Effects of aggregation of drug and diagnostic codes on the performance of the high-dimensional propensity score algorithm: an empirical example

Table 4 Geometric mean of risk ratios for different cohort size, outcome incidence and exposure prevalence of initiators of celecoxib or NSAIDs (ibuprofen or diclofenac) in a cohort 18–65 years old between 1 July 2003 and 30 September 2004 in the MarketScan database by using the High-Dimensional Propensity Score (hd-PS) adjustment with different aggregation scenarios

Cohort and confounding adjustment method	Base scenario	Combined ATC^* 4th level and CCS^†1st level	% Proportional difference^‡
Condition 1: 50% size sample
Unadjusted	1.02
Basic and hd-PS covariates	0.88	0.83	−9.9%
Basic, extended and hd-PS covariates	0.89	0.84	−8.9%
Condition 2: 20% size sample
Unadjusted	1.10
Basic and hd-PS covariates	0.94	0.87	−12.0%
Basic, extended and hd-PS covariates	0.95	0.88	−11.9%
Condition 3: 50% outcome incidence sample
Unadjusted	1.02
Basic and hd-PS covariates	0.90	0.84	−11.9%
Basic, extended and hd-PS covariates	0.91	0.85	−11.3%
Condition 4: 20% outcome incidence sample
Unadjusted	1.00
Basic and hd-PS covariates	0.85	0.81	−10.4%
Basic, extended and hd-PS covariates	0.86	0.82	−9.8%
Condition 5: 50% exposure prevalence sample
Unadjusted	1.02
Basic and hd-PS covariates	0.88	0.81	−14.4%
Basic, extended and hd-PS covariates	0.88	0.82	−12.7%
Condition 6: 20% exposure prevalence sample
Unadjusted	0.97
Basic and hd-PS covariates	0.89	0.79	−19.3%
Basic, extended and hd-PS covariates	0.89	0.81	−16.3%

Abbreviations: basic covariates included continuous age, gender and calendar year; extended covariates included covariates adjusted for in published studies; hd-PS, high dimensional propensity score.
Base scenario used up to 5-digit ICD-9, procedures, generic drugs for five data dimensions of the hd-PS.
^*ATC: 5 levels of the Anatomical Therapeutic Chemical classification.
^†CCS: Four levels of the Clinical Classification Software; Universal, the most granular CCS code available for each ICD-9 code.
^‡: % proportional difference in absolute degree of estimated confounded between estimates for the specific aggregation scenario and the basic scenario at the same variable selection method on the natural log scale with RCT finding of 0.50. The presumptive amount of confounding in the basic scenario A = │ln(adjusted RR) – ln(0.5)│; in each aggregation method B = │ln(adjusted RR) – ln(0.5)│; and C = B/A – 1.

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