zepid.causal.gformula.TimeFixed.TimeFixedGFormula

class zepid.causal.gformula.TimeFixed.TimeFixedGFormula(df, exposure, outcome, exposure_type='binary', outcome_type='binary', standardize='population', weights=None)

G-formula for time-fixed exposure and single endpoint, also referred to as the g-computation algorithm formula. Uses the Snowden trick to calculate the marginal treatment under the specified exposure plan

The g-formula can be expressed as

\[E[Y^a] = \sum_l E[Y|A=a,L=l] \times \Pr(L=l)\]

When L is continuous, the summation becomes an integral.

Currently, TimeFixedGFormula only supports binary or continuous outcomes. For binary outcomes a logistic regression model to predict probabilities of outcomes via statsmodels. For continuous outcomes a linear regression or a Poisson regression model can be used to predict outcomes.

Binary and multivariate exposures are supported. For binary exposures, a string object of the column name for the exposure of interest should be provided. For multivariate exposures, a list of string objects corresponding to disjoint indicator terms for the exposure should be provided. Multivariate exposures require the user to custom specify treatments when fitting the g-formula. A list of the custom treatment must be provided and be the same length as the number of disjoint indicator columns. See https://github.com/pzivich/Python-for-Epidemiologists/tree/master/3_Epidemiology_Analysis/c_causal_inference/1_time-fixed-treatments for examples (highly recommended)

Key options for treatments:

  • ‘all’ -all individuals are given treatment
  • ‘none’ -no individuals are given treatment
  • custom treatments -create a custom treatment. When specifying this, the dataframe must be referred to as ‘g’. The following is an example that selects those whose age is 30 or younger and are females: treatment="((g['age0']<=30) & (g['male']==0))

Note

Custom treatments use a “magic-g” parameter. Internally, the g-formula implementation names the data set as g. Therefore, when using custom treatment specifications, the data set must be referred to as g when following the pandas selection syntax

Parameters:
  • df (DataFrame) – Pandas dataframe containing the variables of interest
  • exposure (str, list) – Column name for exposure variable label or a list of disjoint indicator exposures
  • outcome (str) – Column name for outcome variable
  • outcome_type (str, optional) – Outcome variable type. Currently only ‘binary’, ‘normal’, and ‘poisson variable types are supported
  • standardize (str, optional) – Who the estimate corresponds to. Options are the entire population, the exposed, or the unexposed. See Sato & Matsuyama Epidemiology (2003) for details on weighting to exposed/unexposed. Weighting to the exposed or unexposed is also referred to as SMR weighting. Options for standardization are: * ‘population’ : weight to entire population * ‘exposed’ : weight to exposed individuals * ‘unexposed’ : weight to unexposed individuals
  • weights (str, optional) – Column name for weights. Default is None, which assumes every observations has the same weight (i.e. 1)

Examples

Setting up the environment

>>> from zepid import load_sample_data, spline
>>> from zepid.causal.gformula import TimeFixedGFormula
>>> df = load_sample_data(timevary=False)
>>> df[['cd4_rs1', 'cd4_rs2']] = spline(df, 'cd40', n_knots=3, term=2, restricted=True)
>>> df[['age_rs1', 'age_rs2']] = spline(df, 'age0', n_knots=3, term=2, restricted=True)

G-formula with a binary treatment and outcome

>>> g = TimeFixedGFormula(df, exposure='art', outcome='dead')
>>> g.outcome_model(model='art + male + age0 + age_rs1 + age_rs2 + cd40 + cd4_rs1 + cd4_rs2 + dvl0')

>>> # Return the estimated marginal outcome under treat-all
>>> g.fit(treatment='all')
>>> g.marginal_outcome

>>> # Return the estimated marginal outcome under treat-none
>>> g.fit(treatment='all')
>>> g.marginal_outcome

>>> # Return the estimated marginal outcome under custom treatment (treat all females under 40)
>>> g.fit(treatment="((g['male']==0) & (g['age0']<=40))")
>>> g.marginal_outcome

G-formula with a categorical treatment and binary outcome

>>> # Creating categorical variable for CD4 count
>>> df['cd4_1'] = np.where(((df['cd40'] >= 200) & (df['cd40'] < 400)), 1, 0)
>>> df['cd4_2'] = np.where(df['cd40'] >= 400, 1, 0)

>>> g = TimeFixedGFormula(df,exposure=['art_male', 'art_female'], outcome='dead', exposure_type='categorical')
>>> g.outcome_model(model='cd4_1 + cd4_2 + art + male + age0 + age_rs1 + age_rs2 + dvl0')

>>> # Return marginal outcome under all in reference category (CD4 < 200)
>>> g.fit(treatment=["False", "False"])

>>> # Return marginal outcome under all in category 1 (CD4 >= 200 & CD4 < 400)
>>> g.fit(treatment=["True", "False"])

>>> # Return marginal outcome under all in category 2 (CD4 > 400)
>>> g.fit(treatment=["False", "True"])

G-formula with binary exposure and continuous (normal-distributed) outcome

>>> g = TimeFixedGFormula(df,exposure='art', outcome='cd4', outcome_type='normal')
>>> g.outcome_model(model='art + male + age0 + age_rs1 + age_rs2 + dvl0  + cd40 + cd4_rs1 + cd4_rs2')

G-formula with binary exposure and continuous (Poisson-distributed) outcome

>>> g = TimeFixedGFormula(df,exposure='art', outcome='cd4', outcome_type='poisson')
>>> g.outcome_model(model='art + male + age0 + age_rs1 + age_rs2 + dvl0  + cd40 + cd4_rs1 + cd4_rs2')

G-formula with binary outcome and exposure. With a stochastic treatment/intervention

>>> g = TimeFixedGFormula(df,exposure='art', outcome='cd4', outcome_type='poisson')
>>> g.outcome_model(model='art + male + age0 + age_rs1 + age_rs2 + dvl0  + cd40 + cd4_rs1 + cd4_rs2')
>>> g.fit_stochastic(p=0.75)

G-formula with binary outcome and exposure. With a conditional stochastic treatment/intervention

>>> g = TimeFixedGFormula(df,exposure='art', outcome='cd4')
>>> g.outcome_model(model='art + male + age0 + age_rs1 + age_rs2 + dvl0  + cd40 + cd4_rs1 + cd4_rs2')
>>> g.fit_stochastic(p=[0.65, 0.85], conditional=["g['male']==1", "g['male']==0"])

References

JM Snowden, S Rose, and KM Mortimer. “Implementation of G-computation on a simulated data set: demonstration of a causal inference technique.” American Journal of Epidemiology 173.7 (2011): 731-738.

J Ahern, KE Colson, C Margerson-Zilko, A Hubbard, & S Galea. (2016). Predicting the population health impacts of community interventions: the case of alcohol outlets and binge drinking. American Journal of Public Health, 106(11), 1938-1943.

J Ahern, A Hubbard, & S Galea. (2009). Estimating the effects of potential public health interventions on population disease burden: a step-by-step illustration of causal inference methods. American Journal of Epidemiology, 169(9), 1140-1147.

__init__(df, exposure, outcome, exposure_type='binary', outcome_type='binary', standardize='population', weights=None)

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(df, exposure, outcome[, …]) Initialize self.
fit(treatment[, predict_missing]) Fit the parametric g-formula as specified.
fit_stochastic(p[, conditional, samples, …]) Fits the g-formula for a stochastic intervention.
outcome_model(model[, print_results]) Build the outcome regression model.
plot_kde([bw_method, fill, color]) Generates a Kernel Density plot of the accuracy of the model predicted outcomes.
run_diagnostics([decimal]) Runs diagnostics for the g-formula regression model used.