Introduction

One of the most important aspects of clinical decision making is selecting treatment strategies for individual patients. A patient's general health, demographic status and disease severity will influence both the choice of therapy and the prognosis. For patients with coronary artery disease (CAD), the patient's risk profile can determine whether a more invasive, and costly, strategy is indicated. Because CAD accounts for a major portion of cardiovascular disease (the U.S.A.'s number one cause of death, with incurred costs exceeding $150 billion annually [1]), these decisions are relevant to society as well as to individual patients.

This study addresses some of the methodological issues in using observational data to create prognostic models for CAD patients under different therapeutic options. Currently, the three primary options after diagnosis by cardiac catheterization are medical therapy (MED), percutaneous transluminal coronary angioplasty (PTCA), and coronary artery bypass graft surgery (CABG), the latter two being revascularization procedures.

Ideally, data to assess the influence of treatment strategy on prognosis would come from randomized trials. However, these trials are expensive and often have limited sample size and follow-up. Further, they cannot always be generalized to the broader spectrum of patients and practice settings. Thus, observational data must sometimes supply information for medical decision-making. In this case, the choice of therapy, the prognosis, and the relative survival benefit depend to a great extent on the patient's risk profile. In particular, because treatment groups are not necessarily comparable prior to treatment, quantitative statistical models that attempt to account for treatment selection bias while estimating survival under alternative treatment strategies are needed. In addition to the selection bias that is inherent in treatment comparisons with such data, a number of other issues are relevant, and these additional issues are the focus of this manuscript.

1.1. Issues in assessing prognosis for CAD patients using observational data sources

A fundamental difficulty when using observational data to estimate prognosis for CAD patients involves defining treatment-specific survival. Physicians and patients who initially select a less invasive treatment option understand that later cross-over to a more invasive alternative is possible. For example, a patient may begin treatment with medical therapy, but later undergo CABG. The initial post-catheterization treatment 'strategy' incorporates this potential change in treatment. The prognosis that includes survival from treatment initiation through any subsequent cross-overs will be designated as arising from a 'treatment strategy' perspective. This perspective is in distinction to the 'single treatment' perspective, which evaluates prognosis while receiving only the initial treatment and censors at any cross-over, such as expected survival while on MED (described further in Section 1.2).

In randomized trials, treatment assignment is unbiased and survival time is initiated at randomization. Observational studies of CAD patients, however, often lack an explicitly recorded treatment assignment and thus have no uniformly logical treatment initiation time. Although the treatment decision occurs soon after the catheterization, it is generally not recorded in the observational data set. Furthermore, personal reasons or scheduling difficulties can delay the actual performance of a procedure for several days; consequently, some patients could be lost to follow-up if they go elsewhere for procedures or some may die while awaiting revascularization. For such patients, if no revascularization procedure has occurred following catheterization, a default assignment to the medical therapy arm would attribute both early deaths and early losses to follow-up to MED. This policy assumes medical survival time begins at catheterization, whereas procedural survival begins at the procedure date. Using this convention and assuming the patient has survived the catheterization procedure, medical survival is unconditional, but procedural survival is implicitly conditioned on surviving to receive the procedure. This problem is similar to one described in transplantation literature. When patients who do not survive long enough to undergo transplantation are, in analyses, assigned to the non-transplant group, this creates a selection 'waiting time' bias in favour of the transplantation group. The methodological problem of when to begin 'survival time' has led to a serious and sustained debate questioning if heart transplantation survival benefits may have been caused by selection bias [2-5]. With the pace of care increasing, the delay from catheterization to PTCA is often far shorter than the delay from catheterization to CABG. Hence the potential 'waiting time bias' is particularly favourable toward CABG. This dilemma underscores the need for establishing an equitable 'treatment initiation' time.

A further issue in assessing prognosis is that peri-procedural care (usually defined as the first 30 days following a procedure) and long-term care are generally handled differently and by different types of care providers. The early survival after catheterization and treatment assignment is a variable component of overall survival that depends to a great extent on institutional constraints and individual care providers. This 'problem' also exists when physicians wish to make decisions based on RCT data. It is especially true for CABG and PTCA, which depend on the skill of the operator. Hence, local effects on early mortality need to be considered in long-term prognosis. Also, the factors that are important determinants of this early risk may differ from those affecting long-term survival.

An additional statistical concern is the differential risk associated with alternative treatments in the early period. CABG is known to incur a much higher early risk than either PTCA or MED, but this risk declines sharply in the first few days after the surgery. Because the early hazards for the three treatments are not proportional, a simple proportional hazards survival model cannot be used directly to obtain estimates of relative treatment hazards. Treatment effects in the later interval are more likely to conform to proportional hazards.

A survival model that allows the variable 30-day mortality component to be estimated independently (possibly locally) and then coupled with the long-term component may be used to compare prognosis under different short-term scenarios. In addition, estimates of the conditional survival (dependent on surviving this initial 30-day period) can be used by patients and providers following a successful procedure, or by those who want data that is not influenced by the early mortality rate.

1.2. Previous approaches

Some of the earliest observational prognostic assessments for CAD patients came from the CASS multi-site data registry [6,7]. Acknowledging the difficulties of determining treatment assignment and exposure time, these studies performed analyses using several methods. One comparative analysis between MED and CABG assigned patients to medical therapy unless CABG was performed within an established time window. Patients who did not undergo CABG and either died or were lost to follow-up before the average time to CABG were excluded from analysis to avoid biasing the estimates against medical therapy survival. This exclusion addressed the potential for waiting time bias, although the time to CABG is a skewed distribution with a heavy tail and a mean that is far greater than the median.

Another CASS method used what we designate as the 'single treatment' perspective for medical therapy, a method that was also used for survival comparisons in the Duke Cardiovascular Database [8-10]. In these comparisons, medical survival represented the interval of time a patient spent on medical therapy prior to death, revascularization or loss to follow-up. The medical survival of a patient who crossed over from medicine to a procedure was censored at the time of the procedure, and that patient's remaining survival was analysed as procedural survival. Whereas survival time for medical patients began at catheterization, the procedural survival times began at the time of procedure. Patients who died in the first few days after catheterization without undergoing a procedure, including those few deaths due to catheterization, were assumed to be medical failures.

Blackstone et al. [11] used parametric modelling of a cumulative hazard function to estimate survival to different time-related events following cardiac valve surgery. Their approach allows a time-varying decomposition of the hazard into as many as three phases, with the incorporation of potentially different covariates into each phase. Using this method, the problems of non-proportional early hazards and a separate covariate set for different time periods can be addressed directly. Treatment comparisons are not an issue in these analyses. Hence, because valve surgery has a logical treatment initiation and assignment, whereas medical therapy does not, this method does not address the issues of treatment assignment and initiation.

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