fix(medications): widen the medication-effect intervals to a week of lag

The automatic Newey-West rule gives a lag of 3 on 30 to 270 daily
values, which leaves most of a physiological series' carry-over out of
the intervals. The lag is now at least 7. Reference values are
recomputed with statsmodels at the new default, and the lag-3 values
stay pinned with an explicit lag. A fit whose residual autocorrelation
exceeds 0.5 is flagged, and the card, the clinician view and the PDF
say the ranges may still be too narrow.

docs/api/openapi.yaml

@@ -54898,12 +54898,18 @@ components:
                                 type: integer
                                 minimum: -9007199254740991
                                 maximum: 9007199254740991
+                                description: "Newey–West lag applied: the automatic rule, at least 7 (a week of daily carry-over)."
+                              autocorrelationCaveat:
+                                type: boolean
+                                description: "True when the lag-1 residual autocorrelation exceeds 0.5: the carry-over is strong enough that the
+                                  intervals may still be too narrow, and the read-out says so."
                             required:
                               - n
                               - df
                               - rSquared
                               - residualAutocorrelation
                               - hacLag
+                              - autocorrelationCaveat
                             additionalProperties: false
                           - type: "null"
                       confounders:

messages/de.json

@@ -431,7 +431,8 @@
       "notTracked": "Einnahme nicht erfasst, daher keine Tage wegen ausgelassener Dosen entfernt",
       "endDoseChange": "Zeitraum endet am {date}, vor der ersten Dosisänderung",
       "days": "{before} Tage vor, {after} Tage nach dem Start, {excluded} Tage ausgelassen",
-      "method": "Segmentierte Regression über die Tageswerte von 90 Tagen vor bis höchstens 180 Tagen nach dem Start, Intervalle nach Newey-West. Tage nach dem Start, an denen in den 14 Tagen davor weniger als 80 % der Dosen eingenommen wurden, sind ausgelassen. Beschreibt einen zeitlichen Zusammenhang, keine nachgewiesene Wirkung des Medikaments."
+      "method": "Segmentierte Regression über die Tageswerte von 90 Tagen vor bis höchstens 180 Tagen nach dem Start, Intervalle nach Newey-West. Tage nach dem Start, an denen in den 14 Tagen davor weniger als 80 % der Dosen eingenommen wurden, sind ausgelassen. Beschreibt einen zeitlichen Zusammenhang, keine nachgewiesene Wirkung des Medikaments.",
+      "autocorrelation": "starke Abhängigkeit vom Vortag, die Bereiche können daher noch zu eng sein"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Lege ein Startdatum fest, um die Veränderung zum Start zu sehen.",
         "needBefore": "Für die Veränderung zum Start braucht es Werte an mindestens {days} Tagen, verteilt über {span} Tage vor dem Start.",
         "needAfter": "Für die Veränderung zum Start braucht es Werte an mindestens {days} Tagen, verteilt über {span} Tage seit dem Start und an Tagen mit eingenommenen Dosen.",
-        "fitFailed": "Diese Werte ließen sich nicht auswerten, deshalb wird keine Veränderung zum Start gezeigt."
+        "fitFailed": "Diese Werte ließen sich nicht auswerten, deshalb wird keine Veränderung zum Start gezeigt.",
+        "autocorrelation": "Die Tageswerte hängen stark vom Vortag ab, deshalb können selbst diese Bereiche zu eng sein."
       }
     },
     "import": {

messages/en.json

@@ -431,7 +431,8 @@
       "notTracked": "intake not tracked, so no days left out for missed doses",
       "endDoseChange": "window ends {date}, before the first dose change",
       "days": "{before} days before, {after} days after the start, {excluded} days left out",
-      "method": "Segmented regression on daily values from 90 days before to at most 180 days after the start, with Newey-West intervals. Days after the start on which fewer than 80 % of the doses of the preceding 14 days were taken are left out. Describes an association over time, not a proven effect of the medication."
+      "method": "Segmented regression on daily values from 90 days before to at most 180 days after the start, with Newey-West intervals. Days after the start on which fewer than 80 % of the doses of the preceding 14 days were taken are left out. Describes an association over time, not a proven effect of the medication.",
+      "autocorrelation": "strong day-to-day carry-over, so the ranges may still be too narrow"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Set a start date to see the change at the start.",
         "needBefore": "The change at the start needs readings on at least {days} days spread over {span} days before the start.",
         "needAfter": "The change at the start needs readings on at least {days} days spread over {span} days since the start, on days the doses were taken.",
-        "fitFailed": "These readings could not be fitted, so no change at the start is shown."
+        "fitFailed": "These readings could not be fitted, so no change at the start is shown.",
+        "autocorrelation": "The daily values carry over strongly from one day to the next, so even these ranges may be too narrow."
       }
     },
     "import": {

messages/es.json

@@ -431,7 +431,8 @@
       "notTracked": "toma no registrada, así que no se omitió ningún día por dosis olvidadas",
       "endDoseChange": "el periodo termina el {date}, antes del primer cambio de dosis",
       "days": "{before} días antes, {after} días después del inicio, {excluded} días omitidos",
-      "method": "Regresión segmentada sobre los valores diarios desde 90 días antes hasta como máximo 180 días después del inicio, con intervalos de Newey-West. Se omiten los días posteriores al inicio en los que se tomó menos del 80 % de las dosis de los 14 días anteriores. Describe una asociación en el tiempo, no un efecto demostrado del medicamento."
+      "method": "Regresión segmentada sobre los valores diarios desde 90 días antes hasta como máximo 180 días después del inicio, con intervalos de Newey-West. Se omiten los días posteriores al inicio en los que se tomó menos del 80 % de las dosis de los 14 días anteriores. Describe una asociación en el tiempo, no un efecto demostrado del medicamento.",
+      "autocorrelation": "fuerte dependencia del día anterior, así que los rangos pueden seguir siendo demasiado estrechos"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Indica una fecha de inicio para ver el cambio al inicio.",
         "needBefore": "El cambio al inicio necesita valores de al menos {days} días repartidos en {span} días antes del inicio.",
         "needAfter": "El cambio al inicio necesita valores de al menos {days} días repartidos en {span} días desde el inicio, en días con las dosis tomadas.",
-        "fitFailed": "No se pudieron ajustar estos valores, así que no se muestra el cambio al inicio."
+        "fitFailed": "No se pudieron ajustar estos valores, así que no se muestra el cambio al inicio.",
+        "autocorrelation": "Los valores diarios dependen mucho del día anterior, así que incluso estos rangos pueden ser demasiado estrechos."
       }
     },
     "import": {

messages/fr.json

@@ -431,7 +431,8 @@
       "notTracked": "prises non suivies, aucun jour écarté pour des doses manquées",
       "endDoseChange": "la période s'arrête le {date}, avant le premier changement de dose",
       "days": "{before} jours avant, {after} jours après le démarrage, {excluded} jours écartés",
-      "method": "Régression segmentée sur les valeurs quotidiennes, de 90 jours avant à 180 jours au plus après le démarrage, intervalles de Newey-West. Les jours après le démarrage où moins de 80 % des doses des 14 jours précédents ont été prises sont écartés. Décrit une association dans le temps, pas un effet démontré du médicament."
+      "method": "Régression segmentée sur les valeurs quotidiennes, de 90 jours avant à 180 jours au plus après le démarrage, intervalles de Newey-West. Les jours après le démarrage où moins de 80 % des doses des 14 jours précédents ont été prises sont écartés. Décrit une association dans le temps, pas un effet démontré du médicament.",
+      "autocorrelation": "forte dépendance à la veille, les plages peuvent donc rester trop étroites"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Indique une date de début pour voir le changement au démarrage.",
         "needBefore": "Le changement au démarrage demande des valeurs sur au moins {days} jours répartis sur {span} jours avant le démarrage.",
         "needAfter": "Le changement au démarrage demande des valeurs sur au moins {days} jours répartis sur {span} jours depuis le démarrage, les jours où les doses ont été prises.",
-        "fitFailed": "Ces valeurs n'ont pas pu être ajustées, aucun changement au démarrage n'est donc affiché."
+        "fitFailed": "Ces valeurs n'ont pas pu être ajustées, aucun changement au démarrage n'est donc affiché.",
+        "autocorrelation": "Les valeurs quotidiennes dépendent fortement de la veille, donc même ces plages peuvent être trop étroites."
       }
     },
     "import": {

messages/it.json

@@ -431,7 +431,8 @@
       "notTracked": "assunzione non registrata, quindi nessun giorno escluso per dosi saltate",
       "endDoseChange": "il periodo termina il {date}, prima della prima variazione di dose",
       "days": "{before} giorni prima, {after} giorni dopo l'inizio, {excluded} giorni esclusi",
-      "method": "Regressione segmentata sui valori giornalieri da 90 giorni prima a non oltre 180 giorni dopo l'inizio, con intervalli di Newey-West. Sono esclusi i giorni dopo l'inizio in cui è stato assunto meno dell'80 % delle dosi dei 14 giorni precedenti. Descrive un'associazione nel tempo, non un effetto dimostrato del farmaco."
+      "method": "Regressione segmentata sui valori giornalieri da 90 giorni prima a non oltre 180 giorni dopo l'inizio, con intervalli di Newey-West. Sono esclusi i giorni dopo l'inizio in cui è stato assunto meno dell'80 % delle dosi dei 14 giorni precedenti. Descrive un'associazione nel tempo, non un effetto dimostrato del farmaco.",
+      "autocorrelation": "forte dipendenza dal giorno precedente, quindi gli intervalli possono restare troppo stretti"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Imposta una data di inizio per vedere la variazione all'inizio.",
         "needBefore": "La variazione all'inizio richiede valori in almeno {days} giorni distribuiti su {span} giorni prima dell'inizio.",
         "needAfter": "La variazione all'inizio richiede valori in almeno {days} giorni distribuiti su {span} giorni dall'inizio, nei giorni con le dosi assunte.",
-        "fitFailed": "Non è stato possibile elaborare questi valori, quindi non viene mostrata alcuna variazione all'inizio."
+        "fitFailed": "Non è stato possibile elaborare questi valori, quindi non viene mostrata alcuna variazione all'inizio.",
+        "autocorrelation": "I valori giornalieri dipendono molto dal giorno precedente, quindi anche questi intervalli possono essere troppo stretti."
       }
     },
     "import": {

messages/ko.json

@@ -431,7 +431,8 @@
       "notTracked": "복용 미기록으로 놓친 용량에 따른 제외 없음",
       "endDoseChange": "기간은 첫 용량 변경 전인 {date}에 끝남",
       "days": "시작 전 {before}일, 시작 후 {after}일, 제외 {excluded}일",
-      "method": "시작 90일 전부터 최대 180일 후까지의 일별 값에 대한 분절 회귀, Newey-West 구간. 직전 14일 복용률이 80% 미만인 시작 후 날짜는 제외했습니다. 시간에 따른 연관성을 보여 줄 뿐, 약의 효과를 입증하지 않습니다."
+      "method": "시작 90일 전부터 최대 180일 후까지의 일별 값에 대한 분절 회귀, Newey-West 구간. 직전 14일 복용률이 80% 미만인 시작 후 날짜는 제외했습니다. 시간에 따른 연관성을 보여 줄 뿐, 약의 효과를 입증하지 않습니다.",
+      "autocorrelation": "전날 값에 크게 좌우되므로 범위가 여전히 너무 좁을 수 있음"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "시작 시점의 변화를 보려면 시작일을 설정하세요.",
         "needBefore": "시작 시점의 변화를 보려면 시작 전 {span}일에 걸쳐 최소 {days}일의 측정값이 필요합니다.",
         "needAfter": "시작 시점의 변화를 보려면 시작 후 {span}일에 걸쳐, 용량을 복용한 날 기준으로 최소 {days}일의 측정값이 필요합니다.",
-        "fitFailed": "이 측정값으로는 계산할 수 없어 시작 시점의 변화를 표시하지 않습니다."
+        "fitFailed": "이 측정값으로는 계산할 수 없어 시작 시점의 변화를 표시하지 않습니다.",
+        "autocorrelation": "하루 값이 전날 값에 크게 좌우되므로 이 범위도 너무 좁을 수 있습니다."
       }
     },
     "import": {

messages/nl.json

@@ -431,7 +431,8 @@
       "notTracked": "inname niet bijgehouden, dus geen dagen weggelaten om gemiste doses",
       "endDoseChange": "periode eindigt op {date}, vóór de eerste dosiswijziging",
       "days": "{before} dagen voor, {after} dagen na de start, {excluded} dagen weggelaten",
-      "method": "Gesegmenteerde regressie op de dagwaarden van 90 dagen vóór tot hoogstens 180 dagen na de start, met Newey-West-intervallen. Dagen na de start waarop minder dan 80% van de doses van de 14 dagen ervoor is ingenomen, zijn weggelaten. Beschrijft een samenhang in de tijd, geen bewezen effect van het medicijn."
+      "method": "Gesegmenteerde regressie op de dagwaarden van 90 dagen vóór tot hoogstens 180 dagen na de start, met Newey-West-intervallen. Dagen na de start waarop minder dan 80% van de doses van de 14 dagen ervoor is ingenomen, zijn weggelaten. Beschrijft een samenhang in de tijd, geen bewezen effect van het medicijn.",
+      "autocorrelation": "sterke afhankelijkheid van de vorige dag, dus de bereiken kunnen nog te smal zijn"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Stel een startdatum in om de verandering bij de start te zien.",
         "needBefore": "Voor de verandering bij de start zijn waarden op minstens {days} dagen nodig, verspreid over {span} dagen vóór de start.",
         "needAfter": "Voor de verandering bij de start zijn waarden op minstens {days} dagen nodig, verspreid over {span} dagen sinds de start en op dagen waarop de doses zijn ingenomen.",
-        "fitFailed": "Deze waarden konden niet worden verwerkt, dus er wordt geen verandering bij de start getoond."
+        "fitFailed": "Deze waarden konden niet worden verwerkt, dus er wordt geen verandering bij de start getoond.",
+        "autocorrelation": "De dagwaarden hangen sterk af van de vorige dag, dus zelfs deze bereiken kunnen te smal zijn."
       }
     },
     "import": {

messages/pl.json

@@ -431,7 +431,8 @@
       "notTracked": "przyjmowanie nie jest rejestrowane, więc nie pominięto dni z powodu opuszczonych dawek",
       "endDoseChange": "okres kończy się {date}, przed pierwszą zmianą dawki",
       "days": "{before} dni przed, {after} dni po rozpoczęciu, pominięto {excluded} dni",
-      "method": "Regresja segmentowa na wartościach dziennych od 90 dni przed do najwyżej 180 dni po rozpoczęciu, przedziały Neweya-Westa. Pominięto dni po rozpoczęciu, w których w ciągu poprzednich 14 dni przyjęto mniej niż 80% dawek. Opisuje związek w czasie, a nie udowodnione działanie leku."
+      "method": "Regresja segmentowa na wartościach dziennych od 90 dni przed do najwyżej 180 dni po rozpoczęciu, przedziały Neweya-Westa. Pominięto dni po rozpoczęciu, w których w ciągu poprzednich 14 dni przyjęto mniej niż 80% dawek. Opisuje związek w czasie, a nie udowodnione działanie leku.",
+      "autocorrelation": "silna zależność od poprzedniego dnia, więc zakresy mogą nadal być zbyt wąskie"
     }
   },
   "errorBoundary": {
@@ -2412,7 +2413,8 @@
         "needStart": "Ustaw datę rozpoczęcia, aby zobaczyć zmianę na początku.",
         "needBefore": "Do zmiany na początku potrzeba pomiarów z co najmniej {days} dni rozłożonych na {span} dni przed rozpoczęciem.",
         "needAfter": "Do zmiany na początku potrzeba pomiarów z co najmniej {days} dni rozłożonych na {span} dni od rozpoczęcia, w dni z przyjętymi dawkami.",
-        "fitFailed": "Nie udało się dopasować tych pomiarów, więc zmiana na początku nie jest pokazana."
+        "fitFailed": "Nie udało się dopasować tych pomiarów, więc zmiana na początku nie jest pokazana.",
+        "autocorrelation": "Wartości dzienne silnie zależą od poprzedniego dnia, więc nawet te zakresy mogą być zbyt wąskie."
       }
     },
     "import": {

src/components/clinician/activity-effect-sections.tsx

@@ -167,6 +167,11 @@ export function MedicationEffectSection({
                     e.days.excludedLowAdherence + e.days.excludedNotTaking,
                 })}
               </p>
+              {e.fit?.autocorrelationCaveat ? (
+                <p className="text-muted-foreground text-xs">
+                  {t("medications.efficacy.segmented.autocorrelation")}
+                </p>
+              ) : null}
               {e.confounders.map((c) => (
                 <p
                   key={`${c.medicationName}:${c.event}:${c.date}`}

src/components/medications/detail/efficacy/__tests__/change-at-start-summary.test.tsx

@@ -37,7 +37,8 @@ const present: EfficacySegmented = {
     df: 146,
     rSquared: 0.6,
     residualAutocorrelation: 0.3,
-    hacLag: 4,
+    hacLag: 7,
+    autocorrelationCaveat: false,
   },
   confounders: [
     { medicationName: "Example B", event: "started", date: "2026-02-10" },
@@ -70,6 +71,20 @@ describe("ChangeAtStartSummary", () => {
     expect(html).toContain("describes the starting dose");
     expect(html).toContain("Example B started on");
     expect(html).not.toMatch(/work(s|ing)|effective|successful/i);
+    expect(html).not.toContain("medication-wirkung-autocorrelation");
+  });
+
+  it("warns when the daily values carry over strongly", () => {
+    const html = render({
+      ...present,
+      fit: {
+        ...present.fit!,
+        residualAutocorrelation: 0.7,
+        autocorrelationCaveat: true,
+      },
+    });
+    expect(html).toContain("medication-wirkung-autocorrelation");
+    expect(html).toContain("even these ranges may be too narrow");
   });
 
   it("names the missing floor instead of a number", () => {

src/components/medications/detail/efficacy/change-at-start-summary.tsx

@@ -125,6 +125,14 @@ export function ChangeAtStartSummary({
           {t("medications.efficacy.segmented.notTracked")}
         </p>
       ) : null}
+      {segmented.fit?.autocorrelationCaveat ? (
+        <p
+          className="text-muted-foreground text-xs"
+          data-slot="medication-wirkung-autocorrelation"
+        >
+          {t("medications.efficacy.segmented.autocorrelation")}
+        </p>
+      ) : null}
       {segmented.window.endReason === "dose_change" ? (
         <p className="text-muted-foreground text-xs">
           {t("medications.efficacy.segmented.endDoseChange")}

src/lib/doctor-report-pdf/__tests__/activity-effect-sections.test.ts

@@ -81,7 +81,8 @@ const EFFECT: EfficacySegmented = {
     df: 141,
     rSquared: 0.55,
     residualAutocorrelation: 0.31,
-    hacLag: 4,
+    hacLag: 7,
+    autocorrelationCaveat: false,
   },
   confounders: [
     { medicationName: "Other drug", event: "started", date: "2026-02-14" },
@@ -218,6 +219,34 @@ describe("doctor report v1.44 sections", () => {
     expect(text).toContain("5 days after the start left out");
     expect(text).toContain("Other drug started on");
     expect(text).toContain("not a proven effect");
+    expect(text).not.toContain("carry-over");
+  });
+
+  it("notes strong day-to-day carry-over in the effect notes", async () => {
+    const text = (
+      await textOf(
+        render(
+          data({
+            medicationEffects: [
+              {
+                medicationName: "Example ACE inhibitor",
+                startsOn: "2026-03-02",
+                targets: [
+                  {
+                    type: "BLOOD_PRESSURE_SYS",
+                    effect: {
+                      ...EFFECT,
+                      fit: { ...EFFECT.fit!, autocorrelationCaveat: true },
+                    },
+                  },
+                ],
+              },
+            ],
+          }),
+        ),
+      )
+    ).replace(/\s+/g, " ");
+    expect(text).toContain("strong day-to-day carry-over");
   });
 
   it("names the missing floor instead of printing numbers", async () => {

src/lib/doctor-report-pdf/activity-effect-sections.ts

@@ -232,6 +232,9 @@ export function buildMedicationEffectSection(
       if (e.adherence.status === "not_tracked") {
         extras.push(t("doctorReport.medicationEffect.notTracked"));
       }
+      if (e.fit?.autocorrelationCaveat) {
+        extras.push(t("doctorReport.medicationEffect.autocorrelation"));
+      }
       if (e.window.endReason === "dose_change") {
         extras.push(
           t("doctorReport.medicationEffect.endDoseChange", {

src/lib/medications/efficacy/__tests__/segmented-effect.test.ts

@@ -173,6 +173,25 @@ describe("buildSegmentedEffect", () => {
     expect(r.present).toBe(true);
     expect(r.levelChange!.includesZero).toBe(true);
   });
+
+  it("flags strong residual autocorrelation for a caveat, not a clean fit", () => {
+    // A slow wave around the line: neighbouring residuals share a sign.
+    const wavy = series(-60, 59).map((p, i) => ({
+      day: p.day,
+      value: p.value + 4 * Math.sin(i / 6),
+    }));
+    const r = buildSegmentedEffect(input({ dayValues: wavy }));
+    expect(r.fit!.residualAutocorrelation).toBeGreaterThan(0.5);
+    expect(r.fit!.autocorrelationCaveat).toBe(true);
+    expect(r.fit!.hacLag).toBe(7);
+    // Alternating noise: negative carry-over, no caveat.
+    const alternating = series(-60, 59).map((p, i) => ({
+      day: p.day,
+      value: p.value + (i % 2 === 0 ? 2 : -2),
+    }));
+    const clean = buildSegmentedEffect(input({ dayValues: alternating }));
+    expect(clean.fit!.autocorrelationCaveat).toBe(false);
+  });
 });
 
 describe("notTakingPredicate", () => {

src/lib/medications/efficacy/segmented-effect.ts

@@ -48,6 +48,12 @@ export const ADHERENCE_LOOKBACK_DAYS = 14;
 export const ADHERENCE_FLOOR = 0.8;
 /** Confidence level of every interval. */
 export const SEGMENTED_LEVEL = 0.95;
+/**
+ * Lag-1 residual autocorrelation above which the read-out carries a caveat:
+ * the carry-over is then strong enough that even the widened intervals may be
+ * too narrow.
+ */
+export const AUTOCORRELATION_CAVEAT = 0.5;
 
 /** An estimate in display terms: the unit per day for a level, per week for a slope. */
 export interface EfficacyEstimate {
@@ -106,6 +112,8 @@ export interface EfficacySegmented {
     rSquared: number;
     residualAutocorrelation: number;
     hacLag: number;
+    /** True above {@link AUTOCORRELATION_CAVEAT}: renderers add the caveat line. */
+    autocorrelationCaveat: boolean;
   } | null;
   /** Other medication changes inside the window, oldest first. */
   confounders: EfficacyConfounder[];
@@ -311,6 +319,8 @@ export function buildSegmentedEffect(
       rSquared: fit.rSquared,
       residualAutocorrelation: fit.residualAutocorrelation,
       hacLag: fit.hacLag,
+      autocorrelationCaveat:
+        fit.residualAutocorrelation > AUTOCORRELATION_CAVEAT,
     },
     confounders,
   };

src/lib/stats/__tests__/segmented-regression.test.ts

@@ -2,16 +2,22 @@
  * Exact statistics for the segmented (interrupted time series) regression.
  *
  * The reference values for the noisy fixtures were computed independently
- * with statsmodels 0.14 (`OLS(...).fit(cov_type="HAC", cov_kwds={"maxlags":
- * L, "use_correction": True}, use_t=True)`, L = floor(4·(n/100)^(2/9))) and
- * scipy's `stats.t`. The fixture generator below is the same deterministic
+ * with statsmodels 0.14.4 (`OLS(...).fit(cov_type="HAC", cov_kwds={"maxlags":
+ * L, "use_correction": True}, use_t=True)`) and scipy's `stats.t`, at the
+ * default lag L = max(7, floor(4·(n/100)^(2/9))) = 7 and, to pin the HAC meat
+ * at a second lag, at the automatic L = 3 passed explicitly. To recompute:
+ * build the fixture below in Python (Python's floored `%`), fit the design
+ * [1, t, D, t·D] with the call above at each L, and read `params`, `bse` and
+ * `conf_int(0.05)`; the coefficients and R² do not depend on L. The fixture generator below is the same deterministic
  * formula the reference script used, so a drift in the estimator, the HAC
  * meat, the small-sample factor or the t quantile fails here.
  */
 import { describe, expect, it } from "vitest";
 
 import {
+  defaultHacLag,
   fitSegmentedRegression,
+  MIN_HAC_LAG,
   neweyWestLag,
   studentTCdf,
   studentTQuantile,
@@ -62,10 +68,27 @@ describe("fitSegmentedRegression", () => {
     expect(fit!.rSquared).toBeCloseTo(1, 12);
   });
 
-  it("matches statsmodels HAC on a contiguous 90-day series", () => {
+  it("matches statsmodels HAC on a contiguous 90-day series at the default lag", () => {
     const fit = fitSegmentedRegression(fixture(40, 50))!;
     expect(fit.n).toBe(90);
     expect(fit.df).toBe(86);
+    expect(fit.hacLag).toBe(7);
+    expect(fit.levelChange.estimate).toBeCloseTo(-7.336815685253282, 9);
+    expect(fit.intercept.standardError).toBeCloseTo(0.3926378134611552, 9);
+    expect(fit.preSlope.standardError).toBeCloseTo(0.015434960504949637, 10);
+    expect(fit.levelChange.standardError).toBeCloseTo(0.5544100003043471, 9);
+    expect(fit.slopeChange.standardError).toBeCloseTo(0.02119259135971675, 10);
+    expect(fit.levelChange.ciLow).toBeCloseTo(-8.43894628913928, 8);
+    expect(fit.levelChange.ciHigh).toBeCloseTo(-6.234685081367285, 8);
+    expect(fit.slopeChange.ciLow).toBeCloseTo(-0.07897452738576954, 9);
+    expect(fit.slopeChange.ciHigh).toBeCloseTo(0.005284427179883318, 9);
+    expect(fit.rSquared).toBeCloseTo(0.8683372493940129, 10);
+  });
+
+  it("matches statsmodels HAC on a contiguous 90-day series at lag 3", () => {
+    const fit = fitSegmentedRegression(fixture(40, 50), { hacLag: 3 })!;
+    expect(fit.n).toBe(90);
+    expect(fit.df).toBe(86);
     expect(fit.hacLag).toBe(3);
     expect(fit.intercept.estimate).toBeCloseTo(139.46950523140714, 9);
     expect(fit.preSlope.estimate).toBeCloseTo(-0.09725785860840647, 10);
@@ -82,9 +105,24 @@ describe("fitSegmentedRegression", () => {
     expect(fit.rSquared).toBeCloseTo(0.8683372493940129, 10);
   });
 
-  it("matches statsmodels HAC on a series with gaps", () => {
+  it("matches statsmodels HAC on a series with gaps at the default lag", () => {
     const fit = fitSegmentedRegression(fixture(30, 30, { gaps: true }))!;
     expect(fit.n).toBe(48);
+    expect(fit.hacLag).toBe(7);
+    expect(fit.levelChange.estimate).toBeCloseTo(-6.123258149435133, 9);
+    expect(fit.levelChange.standardError).toBeCloseTo(0.7919225818543464, 9);
+    expect(fit.levelChange.ciLow).toBeCloseTo(-7.71927324237417, 8);
+    expect(fit.levelChange.ciHigh).toBeCloseTo(-4.527243056496095, 8);
+    expect(fit.slopeChange.estimate).toBeCloseTo(-0.11857109294626766, 10);
+    expect(fit.slopeChange.ciLow).toBeCloseTo(-0.22143394263874167, 9);
+    expect(fit.slopeChange.ciHigh).toBeCloseTo(-0.01570824325379365, 9);
+  });
+
+  it("matches statsmodels HAC on a series with gaps at lag 3", () => {
+    const fit = fitSegmentedRegression(fixture(30, 30, { gaps: true }), {
+      hacLag: 3,
+    })!;
+    expect(fit.n).toBe(48);
     expect(fit.hacLag).toBe(3);
     expect(fit.levelChange.estimate).toBeCloseTo(-6.123258149435133, 9);
     expect(fit.levelChange.standardError).toBeCloseTo(0.9608527406825199, 9);
@@ -106,9 +144,16 @@ describe("fitSegmentedRegression", () => {
     expect(fitSegmentedRegression(fixture(2, 2, { noise: false }))).toBeNull();
   });
 
-  it("uses the automatic Newey–West lag", () => {
+  it("uses the automatic Newey–West lag, never below a week", () => {
     expect(neweyWestLag(90)).toBe(3);
     expect(neweyWestLag(30)).toBe(3);
     expect(neweyWestLag(10)).toBe(2);
+    expect(MIN_HAC_LAG).toBe(7);
+    expect(defaultHacLag(90)).toBe(7);
+    expect(defaultHacLag(270)).toBe(7);
+    expect(defaultHacLag(100_000)).toBe(neweyWestLag(100_000));
+    // A short series clamps to n − 1.
+    expect(fitSegmentedRegression(fixture(4, 4))!.hacLag).toBe(7);
+    expect(fitSegmentedRegression(fixture(3, 3))!.hacLag).toBe(5);
   });
 });

src/lib/stats/segmented-regression.ts

@@ -13,11 +13,14 @@
  * Daily health series are autocorrelated: today's blood pressure says a lot
  * about tomorrow's. Plain OLS standard errors ignore that and come out too
  * narrow, so the covariance here is the Newey–West estimator (Bartlett
- * kernel) with the usual automatic lag `floor(4·(n/100)^(2/9))` and the
- * small-sample factor n/(n−k). Intervals use Student's t with n−k degrees of
- * freedom. This matches `statsmodels` OLS `cov_type="HAC"` with
- * `use_correction=True` and `use_t=True`; the unit tests pin it to values
- * computed there.
+ * kernel) and the small-sample factor n/(n−k). The lag is the usual automatic
+ * `floor(4·(n/100)^(2/9))`, but never below {@link MIN_HAC_LAG}: on 30 to 270
+ * daily values the automatic rule gives 3, while a physiological series
+ * carries over for about a week (weight, resting heart rate, blood pressure
+ * under a new medication), and three lags leave most of that out. Intervals
+ * use Student's t with n−k degrees of freedom. This matches `statsmodels` OLS
+ * `cov_type="HAC"` with `use_correction=True` and `use_t=True` at the same
+ * `maxlags`; the unit tests pin it to values computed there.
  *
  * Observations are taken in the order given, which for a daily series with
  * gaps treats a gap as adjacent days. That is a known approximation of the
@@ -61,11 +64,19 @@ export interface SegmentedFit {
 
 const K = 4;
 
+/** Smallest Newey–West lag applied: a week of daily carry-over. */
+export const MIN_HAC_LAG = 7;
+
 /** Automatic Newey–West lag: floor(4·(n/100)^(2/9)). */
 export function neweyWestLag(n: number): number {
   return Math.floor(4 * Math.pow(n / 100, 2 / 9));
 }
 
+/** The lag applied by default: the automatic rule, at least {@link MIN_HAC_LAG}. */
+export function defaultHacLag(n: number): number {
+  return Math.max(MIN_HAC_LAG, neweyWestLag(n));
+}
+
 /** Invert a small symmetric positive-definite matrix (Gauss–Jordan). */
 function invert(matrix: number[][]): number[][] | null {
   const size = matrix.length;
@@ -131,7 +142,7 @@ export function fitSegmentedRegression(
   );
 
   // Meat: Σ e_t² x_t x_tᵀ + Σ_l w_l Σ_t e_t e_{t−l} (x_t x_{t−l}ᵀ + x_{t−l} x_tᵀ)
-  const lag = Math.max(0, Math.min(options.hacLag ?? neweyWestLag(n), n - 1));
+  const lag = Math.max(0, Math.min(options.hacLag ?? defaultHacLag(n), n - 1));
   const meat = Array.from({ length: K }, () => new Array<number>(K).fill(0));
   for (let l = 0; l <= lag; l++) {
     const w = l === 0 ? 1 : 1 - l / (lag + 1);

src/lib/validations/medication-efficacy.ts

@@ -137,7 +137,17 @@ const segmentedSchema = z
         df: z.number().int(),
         rSquared: z.number(),
         residualAutocorrelation: z.number(),
-        hacLag: z.number().int(),
+        hacLag: z
+          .number()
+          .int()
+          .describe(
+            "Newey–West lag applied: the automatic rule, at least 7 (a week of daily carry-over).",
+          ),
+        autocorrelationCaveat: z
+          .boolean()
+          .describe(
+            "True when the lag-1 residual autocorrelation exceeds 0.5: the carry-over is strong enough that the intervals may still be too narrow, and the read-out says so.",
+          ),
       })
       .nullable(),
     confounders: z.array(