Time scale and adjusted survival curves for marginal structural cox models

Abstract

Typical applications of marginal structural time-to-event (e.g., Cox) models have used time on study as the time scale. Here, the authors illustrate use of time on treatment as an alternative time scale. In addition, a method is provided for estimating Kaplan-Meier-type survival curves for marginal structural models. For illustration, the authors estimate the total effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome (AIDS) or death in 1,498 US men and women infected with human immunodeficiency virus and followed for 6,556 person-years between 1995 and 2002; 323 incident cases of clinical AIDS and 59 deaths occurred. Of the remaining 1,116 participants, 77% were still under observation at the end of follow-up. By using time on study, the hazard ratio for AIDS or death comparing always with never using highly active antiretroviral therapy from the marginal structural model was 0.52 (95% confidence interval: 0.35, 0.76). By using time on treatment, the analogous hazard ratio was 0.44 (95% confidence interval: 0.32, 0.60). In time-to-event analyses, the choice of time scale may have a meaningful impact on estimates of association and precision. In the present example, use of time on treatment yielded a hazard ratio further from the null and more precise than use of time on study as the time scale.

Figure 1.

Schematic diagram comparing time-on-study time scale and time-on-treatment time scale.

Figure 2.

Inverse probability of treatment and censoring weighted cumulative incidence by treatment with highly active antiretroviral therapy (HAART) on time to acquired immunodeficiency syndrome (AIDS) or death for 1,498 human immunodeficiency virus-positive US men and women, 1995–2002. Time scale is time on study.

Figure 3.

Inverse probability of treatment and censoring weighted Kaplan-Meier curves for the effect of highly active antiretroviral therapy (HAART) on time to acquired immunodeficiency syndrome (AIDS) or death for 1,498 human immunodeficiency virus-positive US men and women, 1995–2002. Time scale is time on treatment (i.e., time since HAART initiation).