This function generates a time trend for given time points in the trial according to an inverted-u function.
Arguments
- j
Time points for which the trend should be generated.
- lambda
Strength of time trend.
- N_peak
Point at which the time trend switches direction in terms of overall sample size.
- n_total
Total sample size in the trial.
- trend_mean
Integer. In case of random time trends, the strength of the time trend will be generated from N(
trend_mean,trend_var).- trend_var
Integer. In case of random time trends, the strength of the time trend will be generated from N(
trend_mean,trend_var).
Details
The time trend is generated according to the function
$$f(j) = \lambda \cdot \frac{j-1}{N-1} \hspace{0.2cm} \mathrm{for} \hspace{0.2cm} j \leq N_p$$ $$f(j) = -\lambda \cdot \frac{j-N_p}{N-1} + \lambda \cdot \frac{N_p-1}{N-1} \hspace{0.2cm} \mathrm{for} \hspace{0.2cm} j > N_p$$
where \(N\) is the total sample size (parameter n_total) and \(N_p\) (parameter N_peak) indicates the point at which the trend switches direction.