add jeffreys correction

Author: Jingjing Tang

quidel_covidtest/delphi_quidel_covidtest/data_tools.py

@@ -166,7 +166,8 @@ def raw_positive_prop(positives, tests, min_obs):
     # nan out any days where there are insufficient observations
     # this also elegantly sidesteps 0/0 division.
     tests[tests < min_obs] = np.nan
-    positive_prop = positives / tests
+    # Jeffreys Correction for estimates
+    positive_prop = (positives+0.5) / (tests+1)
     se = np.sqrt(_prop_var(positive_prop, tests))
     sample_size = tests
     return positive_prop, se, sample_size

quidel_covidtest/tests/test_data_tools.py

@@ -91,12 +91,12 @@ def test__geographical_pooling(self, min_obs, expected):
 
     @pytest.mark.parametrize("min_obs, expected_pos_prop, expected_se, expected_sample_sz", [
         (3,  # one case of tests < min_obs
-         np.array([np.nan, 1/2, 1/2, 4/10]),
-         np.array([np.nan, np.sqrt(0.25/4), np.sqrt(0.25/6), np.sqrt(0.24/10)]),
+         np.array([np.nan, 2.5/5, 3.5/7, 4.5/11]),
+         np.array([np.nan, np.sqrt(2.5**2/5**2/4), np.sqrt(3.5**2/7**2/6), np.sqrt(4.5*6.5/11**2/10)]),
          np.array([np.nan, 4, 6, 10])),
         (1,  # no cases of tests < min_obs
-         np.array([1/2, 2/4, 3/6, 4/10]),
-         np.array([np.sqrt(0.25/2), np.sqrt(0.25/4), np.sqrt(0.25/6), np.sqrt(0.24/10)]),
+         np.array([1.5/3, 2.5/5, 3.5/7, 4.5/11]),
+         np.array([np.sqrt(1.5**2/3**2/2), np.sqrt(2.5**2/5**2/4), np.sqrt(3.5**2/7**2/6), np.sqrt(4.5*6.5/11**2/10)]),
          np.array([2, 4, 6, 10])),
     ])
     def test_raw_positive_prop(self, min_obs, expected_pos_prop, expected_se, expected_sample_sz):
@@ -123,16 +123,16 @@ def test_raw_positive_prop(self, min_obs, expected_pos_prop, expected_se, expect
          2,
          None,
          None,
-         np.array([np.nan, 1/2, 1/2, 7/16]),
-         np.array([np.nan, np.sqrt(0.25/6), np.sqrt(0.25/10), np.sqrt(63/256/16)]),
+         np.array([np.nan, 3.5/7, 5.5/11, 7.5/17]),
+         np.array([np.nan, np.sqrt(3.5**2/7**2/6), np.sqrt(5.5**2/11**2/10), np.sqrt(7.5*9.5/17**2/16)]),
          np.array([np.nan, 6, 10, 16]),
          ),
         (3,  # parents case
          2,
          np.array([3, 7, 9, 11]),
          np.array([5, 10, 15, 20]),
-         np.array([1.6/3, 1/2, 1/2, 7/16]),
-         np.array([np.sqrt(56/225/3), np.sqrt(0.25/6), np.sqrt(0.25/10), np.sqrt(63/256/16)]),
+         np.array([(1 + 0.6 + 0.5)/(2 + 1 + 1), 3.5/7, 5.5/11, 7.5/17]),
+         np.array([np.sqrt(2.1 * 1.9/4**2/3), np.sqrt(3.5**2/7**2/6), np.sqrt(5.5**2/11**2/10), np.sqrt(7.5*9.5/17**2/16)]),
          np.array([3, 6, 10, 16]),
          ),
     ])