Deriving and Modelling Fertility Variables in the NCDS and BCS70

1. Deriving and Modelling Fertility Variables in the NCDS and BCS70 Dylan Kneale, Institute of EducationSupervisors: Professor Heather Joshi & Dr Jane Elliott

2. Pathways to Parenthood: Exploring the influence of Context as a Predictor of Timing to Parenthood • Overall Aims1. Define early parenthood…teenage?2. Explore strength of different ‘known’ sets of predictors of early parenthood3. Explore the influence of context as a predictor of early parenthood4. Explore the influence of context on the other side of the spectrum: postponement and childlessness

3. i. Deriving fertility variables (NCDS)ii. Modelling fertility variables (NCDS & BCS70) NCDS 1991 NCDS (Age 33) 2004 NCDS (Age 46) 1965 NCDS (Age 7) 1974 NCDS (Age 16) 1958 NCDS Birth 1969 NCDS (Age 11) 1981 NCDS (Age 23) 2000 NCDS (Age 42) 2000 BCS70 (Age 30) 1986 BCS70 (Age 16) 1975 BCS70 (Age 5) BCS70 1970 BCS70 Birth 1980 BCS70 (Age 10) 1996 BCS70 (Age 26) 2004 BCS70 (Age 34)

4. Deriving fertility variables (NCDS) I • Fertility variables collected at all waves since childhood (Age 23, 33, 41/42, 46 years) • 2004 sweep allows for analysis of full fertility schedule adding to previous analyses of NCDS cohort e.g. Holdsworth & Elliott (2001) • Want to create variables for Event History Analysis • First attempt to create variable for modelling entry into parenthood in Event History terms could work as: Time to first parenthood (Event) = Minimum Recorded Child’s Date of Birth (Age 23, 33, 41/42, 46 years) Childless cohort members (Censored) = Maximum Recorded Interview Date (Age 23, 33, 41/42, 46 years)

5. Deriving fertility variables (NCDS) II • Using this method produces the following summary KM statistics: • Median estimates of entry to parenthood are higher than other sources for NCDS. • However, of more concern; estimates of childlessness using data up to 46 years don’t differ significantly from those up to 33 years. • Equivalent of only additional 3.3% of women becoming mothers (Holdsworth & Elliott 2001). • ONS estimates transition between 33 and 46 years at twice this rate

6. Deriving fertility variables (NCDS) III • Possible discrepancy at age 41/42 years: Partially complete fertility history collected • ^ Symbol reflects a ‘text fill’ – used in CAPI questionnaires. • Text fill used to tailor questionnaire to respondent. “Since 1991” meant to be applicable to all those present at age 33 years but not those missing. • Possible that this filter was used for those rejoining the study at age 41/42 and 46 years when not needed? • Build up evidence for this:

7. Deriving fertility variables (NCDS) IV • Evidence 1: Those rejoining the study had a lower number of births recorded before 1991 than those continuing. 6.3% of births recorded at 41/42 years occurred before previous interview for those continuing in the study 3.7% of births for those re-entering the study occurred before 1991 • Evidence 2: Those recorded as childless had children using information from other sources: Of 880 cohort members recorded as being childless at 41/42 years and not present at data collection at 33 years 12% had children living elsewhere (natural?) Conclusive proof: 44% had natural children over 9 years old living with them in household

8. Deriving fertility variables (NCDS) V • Evidence suggests that filter applied to both those continuing study and rejoining study. • In which case, fertility histories collected that do not include age 33 years may have to be capped or excluded:

9. Deriving fertility variables (NCDS) VI • New method gives following summary KM statistics: • More importantly, those detected as being possible parents at a later wave of data collection but with no accurate fertility history are censored at an earlier point – this applies to 430+ cohort members. Has implications for the whole fertility schedule for men and women. • This factor could be responsible for inflated estimates of childlessness among NCDS cohort members found in other sources. • The method used here results in slightly smaller sample but one that errs on the side of caution

10. Modelling fertility variables (NCDS & BCS70) Can see how highest hazard of entry into parenthood is reached among NCDS earlier than among BCS70 cohort. Inverse bathtub shape of hazard for NCDS. For BCS70, shape is a little more variable. However, this applies to whole distribution. Interest in my particular case is entry to early parenthood

11. Modelling fertility (NCDS & BCS70) I • Strategies for event history modelling using parenthood data: • Have continuous data (as opposed to discrete) – first stage in guiding model selection • Began with a Cox’s Proportional Hazards Model as find it intuitive and easier to compute and interpret. Also can use same model when hazard is different between data as no assumption made. • Basic model: • At each point, model is estimated through comparing the characteristics of an individual experiencing an event compared to those who remain in the risk set. • Used Tenure as an example to assess suitability. Tenure is a universal predictor in other models.

12. Modelling fertility (NCDS & BCS70) III • A fundamental assumption of Cox Proportional Hazard Model is that the Hazard remains proportional throughout the observation period. • Assessed validity of assumption graphically and through statistical test. Numerous ways of assessing graphically. According to the PH assumption, while difference in cumulative hazard would vary absolutely, difference in log cumulative hazard should remain constant with no systematic variation with time (Singer and Willett 2003)

13. Modelling fertility (NCDS & BCS70) III • Also tested PH assumption through Schoenfeld residual test – examining departure from 0. Significantly different suggests not Proportional e.g.: • Possible solutions • Limit observation time • Consider Using Time Varying Covariates • Consider using a different model

14. Modelling fertility (NCDS & BCS70) IV • Limiting observation time to between 16-20 years did work but against message and evidence presented in rest of thesis. • Using a time varying covariate is okay for Tenure as data supports this. However, may be poorer strategy in terms of data for larger models. Plus computationally difficult.

15. Modelling fertility (NCDS & BCS70) V • Stratification not really an option with my data – know that numerous factors predict early parenthood and potentially split sample. • Tried interacting Tenure with time to make the model explicitly non-proportional: where • Interaction terms are significant. However, in extended models interacting time with covariates will be computationally difficult and also difficult to interpret. • Use the AIC from these models to compare with other modelling strategies.

16. Modelling fertility (NCDS & BCS70) VI • Alternative modelling strategies. Want an alternative that: • Can be used for both genders and both cohorts • Know that hazards are not monotonic – want alternative that can deal with these. Can rule out PH models. Can rule out only monotonic models - Weibull, Gompertz and Exponential distributions (Wu and Chuang 2002) Left with 3 types of Accelerated Failure Time Models – Gamma, Log-logistic and Lognormal models

17. Modelling fertility (NCDS & BCS70) VII • Accelerated Failure Time Models analogous to simple linear model and do not model the hazard directly but model survival time. • Specification (distribution) for the δterm and intercept distinguishes between models – follow the normal, logistic or gamma distribution • Test these models using tenure and compare results using AIC (Akaike’s Information Criteria) to find best fit. • For NCDS, all three models produced very similar results. Little differentiation either in parameter values or model fitting statistics, as other studies (Kwong and Hutton 2003; Cleves, Gould et al. 2004; Ghilagaber 2005). AIC estimates for all three distributions are all similar and all substantially lower than the AIC for the best fitting Cox model constructed (inc Time interacted model).

19. Modelling fertility (NCDS & BCS70) X • When examining differences in AIC, Log-logistic gives marginally poorer fitting values consistently leaving choice between Gamma and Lognormal models. • Gamma model is particularly suitable for “bath-tub” shape distribution and used often in Demography for modelling mortality. Inverse is suitable for fertility and would be suitable for modelling whole NCDS fertility distribution. • However, as I am modelling early fertility then Gamma model not as suitable – tries to model concave shape when one not always present. • Therefore using Lognormal models to model entry into first parenthood in early adulthood

20. Modelling fertility (NCDS & BCS70) XI • Univariate results (Time Ratio) for 16-23 years:

22. Conclusions – challenges I found when modelling fertility • When deriving NCDS fertility variables need to acknowledge that participation at Wave 5 (Age 33 years) is crucial in determining inclusion criteria. • Failure to adjust for this leads to modest change in median survival time and larger changes in estimates of childlessness • CAPI filters? • Traditional Cox model was not suited to my data even after allowing for Time varying covariates etc • Final choice between Gamma and Lognormal Accelerated Failure Time models. Gamma more suitable for whole distribution; Lognormal for early parenthood