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Please see updated text with minor edits: Most of these models assume the background response is zero and the absolute response (or initial response) is increasing. In other words, most of these models are able to fit a monotonic curve for either direction. The polynomial 2 model is an exception because it has two parameterizations. By default, the biphasic parameterization will be used in tcpl. A biphasic polynomial 2 model is able to fit a curve to responses that are increasing first and then decreasing, and vice versa (assuming the background response is zero). In applications in which biphasic responses are not reasonable, polynomial 2 can be fit using the monotonic only parameterization.

Upon completion of the model fitting, each model gets a success designation: 1 if the model optimization converges, 0 if the optimization fails, and NA if 'nofit' was set to TRUE within tcplfit2_core function from tcplFit2 . Similarly, if the Hessian matrix was successfully inverted then 1 is returned to indicate a successful covariance calculation (cov); otherwise 0 is returned. Finally, in cases where 'nofit' was set to TRUE (within tcplFit2::tcplfit2_core ) or the model fit failed the Akaike information criterion (aic), root mean squared error (rme), model estimated responses (modl), model parameters (parameters), and the standard deviation of model parameters (parameter sds) are set to NA. A complete list of model output parameters is provided in Table 8 below.

Consider updated text: For each concentration series, several potency or point-of-departure (POD) estimates are calculated on the winning model. The major estimates include: (1) the activity concentration at the specified benchmark response (BMR) ($\mathit{bmd}$), (2) the activity concentration at $50%$ of the maximal response ($\mathit{ac50}$), (3) the activity concentration at the efficacy cutoff ($\mathit{acc}$), (4) the activity concentration at $10%$ of the maximal response, and (5) the concentration at $5%$ of the maximal response. There are several additional potency and uncertainty estimates included as part of the level 5. The POD estimates mentioned in here are summarized in Figure 4. The winning model may return a $\mathit{bmd}$ estimate that falls outside of the tested concentration range, so bounds are placed to censor the estimate values. The lower and upper bounds for $\mathit{bmd}$ estimates are $0.1*\text{the lowest test concentration}$ and $10*\text{the the highest test concentration}$, respectively. If the calculated $\mathit{bmd}$ estimate is below or above the lower or the upper bounds, the value at the bound will be returned as the bounded $\mathit{bmd}$ estimate instead.