Daniel G Polhamus, Ph.D., Jonathan L French Sc.D.
Metrum Research Group, Tariffville CT
Objectives: Matching methodology in pharmacometrics has been used by the FDA [1] for determining drug effect in the presence of confounding variables. Common matching methods include Mahalanobis distance (MD) and propensity scores (PS). MD is cov matrix normalized Euclidean distance and expects continuous data, PS [2] models conditional treatment probability and allows mixed data. Assessment after matching is crucial and typically includes univariate measures like standardized bias and QQ-plots. Curiously, multivariate comparisons of the covariate distribution are rarely considered. In the case where all data is continuous, we can expect methods that explicitly account for the multivariate distribution of covariates (MD) will retain multivariate balance. However, in data more typical of medical trials can we expect the same? We investigate MD and PS methods to evaluate matching bias and examine new methods for comparing the covariance structure between matched patient samples of mixed data types.
Methods: Using publicly available oncology data (R::colon), we generate hypothetical exposure and confoundedness with exposure as a function of 8 qualitative + 2 quantitative covariates. Matches are found on distances of: A) MD, B) MD (0.25 calipers), C) PS matching (0.25 calpers), and D) MD on continuous covariates (0.25 PS calipers). We bootstrap univariate and multivariate summaries of the matched data to quantify similarity. Heterogeneous covariance matrices (HCM) using appropriate correlations are used to correctly quantify mixed data type correlation for comparison.
Results: PS methods result generally in smaller bias between matched samples, with maximal standardized bias [90% CI] of A) 0.38 [0.25, 0.54], B) 0.37 [0.25, 0.55], C) 0.25 [0.14, 0.4], and D) 0.23 [0.14, 0.5]. MD methods better preserved the multivariate structure of the data per MSE on the element-wise difference of HCMs: A) 1.96 [1, 3.2], B) 1.92 [1.04, 3.47], C) 3 [1.72, 4.96], and D) 2.83 [1.59, 4.82].
Conclusions: Matching with mixed data is simplified by using propensity score methods, but it is important to assess both univariate and multivariate balance after matching. Our results indicate that while PS leads to low bias in matched samples, it does not preserve pairwise correlations as well as MD. We suggest use of MD within propensity scores when possible, and addition of multivariate screening using HCM’s as an additional tool in the repertoire of selecting optimal matches.
References:
[1] Yang, J., Zhao, H., Garnett, C., Rahman, A., Gobburu, J. V., Pierce, W., Schechter, G., Summers, J., Keegan, P., Booth, B. and Wang, Y. (2013), The Combination of Exposure-Response and Case-Control Analyses in Regulatory Decision Making. Journal of Clinical Pharma, 53: 160–166. doi: 10.1177/0091270012445206
[2] ROSENBAUM, P. R. and RUBIN, D. B. (1983b). The central role of the propensity score in observational studies for causal effects. Biometrika 70 41–55. MR0742974
[3] GU, X. and ROSENBAUM, P. R. (1993). Comparison of multivariate matching methods: Structures, distances, and algorithms. J. Comput. Graph. Statist. 2 405–420.
Reference: PAGE 24 () Abstr 3638 [www.page-meeting.org/?abstract=3638]
Poster: Methodology - Covariate/Variability Models