**4.3.1 The effect of design misspecification**

We first assessed bias and precision in disease risk estimation (relative risk and penetrance) for the retrospective likelihood with correct design adjustment for family data from different study designs. The results are summarized in Table 2.

With the correct design adjustment, the estimates of both the log relative risk and penetrance appeared unbiased; the absolute values of bias were less than 0.05 under both high and low penetrance models regardless of the study design. The magnitude of the bias was much smaller than the standard errors. In the log relative risk estimation, the precision of clinic-based designs was higher (smaller standard errors) than that of population-based designs. The population-based designs provided more accurate and precise estimates of the log relative risk for high penetrance than for low penetrance, whereas the clinic-based designs performed better for low penetrance. However, in the penetrance estimation, all designs provided more precise penetrance estimates (smaller standard errors) for high penetrance than for low penetrance.

We then examined the effect of design misspecification in terms of bias and precision of the log relative risk and penetrance estimates obtained from the retrospective likelihoods when the study design was misspecified. The clinic-based ascertainment correction was applied to the family data under the population-based designs and the population-based ascertainment correction to the clinic-based study. It is worth noting that the clinic-based design with the population-based correction provided relatively large bias in both disease risks, however, the bias in the population-based design with the clinic-based ascertainment correction was not notably large. Especially, under POP+ design (with affected and mutation carrier probands), the clinic-based retrospective likelihood yielded estimates at least as accurate as those from probands-only adjustment (correct design), although their standard errors were larger under the misspecified design.
