The R package JM has been developed by Rizopoulos (2010) to fit joint models using Weibull baseline hazard, piecewise-constant baseline hazard, spline approximation of the baseline hazard and unspecified baseline hazard functions.
Hazard ratios were rarely reported directly, so we had to use the ratio of the observed median duration of symptoms in each group as an approximation to the hazard ratio.
These approaches involve the approximation of the log hazard ratio and its variance using available count statistics.
Moreover, the hazard difference is only a valid approximation of the risk difference if event rates are low, for instance less than 5% [ 16, 18].
We used MSRs as an approximation of the gold standard hazard ratio approach (Michiels et al, 2005; Tierney et al, 2007).
When the risk is low, logistic and Cox regression usually produce similar results and the odds ratio can be regarded as an approximation of the more accurate hazard ratio that also takes time to the event into account.
In that sense, the sub-hazard ratio appears to be a better approximation of the relative risk than the odds ratio [ 23].
This reflects the advantage of our method and possibly the limitation of the diffusion approximation, which assumes that the values of the hazard functions are approximately constants between two observation/latent states.
We assumed relative risks to be a valid approximation of hazard ratio, 21 enabling the use of one consistent measure.
In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments.
