The data for the entire cohort of 1340 subjects including all fixed and time-dependent variables was represented in counting process notation suitable for Cox regression of time-dependent exposure [11 ]. Multiple records (with consecutive start and end times) were created for each subject to account for every change in exposure to any of the time-dependent variables over the study period.
The hazard ratio (HR) of pacemaker insertion associated with amiodarone doses >200 mg per day was estimated using a Cox proportional-hazards model including all fixed and time-dependent covariates. The timescale used in the model was time since first prescription of amiodarone. Non-significant variables (other than age and sex) were sequentially removed if the resultant model had no significant increase in Akaike Information Criteria (AIC) and no significant change in the HR for amiodarone dose.
The nested case-control approach was also used to estimate the HR of pacemaker insertion associated with amiodarone doses >200 mg per day. Cases of pacemaker insertion were identified and controls were randomly selected from the risk-set of each case (i.e. subjects present in the cohort at the time the case is defined). After selecting all controls and recording their index dates (i.e. the time, in cohort time, at which the respective case is defined) the relevant time-dependent covariate information was retrieved by merging with the database configured in counting process notation. The relevant subject record was selected by requiring that the index date fall within the start and end time of the subject record for each control.
The nested case-control approach was repeated using 4, 8, 16, 32, and 64 controls per case. For each number of controls per case, random sampling of controls for all cases and conditional logistic regression analysis was repeated 100 times using the OUTEST option in the PROC PHREG statement to create an output SAS data containing all the parameter estimates [11 ]. The mean and standard deviation (SD) of the parameter estimates for each number of controls per case was calculated.
Computational times for regression models of time-dependent exposures using nested case-control and survival analysis methodologies were compared. The nested case-control samples with 4 and 32 controls per case were analyzed using conditional logistic regression with the PHREG procedure in SAS Release 8.2 [12 ]. The full cohort was analyzed using Cox regression adapted for analysis of time-dependent covariates with the PHREG procedure in SAS Release 8.2. Ties were handled using the TIES = EFRON option in the PHREG procedure [11 ]. All analyses were performed using an Intel Pentium 4 computer with a 1.80 GHz central processing unit (CPU) and 256 MB of random access memory (RAM).
Relative computational efficiencies were evaluated by comparing the CPU times of the three regression models used to analyze the cohort. Relative increases in computational time as a function of sample size were quantified by repeating the analyses on progressively larger cohorts. This was done by progressive doubling of the original cohort to 2, 4, 8, and 32 times its original size. Given that the objective was to compare computational times, all fixed and time-dependent exposures were included in all models regardless of statistical significance.
The computational efficiency of the Cox regression model was also compared to the conditional logistic regression model where the nested case-control sample included all possible controls for each case. This comparison was performed for the original cohort of 1340 subjects with 53 cases (including 2 ties). All analyses were performed using the PHREG procedure. Ties were handled using the TIES = EFRON option in the PHREG procedure, and subsequently using the TIES = DISCRETE option in the PHREG procedure for comparison.
The hazard ratio (HR) of pacemaker insertion associated with amiodarone doses >200 mg per day was estimated using a Cox proportional-hazards model including all fixed and time-dependent covariates. The timescale used in the model was time since first prescription of amiodarone. Non-significant variables (other than age and sex) were sequentially removed if the resultant model had no significant increase in Akaike Information Criteria (AIC) and no significant change in the HR for amiodarone dose.
The nested case-control approach was also used to estimate the HR of pacemaker insertion associated with amiodarone doses >200 mg per day. Cases of pacemaker insertion were identified and controls were randomly selected from the risk-set of each case (i.e. subjects present in the cohort at the time the case is defined). After selecting all controls and recording their index dates (i.e. the time, in cohort time, at which the respective case is defined) the relevant time-dependent covariate information was retrieved by merging with the database configured in counting process notation. The relevant subject record was selected by requiring that the index date fall within the start and end time of the subject record for each control.
The nested case-control approach was repeated using 4, 8, 16, 32, and 64 controls per case. For each number of controls per case, random sampling of controls for all cases and conditional logistic regression analysis was repeated 100 times using the OUTEST option in the PROC PHREG statement to create an output SAS data containing all the parameter estimates [11 ]. The mean and standard deviation (SD) of the parameter estimates for each number of controls per case was calculated.
Computational times for regression models of time-dependent exposures using nested case-control and survival analysis methodologies were compared. The nested case-control samples with 4 and 32 controls per case were analyzed using conditional logistic regression with the PHREG procedure in SAS Release 8.2 [12 ]. The full cohort was analyzed using Cox regression adapted for analysis of time-dependent covariates with the PHREG procedure in SAS Release 8.2. Ties were handled using the TIES = EFRON option in the PHREG procedure [11 ]. All analyses were performed using an Intel Pentium 4 computer with a 1.80 GHz central processing unit (CPU) and 256 MB of random access memory (RAM).
Relative computational efficiencies were evaluated by comparing the CPU times of the three regression models used to analyze the cohort. Relative increases in computational time as a function of sample size were quantified by repeating the analyses on progressively larger cohorts. This was done by progressive doubling of the original cohort to 2, 4, 8, and 32 times its original size. Given that the objective was to compare computational times, all fixed and time-dependent exposures were included in all models regardless of statistical significance.
The computational efficiency of the Cox regression model was also compared to the conditional logistic regression model where the nested case-control sample included all possible controls for each case. This comparison was performed for the original cohort of 1340 subjects with 53 cases (including 2 ties). All analyses were performed using the PHREG procedure. Ties were handled using the TIES = EFRON option in the PHREG procedure, and subsequently using the TIES = DISCRETE option in the PHREG procedure for comparison.
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