testing the performance of the two-fold fcs algorithm for multiple imputation of longitudinal...
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Testing the performance of the two-fold FCS algorithm for multiple imputation of
longitudinal clinical records
Catherine Welch1, Irene Petersen1, Jonathan Bartlett2, Ian White3, Richard Morris1, Louise Marston1, Kate Walters1,
Irwin Nazareth1 and James Carpenter2
1Department of Primary Care and Population Health, UCL2Department of Medical Statistics, LSHTM
3MRC Biostatistics, Cambridge Funding: MRC
The Health Improvement Network (THIN) primary care database
• GP records• 9 million patients over 15 years in 450 practices• Powerful data source for research into
coronary heart disease (CHD)• Studies complicated by missing data• Up to 38% of health indicator
measurements are missing in newly registered patients1
1Marston et al, 2010 Pharmacoepidemiology and Drug Safety
Partially observed data in THIN
• Missing data never intendedto be recorded
• Data recorded at irregular intervals
• Non-monotone missingness ppattern
Multiple Imputation (MI) and THIN
• Most MI designed for cross-sectional data• Impute both continuous and discrete variables at
many time points – Standard ICE using Stata struggles with this
• New method developed by Nevalainen et al – Two-fold fully conditional specification (FCS) algorithm– Imputes each time point separately– Uses information recorded before and after time point
Nevalainen et al, 2009 Statistics in Medicine
A graphical illustration of the two-fold FCS algorithm
Within-time iteration
Among-time iteration
),,,|( 1,1 ijijiimisij YXXXXf
Nevalainen et al, 2009 Statistics in Medicine
Algorithm validation
• Nevalainen et al– Proposed the two-fold FCS approach– Validated algorithm using data sampled from case-control– 3 time points included with a linear substantive model
• Our previous work
• Imputed data had accurate coefficients and acceptable level of variation in these settings
Simulation
• Before we apply the algorithm to THIN we want to test it in a complex setting similar to THIN
• Test algorithm in simulation study:– Create 1000 full datasets – Remove values– Apply two-fold FCS algorithm– Fit regression model for risk of CHD
• Full data• Complete case data• Imputed data
– Compare results
Advantages of using simulated data
• We know the original distributions so we can compare with distribution of imputed data and test for bias
• Create different scenarios to test the algorithm• Design data so it is close to THIN data
Simple dataset
• 5000 men, 10 years of data• CHD diagnosis from 2000 – yes/no• Age – 5 year age bands• Smoking status recorded in 2000
– smokers, ex- and non-smokers
• Anti-hypertensive drug prescription – yes/no• Systolic blood pressure (mmHg)• Weight (kg)• Townsend score quintile – 1 (least) to 5 (most)• Registration – indicate if patient registered in 1999
Results from exponential regression model
• Outcome : Time to CHD• Exposures in year 2000: age, Townsend score
quintile, weight, blood pressure, smoking status, anti-hypertensive drug treatment, registration in 1999
• Analysis of 1000 datasets
Generated data results
Variables THIN datalog risk
ratio
Full simulated data
Log risk ratio SE
Anti-hypertensive drug treatment
0.2935 0.2868 0.0957
Systolic blood pressure (mmHg)
0.0048 0.0049 0.0026
Weight (kg) 0.0019 0.0019 0.0032
Smoking status
Non-smoker
Reference
Ex-smoker
0.0679 0.0692 0.1074
Current smoker
0.2386 0.2385 0.1143
Adjusted for age, registration in 1999 and Townsend score quintile
Results of fitting exponential regression model
70% missing completely at random (MCAR) missingness mechanisms
• Missing data on blood pressure, weight, smoking• In THIN:
– 30 - 70% missing in any given year, • E.g. 70% missing equivalent to a health indicator recorded
approximately every 3 years
– If one variable is missing other variables also more likely to be missing
70% MCAR results
Variables THIN data Simulated dataLog risk
ratioFull data Complete case
Log risk ratio SE
Log risk ratio SE
Anti-hypertensive drug treatment
0.2935 0.2868 0.0957 0.2852 0.1931
Systolic blood pressure (mmHg)
0.0048 0.0049 0.0026 0.0051 0.0055
Weight (kg) 0.0019 0.0019 0.0032 0.0015 0.0062
Smoking status
Non-smoker
Reference
Ex-smoker
0.0679 0.0692 0.1074 0.0633 0.2151
Current smoker
0.2386 0.2385 0.1143 0.2307 0.2299
Adjusted for age, registration in 1999 and Townsend score quintile
Two-fold FCS algorithm
• Stata ICE – series of chained equations• 3 among-time iterations, 10 within-time iterations• Produce 3 imputed datasets• 1 year time window
i i+1 i+2 i+3i-3 i-2 i-1
Imputing time-independent variables
• Algorithm designed to impute time-dependent variables and does not account for imputing time-independent variables
• Smoking status in 2000 is a time-independent variable
• Need to extend algorithm for this
Imputing time-independent variables
• For each among-time iteration, time-independent variables imputed first
• Algorithm will be cycle through time points with smoking status included as an auxiliary variable.
Impute time-independentvariables
Results following imputation
• We would expect to see similar log risk ratios to the THIN data
• The standard errors for variables with no missing data will be close to those from the full data
• The standard errors for variables with missing data will be smaller to the complete case analysis but not recover to the size of the full data
Results following imputation
Variables THIN data Simulated dataLog risk
ratioFull data Complete case Imputed data
Log risk ratio SE
Log risk ratio SE
Log risk ratio SE
Anti-hypertensive drug treatment
0.2935 0.2868 0.0957 0.2852 0.1931 0.2848 0.1066
Systolic blood pressure (mmHg)
0.0048 0.0049 0.0026 0.0051 0.0055 0.0050 0.0052
Weight (kg) 0.0019 0.0019 0.0032 0.0015 0.0062 0.0023 0.0053
Smoking status
Non-smoker
Reference
Ex-smoker
0.0679 0.0692 0.1074 0.0633 0.2151 0.0654 0.2288
Current smoker
0.2386 0.2385 0.1143 0.2307 0.2299 0.2409 0.2453
Adjusted for age, registration in 1999 and Townsend score quintile
Results following imputation
Variables THIN data Simulated dataLog risk
ratioFull data Complete case Imputed data
Log risk ratio SE
Log risk ratio SE
Log risk ratio SE
Anti-hypertensive drug treatment
0.2935 0.2868 0.0957 0.2852 0.1931 0.2848 0.1066
Systolic blood pressure (mmHg)
0.0048 0.0049 0.0026 0.0051 0.0055 0.0050 0.0052
Weight (kg) 0.0019 0.0019 0.0032 0.0015 0.0062 0.0023 0.0053
Smoking status
Non-smoker
Reference
Ex-smoker
0.0679 0.0692 0.1074 0.0633 0.2151 0.0654 0.2288
Current smoker
0.2386 0.2385 0.1143 0.2307 0.2299 0.2409 0.2453
Adjusted for age, registration in 1999 and Townsend score quintile
Results following imputation
Variables THIN data Simulated dataLog risk
ratioFull data Complete case Imputed data
Log risk ratio SE
Log risk ratio SE
Log risk ratio SE
Anti-hypertensive drug treatment
0.2935 0.2868 0.0957 0.2852 0.1931 0.2848 0.1066
Systolic blood pressure (mmHg)
0.0048 0.0049 0.0026 0.0051 0.0055 0.0050 0.0052
Weight (kg) 0.0019 0.0019 0.0032 0.0015 0.0062 0.0023 0.0053
Smoking status
Non-smoker
Reference
Ex-smoker
0.0679 0.0692 0.1074 0.0633 0.2151 0.0654 0.2288
Current smoker
0.2386 0.2385 0.1143 0.2307 0.2299 0.2409 0.2453
Adjusted for age, registration in 1999 and Townsend score quintile
Results following imputation
Variables THIN data Simulated dataLog risk
ratioFull data Complete case Imputed data
Log risk ratio SE
Log risk ratio SE
Log risk ratio SE
Anti-hypertensive drug treatment
0.2935 0.2868 0.0957 0.2852 0.1931 0.2848 0.1066
Systolic blood pressure (mmHg)
0.0048 0.0049 0.0026 0.0051 0.0055 0.0050 0.0052
Weight (kg) 0.0019 0.0019 0.0032 0.0015 0.0062 0.0023 0.0053
Smoking status
Non-smoker
Reference
Ex-smoker
0.0679 0.0692 0.1074 0.0633 0.2151 0.0654 0.2288
Current smoker
0.2386 0.2385 0.1143 0.2307 0.2299 0.2409 0.2453
Adjusted for age, registration in 1999 and Townsend score quintile
Correlations
• Previous results imply accurate imputations for missing data in 2000
• Alternative method required:– Assess correlations between measurements recorded
at different times
• We would like to maintain the correlations structure in the generated and imputed data at all time points
Correlations
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Cor
rela
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2000 2001 2002 2003 2004 2005 2006 2007 2008 2009Year of weight measurement
correlated with weight measured in 2000
Full simulated data Imputed simulated data
Increase time window
• Increased the time window to 2 and 3 years• This slightly improves the estimates of coefficients
and SE
i i+1 i+2 i+3i-3 i-2 i-1
2 year time window
3 year time window
Increase time window
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2000 2001 2002 2003 2004 2005 2006 2007 2008 2009Year of weight measurement
correlated with weight measured in 2000
Full simulated data 1 year 2 years 3 years
In summary
• The two-fold FCS algorithm gives unbiased imputations with:– 70% missing data– Exponential regression model, and– MCAR missingness mechanisms
• The correlation structure is maintained as the time window increases
Discussion
• Algorithm effective because at least one measurement during follow-up
• Same results with MAR• Future work…
– Introduce censoring– Change smoking status to be time-dependent– Interactions