{
  "plan": {
    "method": "segmented-trend",
    "outcome_column": "ageadjrate",
    "time_columns": [
      "year"
    ],
    "filters": [
      {
        "column": "sex",
        "value": "Both Sexes",
        "reason": "single sex category; keeps one series per state"
      },
      {
        "column": "age",
        "value": "All Ages",
        "reason": "single age category; rate is already age-adjusted"
      },
      {
        "column": "race",
        "value": "All Races-All Origins",
        "reason": "single race/origin category"
      }
    ],
    "group_columns": [
      "state"
    ],
    "reference_group": "United States",
    "series_kind": "discrete",
    "window_start": "1999",
    "window_end": "2018",
    "denominator_column": null,
    "age_column": null,
    "standard_population": "us-2000-11",
    "suppressed_bound": null,
    "rate_per": 100000,
    "breakpoint": "2010",
    "minimum_points": 8,
    "exclude_incomplete": true,
    "rationale": "The question asks how Ohio's annual age-adjusted overdose death rate changed from 1999 to 2018 and how it compared with the US in each year. Each row is a discrete annual value (not a rolling window), so the series is ordered by year. Ohio and United States are both kept as groups, with United States set as reference_group, so the engine reports per-year Ohio and US rates, the absolute difference, the rate ratio, the period(s) where the difference changes sign, and a trend on the difference. The annual path and year-over-year changes are the primary result, and the per-year comparison table should be reported in full (20 rows). The 2010 breakpoint is a single pre-specified candidate for the hypothesised slope change in the 2010s. It is motivated by the hypothesis and by the timing of the prescription-opioid policy and market shifts around 2010, not chosen from the data. The segmented fit is exploratory. Sensitivity should be reported by refitting with alternative break years in the 2010s (for example 2012, 2013, 2014), and by refitting with and without 2018, since a linear two-segment shape may not capture an accelerating series that peaks in 2017 and falls in 2018. Because the early Ohio-US comparison is noisy, with the sign of the difference possibly alternating, describe Ohio as fluctuating around the national rate early and name no single crossover year unless the sign change is persistent. Widening of the gap should be described from the per-year difference and ratio series, and any p-values on them should be treated as descriptive only.",
    "limitations": [
      "Ecological, state-level aggregate data; cannot support individual-level or causal inference.",
      "Only Ohio and United States rows are present and the US series includes Ohio, so the reference is not independent and the gap is slightly understated; difference-trend p-values are not valid formal tests.",
      "No confidence intervals or standard errors on the annual rates, so year-level noise, especially in the early crossings, cannot be quantified.",
      "About 20 annual points that are strongly serially correlated; ordinary least squares p-values overstate precision, so p-values are descriptive only and autocorrelation-robust errors should be used if available.",
      "A segmented linear fit imposes a piecewise-linear shape; the series may accelerate after about 2013 and dip in 2018, so slope estimates depend on the assumed breakpoint and are exploratory.",
      "The 2017-2018 values may be provisional, smoothed, or revised; the 2018 drop should not be interpreted as a turning point, and results should be shown with and without 2018.",
      "No drug-type, opioid, fentanyl or heroin stratification was obtained, so the drivers of any change in slope are out of scope and cannot be attributed.",
      "The dataset was substituted (44rk-q6r2) for the Scout's suggested source, so its vintage and smoothing should be checked against CDC WONDER final values."
    ]
  },
  "n_rows_input": 40,
  "n_rows_analysed": 40,
  "n_suppressed_dropped": 0,
  "series": [
    {
      "group": "state=Ohio",
      "n": 20,
      "first_period": "1999",
      "last_period": "2018",
      "first_value": 4.1504,
      "last_value": 35.931,
      "min": 4.1504,
      "min_period": "1999",
      "max": 46.3469,
      "max_period": "2017",
      "mean": 17.701649999999997,
      "median": 14.512049999999999,
      "absolute_change": 31.780599999999996,
      "percent_change": 765.7237856592135
    },
    {
      "group": "state=United States",
      "n": 20,
      "first_period": "1999",
      "last_period": "2018",
      "first_value": 6.057,
      "last_value": 20.7112,
      "min": 6.057,
      "min_period": "1999",
      "max": 21.7048,
      "max_period": "2017",
      "mean": 12.417480000000001,
      "median": 11.91675,
      "absolute_change": 14.654200000000001,
      "percent_change": 241.9382532606901
    }
  ],
  "findings": [
    {
      "group": "state=Ohio",
      "method": "segmented-trend",
      "breakpoint": "2010",
      "slope_before": 1.0062636363636357,
      "slope_after": 3.5804583333333353,
      "slope_change": 2.5741946969696996,
      "slope_change_p_value": 0.0001798791128519582,
      "slope_change_p_value_hac": 1.4151267124747667e-09,
      "level_change": -2.1514050505050486,
      "level_change_p_value": 0.47706583616585907,
      "durbin_watson": 1.9220314046261862,
      "r_squared": 0.9349314483618368,
      "n_before": 11,
      "n_after": 9,
      "breakpoint_sensitivity": [
        {
          "breakpoint": "2008",
          "slope_change": 1.8989066666666643,
          "slope_change_p_value_hac": 3.431836226827257e-06
        },
        {
          "breakpoint": "2009",
          "slope_change": 2.272160000000001,
          "slope_change_p_value_hac": 3.3634019992946627e-10
        },
        {
          "breakpoint": "2011",
          "slope_change": 2.841987595737596,
          "slope_change_p_value_hac": 2.6845461250758358e-08
        },
        {
          "breakpoint": "2012",
          "slope_change": 3.1081249999999994,
          "slope_change_p_value_hac": 1.961526116188651e-06
        }
      ],
      "interpretation": "Slopes are per period step before and after the pre-specified breakpoint. The breakpoint was fixed in the plan, not chosen from the data; breakpoint_sensitivity refits at nearby periods to show how much the answer depends on that choice, and is not a search for a better one. p_value_hac uses Newey-West standard errors, which allow for correlation between neighbouring periods; ordinary p-values assume none and are too small when neighbours are correlated (a Durbin-Watson statistic well below 2 says they are). This is an interrupted time series association, not proof of causation."
    },
    {
      "group": "state=United States",
      "method": "segmented-trend",
      "breakpoint": "2010",
      "slope_before": 0.6847518181818184,
      "slope_after": 1.2499133333333337,
      "slope_change": 0.5651615151515152,
      "slope_change_p_value": 0.0015142343147757737,
      "slope_change_p_value_hac": 4.494132203959258e-06,
      "level_change": -2.2710571717171715,
      "level_change_p_value": 0.013946952678184061,
      "durbin_watson": 1.4006223151849904,
      "r_squared": 0.9651280209304609,
      "n_before": 11,
      "n_after": 9,
      "breakpoint_sensitivity": [
        {
          "breakpoint": "2008",
          "slope_change": 0.24786000000000047,
          "slope_change_p_value_hac": 0.08633692289658099
        },
        {
          "breakpoint": "2009",
          "slope_change": 0.4004496969696967,
          "slope_change_p_value_hac": 0.0015097693963480585
        },
        {
          "breakpoint": "2011",
          "slope_change": 0.7293206127206137,
          "slope_change_p_value_hac": 1.807440279202411e-08
        },
        {
          "breakpoint": "2012",
          "slope_change": 0.9359675824175819,
          "slope_change_p_value_hac": 6.030027086396811e-13
        }
      ],
      "interpretation": "Slopes are per period step before and after the pre-specified breakpoint. The breakpoint was fixed in the plan, not chosen from the data; breakpoint_sensitivity refits at nearby periods to show how much the answer depends on that choice, and is not a search for a better one. p_value_hac uses Newey-West standard errors, which allow for correlation between neighbouring periods; ordinary p-values assume none and are too small when neighbours are correlated (a Durbin-Watson statistic well below 2 says they are). This is an interrupted time series association, not proof of causation."
    }
  ],
  "warnings": [
    "Restricted to sex='Both Sexes' (single sex category; keeps one series per state); 40 of 40 rows.",
    "Restricted to age='All Ages' (single age category; rate is already age-adjusted); 40 of 40 rows.",
    "Restricted to race='All Races-All Origins' (single race/origin category); 40 of 40 rows.",
    "Restricted to the window 1999-2018 on 'year' as the question asks; 40 of 40 rows retained."
  ],
  "environment": {
    "git_sha": "dc51aea1b750c2bb1b5ca917731326d3d6248520",
    "git_dirty": true,
    "python": "3.14.3",
    "platform": "Linux-x86_64",
    "packages": {
      "pandas": "3.0.5",
      "numpy": "2.5.2",
      "statsmodels": "0.14.6",
      "scipy": "1.18.0",
      "duckdb": "1.5.5"
    },
    "container_digest": null
  },
  "comparisons": [
    {
      "group": "state=Ohio",
      "reference": "state=United States",
      "n_periods": 20,
      "by_period": [
        {
          "period": "1999",
          "value": 4.1504,
          "reference_value": 6.057,
          "difference": -1.9066,
          "ratio": 0.6852237081063233
        },
        {
          "period": "2000",
          "value": 4.9882,
          "reference_value": 6.1749,
          "difference": -1.1867,
          "ratio": 0.8078187501012162
        },
        {
          "period": "2001",
          "value": 6.4705,
          "reference_value": 6.7922,
          "difference": -0.3216999999999999,
          "ratio": 0.9526368481493478
        },
        {
          "period": "2002",
          "value": 8.2032,
          "reference_value": 8.1957,
          "difference": 0.007500000000000284,
          "ratio": 1.0009151140232073
        },
        {
          "period": "2003",
          "value": 6.7936,
          "reference_value": 8.8765,
          "difference": -2.0829000000000004,
          "ratio": 0.7653467019658649
        },
        {
          "period": "2004",
          "value": 9.9421,
          "reference_value": 9.3831,
          "difference": 0.5589999999999993,
          "ratio": 1.0595751936993103
        },
        {
          "period": "2005",
          "value": 10.8982,
          "reference_value": 10.0699,
          "difference": 0.8282999999999987,
          "ratio": 1.0822550372893474
        },
        {
          "period": "2006",
          "value": 13.2315,
          "reference_value": 11.4883,
          "difference": 1.7431999999999999,
          "ratio": 1.1517369845843162
        },
        {
          "period": "2007",
          "value": 13.8858,
          "reference_value": 11.8775,
          "difference": 2.0083,
          "ratio": 1.1690844032835193
        },
        {
          "period": "2008",
          "value": 15.1383,
          "reference_value": 11.8947,
          "difference": 3.243599999999999,
          "ratio": 1.2726928800221946
        },
        {
          "period": "2009",
          "value": 10.8867,
          "reference_value": 11.9388,
          "difference": -1.0521000000000011,
          "ratio": 0.9118755653834555
        },
        {
          "period": "2010",
          "value": 16.0885,
          "reference_value": 12.2966,
          "difference": 3.7919,
          "ratio": 1.3083697932761902
        },
        {
          "period": "2011",
          "value": 17.7178,
          "reference_value": 13.1852,
          "difference": 4.5326,
          "ratio": 1.3437642204896398
        },
        {
          "period": "2012",
          "value": 18.897,
          "reference_value": 13.1422,
          "difference": 5.754799999999998,
          "ratio": 1.4378871117468914
        },
        {
          "period": "2013",
          "value": 20.7926,
          "reference_value": 13.8005,
          "difference": 6.992100000000001,
          "ratio": 1.5066555559581176
        },
        {
          "period": "2014",
          "value": 24.6364,
          "reference_value": 14.6831,
          "difference": 9.953299999999999,
          "ratio": 1.677874563273423
        },
        {
          "period": "2015",
          "value": 29.9118,
          "reference_value": 16.2923,
          "difference": 13.619499999999999,
          "ratio": 1.835947042467914
        },
        {
          "period": "2016",
          "value": 39.1225,
          "reference_value": 19.7851,
          "difference": 19.337400000000002,
          "ratio": 1.977371860642605
        },
        {
          "period": "2017",
          "value": 46.3469,
          "reference_value": 21.7048,
          "difference": 24.6421,
          "ratio": 2.1353295123659284
        },
        {
          "period": "2018",
          "value": 35.931,
          "reference_value": 20.7112,
          "difference": 15.219799999999996,
          "ratio": 1.7348584340839737
        }
      ],
      "first_difference": -1.9066,
      "last_difference": 15.219799999999996,
      "first_ratio": 0.6852237081063233,
      "last_ratio": 1.7348584340839737,
      "widest_difference": 24.6421,
      "widest_difference_period": "2017",
      "crossings": [
        {
          "period": "2002",
          "direction": "above"
        },
        {
          "period": "2003",
          "direction": "below"
        },
        {
          "period": "2004",
          "direction": "above"
        },
        {
          "period": "2009",
          "direction": "below"
        },
        {
          "period": "2010",
          "direction": "above"
        }
      ],
      "difference_trend": {
        "slope_per_period": 1.1098627067669171,
        "p_value": 6.696407460305061e-07,
        "p_value_hac": 1.4509797242352852e-07
      },
      "difference_slope_change": {
        "breakpoint": "2010",
        "slope_change": 2.009033181818184,
        "p_value": 0.00018708986932261363,
        "p_value_hac": 6.23820779178807e-09
      },
      "interpretation": "difference = group minus reference and ratio = group divided by reference, per period. A crossing is the first period after the sign of the difference changes. difference_trend is the slope of the gap per period; difference_slope_change tests whether the group's slope changed at the breakpoint by more than the reference's did. If the reference includes the group (a nation including its states) the two are not independent."
    }
  ]
}