Summary of main findings
Of the 818 families who participated in SPARCLE1, 594 (73%) participated in SPARCLE2. The attrition of 27% between SPARCLE1 and SPARCLE2 was higher than the anticipated rate of 20% .
In order to maintain statistical power for cross-sectional analyses and possible further follow-up in adulthood, we had planned to approach 270 further families, anticipating a response rate of 63% as in SPARCLE1, which would have yielded 170 more participants . However, of the 262 additional families who were targeted using population-based registers, only 63 (24%) agreed to participate, in marked contrast to the response rate of 63% in SPARCLE1 . This disappointing response rate was partly due to targeting 81 families who had been sampled for SPARCLE1 but who had not participated, either because they were untraceable or had declined to participate; only nine (11%) of these families participated in SPARCLE2.
Hence the final cross-sectional sample size was lower than in SPARCLE1, both overall (667 families in SPARCLE2 compared to 818 families in SPARCLE1) and in all regions. The poorer response rate in SPARCLE2 may be a consequence both of families with younger children having a greater propensity to participate in surveys than those with older children  and of a lower response rate in more recent years .
Predictors of drop-out
The predictors of each category of non-response are relevant to the design of future surveys.
Rates of tracing varied between regions and, overall, parents with higher educational qualifications were easier to trace. However, educational qualifications may be a surrogate for socio-economic status, which we did not record because of the difficulties in obtaining a measure that was valid in all countries in the study.
Rates of refusal of traced families likewise varied between regions, parents with higher educational qualifications being more likely to agree to participate. Additionally, if parents had been more stressed when visited in SPARCLE1 or if they had not completed the stress questionnaire, they were more likely to decline to participate in SPARCLE2. Refusal rates varied with the level of the child's walking ability but showed no clear trend with severity of impairment, although parents of less impaired children were generally less willing to participate.
Drop-out due to death was much more common among more severely impaired children, in particular those with feeding and cognitive problems.
Predictors of overall non-response are of interest in the analysis and interpretation of SPARCLE2. They reflected the predictors of the main categories of non-response: failure to trace and refusal to participate. Hence parental educational qualifications and region, which were associated with both these categories of non-response, were strong predictors of overall non-response. Parental stress was also a predictor of overall non-response, although it was a statistically significant predictor only of refusal and not of non-traceability. Parents who were living together but not married and parents who were single (or separated) and living with their own parents were also under-represented in SPARCLE2. This finding is difficult to interpret. It appeared to be due to a combination of factors which were not significant when considered separately: these groups tended to be more difficult to trace, more likely to decline to participate if traced, and their children were more likely to die. It is possible that a difficult family situation, for example a child having poor health, could lead not only to stress – which we found was associated with refusal to participate – but also to marriage break-down, precipitating parents to move in with other partners or with their own parents and hence becoming more difficult to trace.
Although families with more impaired children were more likely to drop out because the child died, severity of impairment was not a significant predictor of overall non-response, partly because death was not a major cause of non-response and partly because parents of living children were more willing to participate if their child was more impaired.
The significant predictors – parental education and stress, family structure and region – may also have been associated with non-response in SPARCLE1 and with non-response of new families approached in SPARCLE2. However, as minimal data about the children and their families were recorded on the registers, we were unable to demonstrate such associations.
Representativeness of sample
Missing data may be classified as: Missing at Random (MAR), if the probability that an observation is missing depends only on observed values and not on missing values, i.e. the missing values behave like a random sample of all values within subclasses defined by the observed data; or Missing Not at Random (MNAR) . A special case of MAR occurs if the missing values are a simple random sample of all data values; in this case, the data are referred to as Missing Completely at Random. For data that are MAR, statistical adjustment such as use of non-response weights can yield unbiased estimates of effects despite the missing data; for MNAR data, this is not possible. However, although it is often assumed that data are MAR, no way to directly test this assumption is available . In the context of SPARCLE, the danger is that non-respondents may have a systematically different quality of life or a different level of participation from respondents, which would invalidate estimates that assume data are MAR. On the other hand, the strength of our analysis of drop-out between SPARCLE1 and SPARCLE2 is that SPARCLE1 provided a wealth of information that could be used to predict drop-out in SPARCLE2 and hence to facilitate estimates that would be valid under the MAR assumption.
The target population, who were selected at random from population-based registers in Denmark, France, Italy, Sweden and the UK, can be regarded as representative of children with cerebral palsy. We cannot be sure that the German participants, who were recruited in other ways because that region did not maintain a population-based register, constitute a representative sample. The distribution of impairment and gender did not differ significantly between the German participants and the target population in other regions but a high proportion of German participants were interviewed before they had reached the prescribed age.
Use of sampling weights
Use of sampling weights is essential to estimate population prevalences from the sample. However, the primary objective of SPARCLE is to estimate associations between outcomes and explanatory variables. Sampling weights may or may not be required to produce unbiased estimates of these associations . If an estimate is valid with or without weights, the weighted estimate will typically be less precise. In general, an unweighted estimate is valid if the simple linear regression model holds, i.e. if it is valid to assume homoscedasticity, no interactions between explanatory variables, no omitted predictors and the sampling rate does not depend on the outcome variable [7, 24]. Therefore, it is essential to conduct the usual checks of any unweighted regression models.
In analyses of the longitudinal sample, sampling weights may be used in order to allow both for the sampling strategy, which varied between regions and levels of walking ability, and for the variation in non-response between regions; they are likely to increase the variance of estimates by about a third. Alternatively, analyses could be adjusted for region and walking ability. In calculating sampling weights, we were unable to allow for differential non-response according to parental educational qualifications, family structure and stress, as such weights would have resulted in an unacceptable increase in the variance of estimates. Additional analyses should therefore be performed, with and without adjusting for these variables, and the estimates compared. Such analyses should demonstrate the effect of any differential non-response, assuming that data are missing at random within cells defined by these variables .
The diversity of sources making up the cross-sectional group makes it doubtful that appropriate sampling weights can be used. Sampling weights would probably increase the variance of estimates by about three-quarters, reflecting the small numbers of families who entered SPARCLE2 by each route in the supplementary sample, so adjustment for factors that determined the sampling design and non-response – region, walking ability, parental educational qualifications, family structure and stress – may be preferable .
Comparison with other studies
We compared our findings with those of other surveys that targeted specific families in order to conduct face-to-face interviews [6, 26, 27].
Foster reported that non-contact rates were higher if the head of the household was single; we found no such association, probably because we had a much smaller sample . Goodman reported that non-contact rates were higher in areas of greater deprivation ; we did not have a measure of deprivation, but we did find higher non-contact rates among parents with lower educational qualifications, which may be correlated with living in a deprived area.
Both Foster and de Winter reported that refusal of traced families was higher if the head of the household had lower educational qualifications [6, 27], consistent with our findings. Goodman reported that parent refusal rates were marginally higher in areas of greater deprivation and child refusal rates increased steadily with increasing deprivation ; we found refusal rates were higher if parents had lower educational qualification or were more stressed, factors which may be associated with greater deprivation. De Winter reported higher refusal rates if the child was a boy or had unsatisfactory school performance ; we found no effect for gender and we had no measure of the child's school performance, although this may be associated with parental stress. Groves and Couper reported higher refusal rates among single person households and in urban areas ; we found no such associations, which may either be due to our smaller sample size or to different determinants of refusal in Europe and the U.S.; they also reported lower refusal rates among households with children under five years old and among households with younger adults; such an effect could partly explain the higher refusal rate in SPARCLE2 than SPARCLE1.