GPS_Classifier Tool (continuous treatments, binary outcomes)¶
As with the other GPS tool, we calculate generalized propensity scores (GPS) but with the classifier we can estimate the point-by-point causal contribution of a continuous treatment to a binary outcome. The GPS_Classifier does this by estimating the log odds of a positive outcome and odds ratio (odds of positive outcome / odds of negative outcome) along the entire range of treatment values:
Currently, the causal-curve package does not contain a TMLE implementation that is appropriate for a binary outcome, so the GPS_Classifier tool will have to suffice for this sort of outcome.
This tool works much like the _GPS_Regressor tool; as long as the outcome series in your dataframe contains
binary integer values (e.g. 0’s and 1’s) the fit()
method will work as it’s supposed to:
>>> df.head(5) # a pandas dataframe with your data
X_1 X_2 Treatment Outcome
0 0.596685 0.162688 0.000039 1
1 1.014187 0.916101 0.000197 0
2 0.932859 1.328576 0.000223 0
3 1.140052 0.555203 0.000339 0
4 1.613471 0.340886 0.000438 1
With this dataframe, we can now calculate the GPS to estimate the causal relationship between treatment and outcome. Let’s use the default settings of the GPS tool:
>>> from causal_curve import GPS_Classifier
>>> gps = GPS()
>>> gps.fit(T = df['Treatment'], X = df[['X_1', 'X_2']], y = df['Outcome'])
>>> gps_results = gps.calculate_CDRC(0.95)
The gps_results
object (a dataframe) now contains all of the data to produce the above plot.
If you’d like to estimate the log odds at a specific point on the curve, use the
predict_log_odds
to do so.
References¶
Galagate, D. Causal Inference with a Continuous Treatment and Outcome: Alternative Estimators for Parametric Dose-Response function with Applications. PhD thesis, 2016.
Moodie E and Stephens DA. Estimation of dose–response functions for longitudinal data using the generalised propensity score. In: Statistical Methods in Medical Research 21(2), 2010, pp.149–166.
Hirano K and Imbens GW. The propensity score with continuous treatments. In: Gelman A and Meng XL (eds) Applied bayesian modeling and causal inference from incomplete-data perspectives. Oxford, UK: Wiley, 2004, pp.73–84.