I am analysing longitudinal BMD Z-scores measured at three skeletal sites (spine, hip, and radius). Patients have repeated measurements over time, and bisphosphonate use is time-varying, meaning that the same patient may be untreated at some visits and treated at others.
I first fitted a joint mixed-effects model containing a three-way interaction between skeletal site, bisphosphonate use, and time:
mixed z_score i.z_sitespine1hip2radius3##i.bisphosphonatesanniv_ year0no1yes##c.anniv_year c.anniv_year##(i.gender1female i.splenectomy1yes i.n370s_homozygous1yes i.ever_smoked i.typetype11type30 c.interval_symptom_tx c.zimran_score c.ert_date1 c.ageatthestartoftreatment c.anniv_bmi c.vitamind_anniv ib2.erttype1alglucerase2velagluceras c.ukg) || subject_id: c.anniv_year, covariance(unstructured) I then tested the three-way interaction using: testparm i.z_site#i.bisphosphonate#c.anniv_year which gave: chi2(2) = 34.90 Prob > chi2 = 0.0000 My interpretation is that this Wald test provides evidence that the association between bisphosphonate use and longitudinal Z-score trajectory differs across skeletal sites. Because the outcomes at the three sites are clinically distinct and the significant interaction suggests site heterogeneity, I would then like to fit separate mixed-effects models for spine, hip, and radius to estimate and present the longitudinal associations within each site. My question is: Is this a statistically appropriate approach: using the joint three-way model primarily as a formal test of heterogeneity across skeletal sites, followed by site-specific mixed-effects models to estimate and present the associations at each site? Or would it be preferable to obtain all site-specific estimates and contrasts directly from the joint model using margins/lincom? I would also be interested in whether there are concerns about multiple testing or other issues that should be addressed when presenting the subsequent site-specific models. Many thanks, Oana
I first fitted a joint mixed-effects model containing a three-way interaction between skeletal site, bisphosphonate use, and time:
mixed z_score i.z_sitespine1hip2radius3##i.bisphosphonatesanniv_ year0no1yes##c.anniv_year c.anniv_year##(i.gender1female i.splenectomy1yes i.n370s_homozygous1yes i.ever_smoked i.typetype11type30 c.interval_symptom_tx c.zimran_score c.ert_date1 c.ageatthestartoftreatment c.anniv_bmi c.vitamind_anniv ib2.erttype1alglucerase2velagluceras c.ukg) || subject_id: c.anniv_year, covariance(unstructured) I then tested the three-way interaction using: testparm i.z_site#i.bisphosphonate#c.anniv_year which gave: chi2(2) = 34.90 Prob > chi2 = 0.0000 My interpretation is that this Wald test provides evidence that the association between bisphosphonate use and longitudinal Z-score trajectory differs across skeletal sites. Because the outcomes at the three sites are clinically distinct and the significant interaction suggests site heterogeneity, I would then like to fit separate mixed-effects models for spine, hip, and radius to estimate and present the longitudinal associations within each site. My question is: Is this a statistically appropriate approach: using the joint three-way model primarily as a formal test of heterogeneity across skeletal sites, followed by site-specific mixed-effects models to estimate and present the associations at each site? Or would it be preferable to obtain all site-specific estimates and contrasts directly from the joint model using margins/lincom? I would also be interested in whether there are concerns about multiple testing or other issues that should be addressed when presenting the subsequent site-specific models. Many thanks, Oana
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