The Hazards of Hazard Ratios

• DOI: 10.1097/ede.0b013e3181c1ea43
• Publication Date: 2009-12-09T08:31:00Z
• Authors: Miguel A. Hernán
• Keywords: Epidemiologic Studies; 03 medical and health sciences; 0302 clinical medicine; Proportional Hazards Models

The hazard ratio (HR) is the main, and often only, effect measure reported in many epidemiologic studies. For dichotomous, non–time-varying exposures, HR defined as exposed groups divided by unexposed groups. all practical purposes, hazards can be thought of incidence rates thus roughly interpreted rate ratio. commonly conveniently estimated via a Cox proportional model, which include potential confounders covariates. Unfortunately, use for causal inference not straightforward even absence unmeasured confounding, measurement error, model misspecification. Endowing with interpretation risky 2 key reasons: may change over time, has built-in selection bias. Here I review these problems some proposed solutions. As an example, will findings from Women's Health Initiative randomized experiment that compared risk coronary heart disease women assigned to combined (estrogen plus progestin) hormone therapy placebo.1 By using discussion focus on shortcomings HR, setting aside issues confounding other serious arise observational followed 16,000 average 5.2 years before study was halted due safety concerns. primary result trial HR. stated abstract1 shown Table 1 article, "Combined associated 1.24."1 In addition, provided HRs during each year follow-up: 1.81, 1.34, 1.27, 1.25, 1.45, 0.70 1, 2, 3, 4, 5, 6+, respectively. Thus, abstract viewed sort weighted period-specific 2. This bring us Problem 1: although studies report only single averaged duration study's follow-up. result, conclusions critically depend WHI would have been 1.8 if had after follow-up, 1.7 years,2 1.2 5 years, and—who knows—perhaps 1.0 10 years. 24% increase researchers journalists consider arbitrary choice follow-up period A shorter could 80% increase, whereas longer might found little or no at all. magnitude depends length because ignores distribution events take value identical entire higher during, say, first lower afterward. Incidentally, same problem arises whether directly cohort study, discussed here, odds properly designed case-control density sampling. One then conclude we should forget about restrict our attention HRs, seem capture potentially time-varying effect. brings 2: To describe bias, (discrete-time) t outcome among those who reached free outcome. Initiative, calculation restricted did develop disease—the "survivors"—between baseline beginning t. 0.7, means treatment arm (the numerator HR) than placebo denominator). However, this apparently protective hardly surprising one bears mind vary their susceptibility disease. certain proportion enrolled were particularly prone they factors (for simplicity, let's refer them "susceptible women"). susceptible course unknown but, randomization, it expected both arms baseline. preferentially excluded developed time—precisely harmful effects (all equally distributed between arms). With progressively increased arm. bias differential less depletion susceptibles, HRs. explain truly preventive any woman time. also described diagrams.3,4 short, uninformative These overcome summarizing appropriately adjusted survival curves, where time individuals are through Another alternative here comparison times unexposed, accomplished accelerated failure models5 rather models. Because analysis experiments routinely Kaplan-Meier curves—or complement, cumulative curve (see Figure report1). contrast (and despite multiple warnings literature3–6), summarized only. possible explanation practice need deal confounding. presented simply unexposed. Rather, measured regression models, inverse probability weighting, methods. Unadjusted data, unadjusted curves. It unexpected most articles epidemiology students traditionally taught estimate but curves.7 next paragraph sketches general procedure obtain curves confounders. First, fit discrete-time (eg, pooled logistic relatively short periods) estimates, person, conditional remaining given exposure, covariates, Allow modeling variable "time follow-up," flexible functional form cubic splines), adding product terms exposure follow-up." Second, subject, multiply model's predicted values subjects combination covariate values. construct (adjusted) under conditions observed covariates (in trials, unconditional marginal, ie, irrespective values). Third, predict subject regardless subject's status. Fourth, separately survivals subjects. last step effectively standardizes empirical results marginal curves: another exposure. above extended number ways. settings exposures confounders, weighting model. used present continuous ("always exposed") ("never studies8 experiments9 when considering adherence-adjusted analyses. dichotomous requires finite levels versus never exposed" do).10 there interest. needs especially careful dose-response assumptions. Sensitivity analyses evaluate possibility extrapolation beyond data. Confidence intervals obtained bootstrapping. So outlaw studies? Of not. misleading, explained above, misleading measures ignore On hand, series increasingly periods informative. approximately 1.8, 1.7, 1.2, indicates increases early part probably much periods. conclusion drawn groups, converge 8 mortality sufficiently long probabilities ensured reach 0, 1. An advantage provide information absolute risks. one-year 0.49% group 0.28% than, 49% 28%. readiness confidence computed standard software. What HRs? Their makes difficult interpret goes greater 5—that is, cross 5. crossing essentially meaningless standpoint. really matters until least 8. Hazards point susceptibles cross. Cumulative measures, such needed summarize data meaningful way. useful intermediate above. summary, more informative easily generated. bad thing see widely