82	supported	-10.12 bpm *	p=0.002	-0.145 bpm/day	p=0.488	0.605

Sleep Efficiency — MIXED (2/7 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	87	supported	+0.67 %	p=0.800	+0.067 %/day	p=0.773	0.133
-2d	2026-04-06	86	supported	+3.57 %	p=0.162	+0.236 %/day	p=0.258	0.143
-1d	2026-04-07	85	supported	+3.50 %	p=0.152	+0.207 %/day	p=0.275	0.146
+0d (actual)	2026-04-08	84	supported	+4.36 %	p=0.063	+0.230 %/day	p=0.182	0.157
+1d	2026-04-09	83	supported	+6.75 % *	p=0.003	+0.322 %/day *	p=0.042	0.184
+2d	2026-04-10	83	supported	+7.08 % *	p=0.003	+0.322 %/day *	p=0.042	0.184
+3d	2026-04-11	82	supported	+5.03 % *	p=0.028	+0.192 %/day	p=0.185	0.167