A comparison of all-subset Cox and accelerated failure time models with Cox step-wise regression for node-positive breast cancer

Summary

Clinical studies usually employ Cox step-wise regression for multivariate investigations of prognostic factors. However, commercial packages now allow the consideration of accelerated failure time models (exponential, Weibull, log logistic, and log normal), if the underlying Cox assumption of proportional hazards is inappropriate. All-subset regressions are feasible for all these models.

We studied a group of 378 node positive primary breast cancer patients accrued at the Henrietta Banting Breast Centre of Women's College Hospital, University of Toronto, between January 1, 1977, and December 31, 1986. 85% of these patients had complete prognostic factor data for multivariate analysis, and 96% of the patients were followed to 1990. There was evidence of marked departures from the proportional hazards assumption with two prognostic factors, number of positive nodes and adjuvant systemic therapy. The data strongly supported the log normal model. The all-subset regressions indicated that three models were similarly good. The variables 1) number of positive nodes, 2) tumour size, and 3) adjuvant systemic therapy were included in all three models along with one of three biochemical receptor variables 1) ER, 2) combined receptor (ER- PgR-; ER+ PgR-; ER- PgR+; ER+ PgR+; or 3) PgR.

Better multivariate modeling was achieved by using quantitative prognostic factors, a check for appropriate underlying model-type, and all-subset variable selection. All-subset regressions should be considered for routine use with the many new prognostic factors currently under evaluation; it is very possible that there may not be a single model that is substantially better than others with the same number of variables.