A pathway EM-algorithm for estimating vaccine efficacy with a non-monotone validation set.
Here, we consider time-to-event data where individuals can experience two or more types of events that are not distinguishable from one another without further confirmation, perhaps by laboratory test. The event type of primary interest can occur only once. The other types of events can recur. If the type of a portion of the events is identified, this forms a validation set. However, even if a random sample of events are tested, confirmations can be missing nonmonotonically, creating uncertainty about whether an individual is still at risk for the event of interest. For example, in a study to estimate efficacy of an influenza vaccine, an individual may experience a sequence of symptomatic respiratory illnesses caused by various pathogens over the season. Often only a limited number of these episodes are confirmed in the laboratory to be influenza-related or not. We propose two novel methods to estimate covariate effects in this survival setting, and subsequently vaccine efficacy. The first is a pathway expectation-maximization (EM) algorithm that takes into account all pathways of event types in an individual compatible with that individual's test outcomes. The pathway EM iteratively estimates baseline hazards that are used to weight possible event types. The second method is a non-iterative pathway piecewise validation method that does not estimate the baseline hazards. These methods are compared with a previous simpler method. Simulation studies suggest mean squared error is lower in the efficacy estimates when the baseline hazards are estimated, especially at higher hazard rates. We use the pathway EM-algorithm to reevaluate the efficacy of a trivalent live-attenuated influenza vaccine during the 2003-2004 influenza season in Temple-Belton, Texas, and compare our results with a previously published analysis.
Department of Biostatistics and Emerging Pathogens Institute, University of Florida, Gainesville, Florida 32611, U.S.A.
Yang
Y
Yang
Fred Hutchinson Cancer Research Center, Seattle, Washington 98109, U.S.A.|Department of Biostatistics, University of Washington, Seattle, Washington 98195, U.S.A.
M Elizabeth
ME
Halloran
Department of Statistics, University of Washington, Seattle, Washington 98195, U.S.A.
Yanjun
Y
Chen
Department of Biostatistics and Emerging Pathogens Institute, University of Florida, Gainesville, Florida 32611, U.S.A.
Eben
E
Kenah
D000465:Algorithms; D003627:Data Interpretation, Statistical; D006801:Humans; D015994:Incidence; D007252:Influenza Vaccines / Q000627:therapeutic use*; D007251:Influenza, Human / Q000453:epidemiology* / Q000517:prevention & control*; D016013:Likelihood Functions; D017063:Outcome Assessment, Health Care / Q000379:methods*; D011379:Prognosis; D015203:Reproducibility of Results; D012307:Risk Factors; D012680:Sensitivity and Specificity; D013781:Texas / Q000453:epidemiology; D016896:Treatment Outcome
D007252:Influenza Vaccines
EM algorithm; Missing data; Vaccine efficacy; Validation set