Table 2.

Distribution of Propensity Score and Weights for the Average Treatment Effect by Method Used to Estimate the Propensity Score^*,^†

	Random Forest‡ Classification		Logistic Regression		Classification Tree		Bagging‡
	Early Childhood Therapy	No Early Childhood Therapy	Early Childhood Therapy	No Early Childhood Therapy	Early Childhood Therapy	No Early Childhood Therapy	Early Childhood Therapy	No Early Childhood Therapy
Propensity score§
Minimum	0.01	0.00	0.02	0.00	0.06	0.00	0.01	0.00
Maximum	0.42	0.54	0.43	0.56	0.64	0.64	0.55	0.59
Mean	0.16	0.06	0.16	0.07	0.39	0.05	0.20	0.07
Average treatment effect weights
Minimum	0.16	0.93	0.15	0.94	0.10	0.93	0.12	0.93
Maximum	4.91	2.01	2.81	2.15	1.08	2.57	8.00	2.26
Mean	0.89	1.00	0.79	1.01	0.27	1.00	0.99	1.01

^*Early Childhood Longitudinal Study, Birth Cohort 2001–2006.

^†Average treatment effect weight is estimated as (1/propensity score) for those children who received early childhood therapy. For the those children who did not receive therapy, the weight is (1/(1−propensity score)). These weights are stabilized so the sum of the weights reflects the size of the original population. We multiplied the weight by the probability of receiving the treatment that the child actually received.

^‡We estimated the propensity score using random forest classification. The out-of-bag error rate for the algorithm for classification of receipt of early childhood therapy was 15.7% across 1,000 trees, where the algorithm chose four random variables at each split of the node. The error rate for bagging was also 15.7% over 1,000 trees.

^§The propensity score includes the following confounders: 9 months BSF-R motor T score, socioeconomic status, length of child's hospital stay after birth, gestational age, birth weight, parental education, race, and age at which the child walked with assistance.