Analyzing Pharmacodynamic Count Data That Rapidly Decrease to Zero

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Abstract
We present a framework for maximum likelihood analysis on count observations that begin high and quickly drop to zero, for example, from hollow fiber drug comparison studies. This simulation study focuses on treating observed counts as Poisson or normally distributed for the purpose of estimating infection rebound after effective treatment. CFU profiles were simulated from inoculation to 96 h post‐treatment. The PK‐PD link was an Emax inhibitory model. Random parameters were pathogen growth and natural decay rates, drug concentration for half‐maximal effect, and drug pathogen kill rate. Other parameters, including PK, were fixed. Parameters were adjusted to attain 67% efficacy at 24 h. Random parameter values were optimized for profiles observed at 24, 48, 72, and 96 h assuming each of four probability assumptions: (1) all CFU measurements were Poisson distributed (truth); (2) CFU < 128 were Poisson, higher values were normally distributed; (3) all observations were normally distributed; and (4) observations were normally distributed but CFU < 10 were censored. CFU‐time profiles were re‐simulated using the optimized parameter densities. Rebound percentage (CFU ≥ 10 at 24 h post‐treatment) was best predicted using strategy 2, above. For limited periodically collected time series count data that quickly fall to 0, the true proportion reaching 0 (lack of rebound) was best modeled by assuming Poisson distribution at low counts. At higher counts (≥ 128), assuming normality is reasonable. Censoring observations leads to biased models.

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