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1 ## Lifelines tool starting.
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2 Using data header = Index(['Unnamed: 0', 'week', 'arrest', 'fin', 'age', 'race', 'wexp', 'mar',
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3 'paro', 'prio'],
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4 dtype='object') time column = week status column = arrest
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5 ### Lifelines test of Proportional Hazards results with prio, age, race, paro, mar, fin as covariates on test
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6 <lifelines.CoxPHFitter: fitted with 432 total observations, 318 right-censored observations>
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7 duration col = 'week'
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8 event col = 'arrest'
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9 baseline estimation = breslow
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10 number of observations = 432
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11 number of events observed = 114
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12 partial log-likelihood = -659.00
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13 time fit was run = 2023-08-09 00:18:43 UTC
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14
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15 ---
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16 coef exp(coef) se(coef) coef lower 95% coef upper 95% exp(coef) lower 95% exp(coef) upper 95%
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17 covariate
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18 prio 0.10 1.10 0.03 0.04 0.15 1.04 1.16
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19 age -0.06 0.94 0.02 -0.10 -0.02 0.90 0.98
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20 race 0.32 1.38 0.31 -0.28 0.92 0.75 2.52
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21 paro -0.09 0.91 0.20 -0.47 0.29 0.62 1.34
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22 mar -0.48 0.62 0.38 -1.22 0.25 0.30 1.29
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23 fin -0.38 0.68 0.19 -0.75 -0.00 0.47 1.00
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24
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25 cmp to z p -log2(p)
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26 covariate
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27 prio 0.00 3.53 <0.005 11.26
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28 age 0.00 -2.95 <0.005 8.28
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29 race 0.00 1.04 0.30 1.75
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30 paro 0.00 -0.46 0.65 0.63
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31 mar 0.00 -1.28 0.20 2.32
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32 fin 0.00 -1.98 0.05 4.40
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33 ---
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34 Concordance = 0.63
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35 Partial AIC = 1330.00
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36 log-likelihood ratio test = 32.77 on 6 df
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37 -log2(p) of ll-ratio test = 16.39
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38
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39
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40 Bootstrapping lowess lines. May take a moment...
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41
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42
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43 Bootstrapping lowess lines. May take a moment...
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44
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45 The ``p_value_threshold`` is set at 0.01. Even under the null hypothesis of no violations, some
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46 covariates will be below the threshold by chance. This is compounded when there are many covariates.
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47 Similarly, when there are lots of observations, even minor deviances from the proportional hazard
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48 assumption will be flagged.
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49
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50 With that in mind, it's best to use a combination of statistical tests and visual tests to determine
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51 the most serious violations. Produce visual plots using ``check_assumptions(..., show_plots=True)``
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52 and looking for non-constant lines. See link [A] below for a full example.
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53
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54 <lifelines.StatisticalResult: proportional_hazard_test>
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55 null_distribution = chi squared
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56 degrees_of_freedom = 1
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57 model = <lifelines.CoxPHFitter: fitted with 432 total observations, 318 right-censored observations>
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58 test_name = proportional_hazard_test
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59
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60 ---
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61 test_statistic p -log2(p)
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62 age km 6.99 0.01 6.93
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63 rank 7.40 0.01 7.26
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64 fin km 0.02 0.90 0.15
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65 rank 0.01 0.91 0.13
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66 mar km 1.64 0.20 2.32
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67 rank 1.80 0.18 2.48
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68 paro km 0.06 0.81 0.31
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69 rank 0.07 0.79 0.34
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70 prio km 0.92 0.34 1.57
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71 rank 0.88 0.35 1.52
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72 race km 1.70 0.19 2.38
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73 rank 1.68 0.19 2.36
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74
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75
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76 1. Variable 'age' failed the non-proportional test: p-value is 0.0065.
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77
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78 Advice 1: the functional form of the variable 'age' might be incorrect. That is, there may be
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79 non-linear terms missing. The proportional hazard test used is very sensitive to incorrect
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80 functional forms. See documentation in link [D] below on how to specify a functional form.
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81
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82 Advice 2: try binning the variable 'age' using pd.cut, and then specify it in `strata=['age',
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83 ...]` in the call in `.fit`. See documentation in link [B] below.
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84
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85 Advice 3: try adding an interaction term with your time variable. See documentation in link [C]
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86 below.
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87
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88
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89 Bootstrapping lowess lines. May take a moment...
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90
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91
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92 Bootstrapping lowess lines. May take a moment...
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93
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94
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95 Bootstrapping lowess lines. May take a moment...
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96
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97
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98 Bootstrapping lowess lines. May take a moment...
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99
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100
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101 ---
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102 [A] https://lifelines.readthedocs.io/en/latest/jupyter_notebooks/Proportional%20hazard%20assumption.html
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103 [B] https://lifelines.readthedocs.io/en/latest/jupyter_notebooks/Proportional%20hazard%20assumption.html#Bin-variable-and-stratify-on-it
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104 [C] https://lifelines.readthedocs.io/en/latest/jupyter_notebooks/Proportional%20hazard%20assumption.html#Introduce-time-varying-covariates
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105 [D] https://lifelines.readthedocs.io/en/latest/jupyter_notebooks/Proportional%20hazard%20assumption.html#Modify-the-functional-form
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106 [E] https://lifelines.readthedocs.io/en/latest/jupyter_notebooks/Proportional%20hazard%20assumption.html#Stratification
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107
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