Methods/Statistics
Choosing the link function for time-to-pregnancy analysis: An example based on assessing folate supplementation in PRESTO Vaishnavi Venkat* Vaishnavi Venkat Lauren A. Wise Kenneth J. Rothman Clarice R. Weinberg
Background: Three approaches to generalized linear model (GLM) analysis of time-to-pregnancy (TTP) data have been proposed, based on choice of the “link” function that connects the per-cycle probability of conception (fecundability) with a linear combination of predictors. We compared the performance of the logit, log, and inverse link functions for data from the PRESTO cohort, with use of folate supplements as the exposure.
Methods: We analyzed data from 15,847 participants who answered the question about folate supplements. Three GLMs were fitted to model the association between folate supplement use and fecundability. Models were adjusted for age, education, income, race, smoking status, and gravid status. Model fit was assessed using the Akaike Information Criterion (AIC), and the Hosmer-Lemeshow test.
Results: Without adjustment, folate supplement use was associated with increased fecundability across all link functions. After adjusting for confounders, the association remained positive in each analysis, but was attenuated. The logit-link model (equivalent to the Cox model for discrete time) yielded a fecundability odds ratio (FOR) of 1.31 (95% CI: (1.23,1.40)), the log-link model a fecundability ratio (FR) of 1.26 (95% CI: (1.18,1.33)), and the inverse-link model a population FR of 1.06 (95% CI: (1.02,1.10)). The logit and log-link models provided better fits than did the inverse-link model, as evidenced by lower AIC values (logit: 49961, log: 49967, inverse: 50153) and higher Hosmer-Lemeshow p-values (logit: 0.73, log: 0.39, inverse: 0.00), which are based on comparing the fitted to observed conception rates.
Conclusion: The logit-link and log-link models outperformed the inverse-link model for the PRESTO TTP data. These findings highlight the importance of careful selection of the link function in TTP analysis, based on comparing the fits and the predictive performances of the resulting models.