1. Understanding Non Response in the 1958 Birth Cohort
Tarek Mostafa, Brian Dodgeon & George B. Ploubidis

2. Outline Introduction to the National Child Development Study (NCDS)
Non-response in NCDS
The three stages strategy
Findings

3. The National Child Development Study (NCDS)
The NCDS follows the lives of all people born in England, Scotland and Wales in one week of March 1958
The target sample was augmented to include immigrants born in the same week, in the first three sweeps (ages 7, 11 and 16)
NCDS experienced attrition over time. Attrition is the discontinued participation of some individuals in a longitudinal survey

4. Response in NCDS

5. Non response in NCDS Types of non-response Wave 0 Wave 1 Wave 2 Wave 3
Birth
Age 7
Age 11
Age 16
Age 23
Age 33
Age 42
Age 46
Age 50
Age 55
Non-contact
223
1,042
410
786
1,867
1,529
1,832
612
835
664
Not issued
920
542
271
1,415
4,248
3,553
4,698
Refusal 80
797
1,151
1,160
1,776
1,148
1,448
1,214
582
Other unproductive
173
202
295
838
1,399
263
109
332
491
Not issued - emigrant
475
701
799
1,196
1,335
1,268
1,272
1,293
1,287
Not issued - dead
821
840
873
960
1,050
1,200
1,324
1,460
1,503
Ineligible 13 11 81
Total
1,143
3,133
3,221
3,904
6,021
7,089
7,139
9,024
8,768
9,225

6. Monotone vs. Non-monotone response
Response patterns
Freq.
Percent
Monotone
5688
30.64
Non-monotone
8329
44.89
All waves
4,541
24.47
Total
18558
100

7. Non-response bias - implications
Missing data:
1- Smaller samples, fewer transitions, incomplete histories. Loss of statistical power due to smaller samples
2- Biases in results: Disproportionate to some groups (mobile, disadvantaged, men, long working hours)

8. What can we do about attrition?
All principled methods rely on the MAR assumption and on the correct identification of predictors of response => maximise the plausibility of MAR
So far selection is arbitrary
Mainly birth characteristics, reflecting economic and social circumstances: SES, housing tenure, accommodation type, London vs. rest of the country…
Selection of predictors matters more for studies with more waves (more missing data)

9. Missing data strategy
Identify predictors of response at each wave of NCDS: Variables from each wave can only predict response on subsequent waves
Thousands of variables are available => selection is done in three stages
Pre – selection:
We exclude routed variables.
We exclude dead respondents from each wave – natural evolution of the sample
Analysis:
Stage 1: univariable regressions within wave
Stage 2: multivariable regressions within wave
Stage 3: multivariable regressions across waves

10. Stage 1: Univariable regressions
Predictors: waves 0 to 8 (including biomedical)
Response outcomes: waves 1 to 9 (including biomedical)
Univariable logistic regressions (one predictor at a time) to predict response in subsequent waves
Analytical sample=non-missing W0 predictors. N=15,150
N of regressions for: (wave0= 19*10); (wave5=100*5); …
The process is automated
Retained predictors with a significant impact on response at p<0.01
N of predictors W0 W1 W2 W3 W4 W5 W6
Biomed W7 W8
Birth
Age 7
Age 11
Age 16
Age 23
Age 33
Age 42
Age 45
Age 46
Age 50
Stage 1 (input) 19 50 48 58 73
100
276 81
155
194

11. Stage 2: Multivariable regressions within wave.
N of predictors W0 W1 W2 W3 W4 W5 W6
Biomed W7 W8
Birth
Age 7
Age 11
Age 16
Age 23
Age 33
Age 42
Age 45
Age 46
Age 50
Stage 1 (input) 19 50 48 58 73
100
276 81
155
194
Stage 2 (input) 11 36 34 47 68
114 39 53
120
N of predictors is reduced after stage 1
Stage 2 consists of multivariable regressions using all predictors from same wave (i.e. 11 for W0, 36 for W1, 120 for W8) that were retained after Stage 1
Variables compete against each other within wave
Using log binomial models (since outcome not always rare)
Retain variables significant at p<0.05
This results in different subsets of predictors from each wave depending on the response outcome

12. Stage 3: Multivariable regressions across waves.
N of predictors W0 W1 W2 W3 W4 W5 W6
Biomed W7 W8
Birth
Age 7
Age 11
Age 16
Age 23
Age 33
Age 42
Age 45
Age 46
Age 50
Stage 1 (input) 19 50 48 58 73
100
276 81
155
194
Stage 2 (input) 11 36 34 47 68
114 39 53
120
Variables entering stage 3:
At this stage we let predictors from different waves compete against each other (e.g. subset of predictors from W0 and W1 predict response in W2; subset of predictors from W0, 1, 2, 3, 4 predict response in W5, …)
Challenge: predictors from different waves => different levels of missingness (due to non-response over time). Predictors from earlier waves are more complete
N of predictors
Resp 1
Resp 2
Resp 3
Resp 4
Resp 5
Resp 6
Biomed
Resp 7
Resp 8
Resp 9
Age 7
Age 11
Age 16
Age 23
Age 33
Age 42
Age 45
Age 46
Age 50
Age 55
Stage 3 (input) 4 13 23 36 52 54 81 86 88
116

13. Stage 3: Multivariable regressions across waves (continued).
Solution: progressive imputation and alternation of MI and response modelling
We impute missing predictors then estimate response models and so on for each wave
Example W2
MI with chained equations and response modelling with log binomial models.
=> Set of predictors of response in each wave (sig at p<0.05). For each response outcome, the predictors can include variables from any previous wave

14. Results from stage 3
The number of predictors of response at each wave is reduced
Predictors include all types of variables: Social, economic, health, and survey related (cooperation with sub-studies)
N of predictors
Resp 1
Resp 2
Resp 3
Resp 4
Resp 5
Resp 6
Biomed
Resp 7
Resp 8
Resp 9
Age 7
Age 11
Age 16
Age 23
Age 33
Age 42
Age 45
Age 46
Age 50
Age 55
Stage 3: input 4 13 23 36 52 54 81 86 88
116
Stage 3: output 9 11 17 24 18 40 34 35 39

15. Examples of predictors for Wave 3 (age 16)
Smoking prior to pregnancy (wave 0, birth)
Physical exercise problems (balance etc) (wave 2, age 11)
Social class of mother's husband (wave 0, birth)
Outpatient Clinic attendances (wave 1, age 7)
Number of  kids aged under 21 in household, including those living away from home (wave 1, age 7)

16. Examples of predictors for Wave 5 (age 33)
Age at birth of first child (wave 4, age 23)
Recoded education apprenticeship and training (wave 4, age 23)
Moved between NCDS4 (age 23) and NCDS5 (age 33) (wave 4, age 23)
Couples joint social class (wave 4, age 23)

17. Examples of predictors for Wave 6 (age 42)
Type of accommodation (wave 4, age 23)
General motor handicap (wave 3, age 16)
Couples joint social class (wave 4, age 23)
Region at NCDS3 (wave 3, age 16)
Current main economic activity (wave 5, age 33)

18. Examples of predictors for Wave 9 (age 55)
Benefits currently received by CM or partner (wave 6, age 42)
Housing tenure (wave 6, age 42)
If CM participated in NCDS5 (wave 5, age 33)
Consent to ESRC archive (wave biomed)
Region at NCDS3 (wave 3, age 16)

19. Conclusions
It is possible to systematically identify predictors of response (maximise the MAR assumption)
Identified predictors of response can be used in any substantive analysis with methods that operate under the MAR assumption
The work will be expanded to the other CLS cohort studies (next will be MCS)
We will provide a list of predictors for each wave and advise researchers on their use
But! We are not suggesting that all these predictors of response should be used
Test different sets/blocks of predictors of response
Watch this space, but probably ok to use early life predictors only
Work in progress- We are planning to augment our “traditional” statistical approach on variable selection with machine learning (SuperLearner) and other procedures Least Absolute Shrinkage and Selection Operator (LASSO)

20. Thank you for your attention!