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

-1.587ms

p=0.696 | CI [-9.57, +6.39]

Jakavi slope change

-0.063ms

p=0.818 | CI [-0.60, +0.48]

Beta-blocker level shift

In range

19.840ms

p<0.001 | CI [+12.41, +27.27]

Beta-blocker slope change

-0.059ms

p=0.826 | CI [-0.58, +0.47]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+7.3342	2.1696	[+3.0634, +11.6049]	p<0.001 *
Baseline trend (b1)	+0.0803	0.0559	[-0.0296, +0.1903]	p=0.151
Jakavi level shift (b2)	-1.5868	4.0531	[-9.5651, +6.3914]	p=0.696
Jakavi slope change (b3)	-0.0632	0.2743	[-0.6031, +0.4767]	p=0.818
Beta-blocker level shift (b4)	+19.8396	3.7738	[+12.4111, +27.2681]	p<0.001 *
Beta-blocker slope change (b5)	-0.0588	0.2673	[-0.5849, +0.4673]	p=0.826

AR(1) Rho

0.237

Durbin-Watson

1.520

Ideal: 2.0

Ljung-Box p

0.000

Fail (autocorrelation remains)

R-squared

0.471

Adj: 0.462 | N=288

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METRIC LOWEST_HEART_RATE

Lowest Heart Rate (bpm)

Jakavi level shift

2.044bpm

p=0.591 | CI [-5.43, +9.51]

Jakavi slope change

0.137bpm

p=0.594 | CI [-0.37, +0.64]

Beta-blocker level shift

In range

-10.893bpm

p=0.001 | CI [-17.34, -4.44]

Beta-blocker slope change

0.017bpm

p=0.947 | CI [-0.48, +0.51]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+82.5796	1.7201	[+79.1932, +85.9659]	p<0.001 *
Baseline trend (b1)	-0.1712	0.0439	[-0.2576, -0.0848]	p<0.001 *
Jakavi level shift (b2)	+2.0435	3.7951	[-5.4279, +9.5149]	p=0.591
Jakavi slope change (b3)	+0.1368	0.2563	[-0.3678, +0.6415]	p=0.594
Beta-blocker level shift (b4)	-10.8925	3.2755	[-17.3411, -4.4439]	p=0.001 *
Beta-blocker slope change (b5)	+0.0169	0.2523	[-0.4799, +0.5137]	p=0.947

AR(1) Rho

0.088

Durbin-Watson

1.806

Ideal: 2.0

Ljung-Box p

0.004

Fail (autocorrelation remains)

R-squared

0.567

Adj: 0.559 | N=279

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METRIC AVERAGE_HEART_RATE

Average Heart Rate (bpm)

Jakavi level shift

2.426bpm

p=0.558 | CI [-5.71, +10.56]

Jakavi slope change

0.238bpm

p=0.396 | CI [-0.31, +0.79]

Beta-blocker level shift

In range

-10.531bpm

p=0.004 | CI [-17.57, -3.49]

Beta-blocker slope change

-0.056bpm

p=0.840 | CI [-0.60, +0.49]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+92.0835	1.9119	[+88.3195, +95.8476]	p<0.001 *
Baseline trend (b1)	-0.2057	0.0487	[-0.3016, -0.1099]	p<0.001 *
Jakavi level shift (b2)	+2.4256	4.1317	[-5.7087, +10.5598]	p=0.558
Jakavi slope change (b3)	+0.2376	0.2797	[-0.3130, +0.7882]	p=0.396
Beta-blocker level shift (b4)	-10.5314	3.5766	[-17.5727, -3.4900]	p=0.004 *
Beta-blocker slope change (b5)	-0.0557	0.2748	[-0.5966, +0.4852]	p=0.840

AR(1) Rho

0.154

Durbin-Watson

1.684

Ideal: 2.0

Ljung-Box p

0.002

Fail (autocorrelation remains)

R-squared

0.509

Adj: 0.500 | N=279

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METRIC SLEEP_EFFICIENCY

Sleep Efficiency (%)

Jakavi level shift

2.290%

p=0.435 | CI [-3.47, +8.05]

Jakavi slope change

-0.233%

p=0.239 | CI [-0.62, +0.16]

Beta-blocker level shift

4.297%

p=0.089 | CI [-0.66, +9.26]

Beta-blocker slope change

0.206%

p=0.291 | CI [-0.18, +0.59]

Parameter	Estimate	Std Error	95% CI	P-value
Intercept (b0)	+77.4068	1.2964	[+74.8545, +79.9592]	p<0.001 *
Baseline trend (b1)	+0.0389	0.0332	[-0.0264, +0.1042]	p=0.242
Jakavi level shift (b2)	+2.2901	2.9273	[-3.4730, +8.0531]	p=0.435
Jakavi slope change (b3)	-0.2329	0.1973	[-0.6214, +0.1555]	p=0.239
Beta-blocker level shift (b4)	+4.2975	2.5185	[-0.6607, +9.2556]	p=0.089
Beta-blocker slope change (b5)	+0.2060	0.1946	[-0.1771, +0.5892]	p=0.291

AR(1) Rho

-0.010

Durbin-Watson

2.001

Ideal: 2.0

Ljung-Box p

0.884

Pass (white noise)

R-squared

0.152

Adj: 0.136 | N=279

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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	202	supported	+15.93 ms *	p<0.001	-0.231 ms/day	p=0.525	0.380
-2d	2026-04-06	201	supported	+17.21 ms *	p<0.001	-0.167 ms/day	p=0.612	0.406
-1d	2026-04-07	200	supported	+19.19 ms *	p<0.001	-0.071 ms/day	p=0.812	0.439
+0d (actual)	2026-04-08	199	supported	+19.84 ms *	p<0.001	-0.059 ms/day	p=0.826	0.471
+1d	2026-04-09	198	supported	+21.37 ms *	p<0.001	-0.002 ms/day	p=0.994	0.498
+2d	2026-04-10	197	supported	+19.66 ms *	p<0.001	-0.116 ms/day	p=0.610	0.506
+3d	2026-04-11	196	supported	+17.63 ms *	p<0.001	-0.233 ms/day	p=0.275	0.507

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	199	supported	-7.94 bpm *	p=0.043	+0.184 bpm/day	p=0.597	0.518
-2d	2026-04-06	198	supported	-8.63 bpm *	p=0.020	+0.138 bpm/day	p=0.658	0.531
-1d	2026-04-07	197	supported	-12.74 bpm *	p<0.001	-0.123 bpm/day	p=0.663	0.550
+0d (actual)	2026-04-08	196	supported	-10.89 bpm *	p=0.001	+0.017 bpm/day	p=0.947	0.567
+1d	2026-04-09	195	supported	-14.68 bpm *	p<0.001	-0.190 bpm/day	p=0.412	0.583
+2d	2026-04-10	195	supported	-14.87 bpm *	p<0.001	-0.190 bpm/day	p=0.412	0.583
+3d	2026-04-11	194	supported	-11.43 bpm *	p<0.001	+0.025 bpm/day	p=0.904	0.586

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	199	supported	-7.13 bpm	p=0.092	+0.132 bpm/day	p=0.726	0.460
-2d	2026-04-06	198	supported	-6.59 bpm	p=0.102	+0.171 bpm/day	p=0.614	0.468
-1d	2026-04-07	197	supported	-12.79 bpm *	p<0.001	-0.225 bpm/day	p=0.462	0.491
+0d (actual)	2026-04-08	196	supported	-10.53 bpm *	p=0.004	-0.056 bpm/day	p=0.840	0.509
+1d	2026-04-09	195	supported	-16.24 bpm *	p<0.001	-0.367 bpm/day	p=0.144	0.530
+2d	2026-04-10	195	supported	-16.61 bpm *	p<0.001	-0.367 bpm/day	p=0.144	0.530
+3d	2026-04-11	194	supported	-11.82 bpm *	p<0.001	-0.070 bpm/day	p=0.761	0.530

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	199	supported	+1.02 %	p=0.722	+0.022 %/day	p=0.931	0.139
-2d	2026-04-06	198	supported	+4.15 %	p=0.131	+0.236 %/day	p=0.312	0.146
-1d	2026-04-07	197	supported	+3.70 %	p=0.159	+0.186 %/day	p=0.384	0.147
+0d (actual)	2026-04-08	196	supported	+4.30 %	p=0.089	+0.206 %/day	p=0.291	0.152
+1d	2026-04-09	195	supported	+6.90 % *	p=0.005	+0.341 %/day	p=0.059	0.167
+2d	2026-04-10	195	supported	+7.24 % *	p=0.005	+0.341 %/day	p=0.059	0.167
+3d	2026-04-11	194	supported	+4.68 %	p=0.060	+0.175 %/day	p=0.290	0.157