{
  "synthetic": true,
  "n": 1600,
  "missing_cells": 0,
  "group_summary": [
    {
      "treatment": 0,
      "count": 839,
      "sum": 202,
      "mean": 0.24076281287246723
    },
    {
      "treatment": 1,
      "count": 761,
      "sum": 280,
      "mean": 0.3679369250985545
    }
  ],
  "channel_summary": [
    {
      "channel": "referral",
      "count": 328,
      "sum": 128,
      "mean": 0.3902439024390244
    },
    {
      "channel": "search",
      "count": 707,
      "sum": 211,
      "mean": 0.2984441301272984
    },
    {
      "channel": "social",
      "count": 565,
      "sum": 143,
      "mean": 0.25309734513274335
    }
  ],
  "two_by_two": {
    "table_rows_treatment_control_columns_success_failure": [
      [
        280,
        481
      ],
      [
        202,
        637
      ]
    ],
    "treatment_risk": 0.3679369250985545,
    "control_risk": 0.24076281287246723,
    "treatment_risk_wilson_ci95": [
      0.33441715009314477,
      0.40278328840044697
    ],
    "control_risk_wilson_ci95": [
      0.21305604033066972,
      0.27083266086272784
    ],
    "risk_difference": 0.1271741122260873,
    "risk_difference_wald_ci95": [
      0.08233114746699072,
      0.17201707698518387
    ],
    "risk_ratio": 1.5282132681073626,
    "risk_ratio_log_ci95": [
      1.312690976821283,
      1.7791207786578276
    ],
    "odds_ratio": 1.8356970832218358,
    "odds_ratio_log_ci95": [
      1.4787521042946086,
      2.278802357448954
    ],
    "pearson_chi2_uncorrected": 30.660214415290593,
    "pearson_p": 3.0740404035692505e-08,
    "df": 1,
    "expected_counts": [
      [
        229.25125,
        531.74875
      ],
      [
        252.74875,
        586.25125
      ]
    ],
    "fisher_two_sided_p": 3.366254746869148e-08
  },
  "formula": "outcome ~ treatment + age + baseline_visits + C(channel, Treatment(reference=\"search\"))",
  "explanatory_glm_converged": true,
  "coefficients": [
    {
      "term": "Intercept",
      "coefficient": -2.545621444152241,
      "adjusted_or": 0.07842430051118558,
      "or_ci95": [
        0.050196441904817056,
        0.12252603326608552
      ],
      "p": 4.990946463732738e-29
    },
    {
      "term": "C(channel, Treatment(reference=\"search\"))[T.referral]",
      "coefficient": 0.4629880970792255,
      "adjusted_or": 1.5888144307712335,
      "or_ci95": [
        1.1973552873753017,
        2.108255855252833
      ],
      "p": 0.0013368822659632128
    },
    {
      "term": "C(channel, Treatment(reference=\"search\"))[T.social]",
      "coefficient": -0.2400927965617607,
      "adjusted_or": 0.7865548680924621,
      "or_ci95": [
        0.6090825885757961,
        1.0157383778882418
      ],
      "p": 0.06572840686391519
    },
    {
      "term": "treatment",
      "coefficient": 0.6573346812444731,
      "adjusted_or": 1.929642362312451,
      "or_ci95": [
        1.5448573864348838,
        2.4102675619939657
      ],
      "p": 6.919336790401965e-09
    },
    {
      "term": "age",
      "coefficient": 0.020953587059492813,
      "adjusted_or": 1.0211746548191227,
      "or_ci95": [
        1.0136800934472143,
        1.0287246266213241
      ],
      "p": 2.4722277234950052e-08
    },
    {
      "term": "baseline_visits",
      "coefficient": 0.13466058755352917,
      "adjusted_or": 1.1441483802395855,
      "or_ci95": [
        1.0732184353432492,
        1.2197661472207038
      ],
      "p": 3.723539930464058e-05
    }
  ],
  "empirical_standardized_predicted_risk": {
    "0": 0.23895527120846766,
    "1": 0.37027253198082133
  },
  "prediction_holdout": {
    "train_n": 1120,
    "test_n": 480,
    "test_prevalence": 0.3020833333333333,
    "roc_auc": 0.6149253731343283,
    "average_precision": 0.4110815721916374,
    "brier_score": 0.2043449565399483,
    "baseline_brier_score": 0.21083041028911562,
    "log_loss": 0.5961969982698511,
    "threshold_prespecified": 0.5,
    "confusion_matrix_rows_actual_columns_predicted": [
      [
        312,
        23
      ],
      [
        126,
        19
      ]
    ],
    "calibration_bins": [
      {
        "bin": "(-0.001, 0.2]",
        "n": 96,
        "predicted_mean": 0.1537920950586,
        "observed_rate": 0.16666666666666666
      },
      {
        "bin": "(0.2, 0.4]",
        "n": 268,
        "predicted_mean": 0.2913012754603345,
        "observed_rate": 0.29850746268656714
      },
      {
        "bin": "(0.4, 0.6]",
        "n": 109,
        "predicted_mean": 0.47730916995385136,
        "observed_rate": 0.4036697247706422
      },
      {
        "bin": "(0.6, 0.8]",
        "n": 7,
        "predicted_mean": 0.6235279837910728,
        "observed_rate": 0.7142857142857143
      }
    ]
  },
  "software_versions": {
    "numpy": "2.3.5",
    "pandas": "2.2.3",
    "scipy": "1.17.0",
    "statsmodels": "0.14.6",
    "scikit-learn": "1.8.0",
    "patsy": "1.0.3"
  },
  "data_sha256": "99e9f9c9e78e482aef615524638fbb4e97899ec6f546eb2d9765f76d2afaab75",
  "chapter_18_teaching_example": {
    "table_rows_treatment_control_columns_success_failure": [
      [
        70,
        130
      ],
      [
        40,
        160
      ]
    ],
    "treatment_risk": 0.35,
    "control_risk": 0.2,
    "treatment_risk_wilson_ci95": [
      0.28728824127358077,
      0.4183653566395992
    ],
    "control_risk_wilson_ci95": [
      0.15045200926098118,
      0.2608551865653788
    ],
    "risk_difference": 0.14999999999999997,
    "risk_difference_wald_ci95": [
      0.06372818267188947,
      0.23627181732811048
    ],
    "risk_ratio": 1.7499999999999998,
    "risk_ratio_log_ci95": [
      1.2513285061615735,
      2.4473988923933008
    ],
    "odds_ratio": 2.1538461538461537,
    "odds_ratio_log_ci95": [
      1.3703524410636527,
      3.3852993692900544
    ],
    "pearson_chi2_uncorrected": 11.28526645768025,
    "pearson_p": 0.0007812461893217228,
    "df": 1,
    "expected_counts": [
      [
        55.0,
        145.0
      ],
      [
        55.0,
        145.0
      ]
    ],
    "fisher_two_sided_p": 0.0011113688295960786
  }
}
