Objective: Clinical trials of therapies for sepsis have been mostly unsuccessful in impacting mortality. This may be partly due to the use of insensitive mortality end points. We explored whether modeling survival was more sensitive than traditional end points in detecting mortality differences in cohorts of patients with sepsis.
Design: Patients were stratified into seven a priori defined paired subgroups that reflected high and low mortality risk according to known clinical risk factors. We fitted an exponential survival model to the high- and low-risk cohort of each subgroup, providing estimates of the rate of dying, long-term survival, and excess day 1 mortality. Mortality in the high- and low-risk cohorts in each subgroup was compared using model parameters, fixed-point mortality, and Kaplan-Meier survival analysis.
Setting: Eight intensive care units within a university teaching institution.
Patients: One hundred thirty patients with severe sepsis or suspected Gram-negative bacteremia.
Measurements and Main Results: Overall mortality of the cohort was 58.5% at 28 days. The survival of the entire cohort was well described by an exponential model (r2 = .99). Modeling identified differences in high- and low-risk cohorts in five of the seven paired subgroups, while conventional end-points only detected differences in 2.
Conclusions: Modeling survival was more sensitive than conventional end-points in identifying survival differences between high- and low-risk subgroups. We encourage further evaluation of modeling in the search for more sensitive mortality end points.
Until the recent study of activated protein C in the treatment of severe sepsis, PROWESS, (1) numerous trials of pharmacotherapeutic agents had failed to demonstrate an improvement in survival. Among the reasons cited for these failures was the choice of short-term fixed-day mortality as the primary end point (2, 3). Mortality is a pivotal outcome, but when measured as the proportion of patients who have died by a fixed time point such as day 28 (i.e., a binary event), it may be insensitive to effects of interventions aimed at disease modification. A survival analysis using a survival function analogous to the Kaplan-Meier estimation method is also expected to be more sensitive than 28-day mortality because temporal information is included. However, this method is descriptive and provides no information beyond 28 days. This has led to a search for alternative end points, for example, acute organ failure, that are complementary to, but distinct from, mortality. However, the validity of these end points is unclear and their use remains controversial. In this study, we consider whether, by including information regarding the time of death, we can produce a mortality-based end point that is sensitive to disease modification.
We hypothesized that the process of dying from sepsis could be mathematically described by a predictable distribution of the number of deaths over time (4). This distribution would vary across subgroups of patients with different baseline risks of death. For example, patients with high Acute Physiology and Chronic Health Evaluation (APACHE) scores would be expected to die at a faster rate than those with low APACHE scores. Specifically, we assumed that the number of survivors follows an exponential decay curve that levels off to a number of ultimate survivors of the sepsis process. The rate of death, or “time constant to death,” quantifies the time scale of the dying process. One might expect that comorbidities or therapies that alter the septic process or its progression to multiple organ dysfunction syndrome would result in changes in the time constant to death, the number of ultimate survivors, or both.
We used a small, retrospective cohort study of patients with sepsis to generate preliminary information on the feasibility of using the concept of time to death as a process parameter in sepsis. We then tested the hypothesis that mathematical modeling would capture differences in the dying process of the high- and the low-mortality risk subgroups not identified with other measures of mortality.
From the CRISMA (Clinical Research, Investigation, and Systems Modeling of Acute Illness) Laboratory (GC, DCA, KGK, WTL-Z), Department of Critical Care Medicine, University of Pittsburgh, Pittsburgh, PA; Georgia Lung Associates (KGK), Austell, GA; Health Process Management (WTL-Z), LLC, Doylestown, PA; Acute Care Consultants of Dublin (NR), Dublin, GA; and the Department of Critical Care Medicine (PKL, MRP), University of Pittsburgh, Pittsburgh, PA.
We, therefore, recommend that intermediate outcomes suggestive of disease modification, such as time constant to death, be considered for inclusion as additional end points in sepsis trials.