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# Table 1 Definitions of the different types of models

Model Definition
Unconditional model The unconditional approach estimates the accrual period by dividing the pre-specified sample size by the number of patients they expect to recruit across all centres each month (e.g. assume a trial requires 400 participants, its estimated centres will recruit 10 participants per month. According to the unconditional model this implies it will take 40 months to recruit all 400 participants. 2
Conditional model The conditional model allows the expected recruitment in any given month to vary, depending on other conditions in the trial such as how many centres are available to recruit (e.g. assume a trial requires 400 participants and that its expected centres 1 and 2 will start recruiting in month 1 and will recruit 5 participants per month each. Also assume its expected that centre 3 will start recruitment in month 6 and will recruit 10 participants per month. According to the conditional model this implies it will take 22.5 months to recruit all participants).2
Possion model The poisson models, assumes the rate that participants are recruited varies according to a poisson distribution. The number of participants recruited within a given month is simulated using a random number generator, from the poisson distribution with mean λ, where λ is the mean number of participants that trialists specify they expect to recruit each day/month. The Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate (λ) and independently of the time since the last event. P(Xt = n) = (e-λt (λt)n )/n!2
Bayesian model A Bayesian analysis starts with a "prior" probability distribution for the value of interest (for example, the recruitment of participants into a trial)--based on previous knowledge--and adds the new evidence as data accumulates (via a model) to produce a "posterior" probability distribution. 10
Monte carlo simulation Markov model A type of quantitative modeling that involves a specified set of mutually exclusive and exhaustive states (e.g., of a given health status), and for which there are transition probabilities of moving from one state to another (including remaining in the same state). In this case a participant moving from a contacted state to a recruited state in a specified time period. Typically, states have a uniform time period, and transition probabilities remain constant over time.
Values are randomly generated from a uniform distribution, if the value generated is less than equal to the transition probability assumed a participant is said to be recruited in that time period.
Monte Carlo simulation considers random sampling of probability distribution functions as model inputs to produce hundreds or thousands of possible outcomes instead of a few discrete scenarios. The results provide probabilities of different outcomes occurring.
Markov chain monte carlo simulations use, monte carlo simulation (random number generation) to decide on the transition probability and whether a participant moves from one state to another (is recruited in this time period or not).8,11