Using follow-up data to adjust for selective non-participation in cross-sectional setting

Transcription

1 Using follow-up data to adjust for selective non-participation in cross-sectional setting Juho Kopra University of Jyväskylä Department of Mathematics and Statistics NoPaHES-project 30th August

2 from cross-sectional surveys (Finrisk studies) No re-contact data is available for Previous solution cannot be used. Instead, we utilize the follow-up data about the smoking-related diseases: Lung cancer and Chronic Obstructive Pulmonary Disease (COPD, keuhkoahtaumatauti in Finnish). 2

3 we utilized from FINRISK studies: People aged years-old (30-59 years-old for 1972 and 1977). from 1972, 1977, 1982, 1987, 1992, 1997, 2002 and We use two areas of Finland: Northern Karelia and North Savonia. In total, the data contain 52,325 persons including 9,928 persons with missing smoking indicator. 3

4 Variables provided by FINRISK survey samples Background knowledge for both participants and non-participants: Area, Age, Gender and Study year. Self-reported indicator of daily smoking. 4

5 Combining information from the National Hospitalization Register and Cause of Death Register, we build a follow-up: Up to the end of Available for both participants and non-participants. Persons age at the time of diagnosis (lung cancer or COPD). Death to other causes and the end of the follow-up are treated as censoring. Persons with no diagnosis have censoring. 5

6 Bayesian methodology (very) briefly Modelling using survival data and 6

7 Bayesian methodology (very) briefly Modelling using survival data and Bayesian methodology (very) briefly Bayesian approach combines the information provided by the data (via likelihood function) and subjective information about parameters of the model (via prior distribution). The scientist decides the prior distributions he wants to use. Results are called posterior distribution, which represents the combination of prior and the data. 7

8 Bayesian methodology (very) briefly Modelling using survival data and We utilized uninformative priors for most of the parameters (not all). The informative priors we used allow identifiability of our model while restricting the unrealistic posterior prevalences. 8

9 9 Modelling 1/2 Use to estimate smoking prevalence based on the survival (follow-up) data. Build a model from three submodels: 1. Participation M given smoking Y and background information X: P (M X, Y ) 2. Smoking Y given the background information X: P (Y X). 3. Survival model for lung cancer or COPD disease age T given smoking Y and background information X: P (T X, Y ) Define an informative prior regarding submodel 1 to allow identifiability, and estimate the posterior for smoking prevalence. Fit the model and simultaneously impute the missing smoking indicators Ỹ P (Y M = 0, X, T )

10 Bayesian methodology (very) briefly Modelling using survival data and Modelling 2/2 Participation P (M X, Y ) is modelled using a logistic distribution explained by gender, study year, age, region and smoking Smoking P (Y X) is modelled using a logistic distribution explained by year of birth. Coefficients vary by gender, region and study year. Survival model for follow-up data P (T X, Y ) uses piecewise constant hasard model. The survival is explained by gender and smoking. 10

11 Bayesian methodology (very) briefly Modelling using survival data and Prior distributions Participation model: Informative prior is required for the η which models how smoking affects participation. η Logistic(µ = 0, s = ) Risk factor model: Uninformative priors; N(0, 1000). Survival model: Baseline hasard is a priori monotonically increasing. Others are uninformative priors; N(0, 1000). 11

12 Bayesian methodology (very) briefly Modelling using survival data and Model fitting Models were implemented with Just Another Gibbs Sampler -software (JAGS). (Plummer, 2003) The imputations for smoking indicator Y i are drawn from fully conditional distribution P (Y i M i = 0, X i, T i ). The model fitting took 107 hours to complete (five days). The high absolute number of missing values (9,928) and computationally intensive algorithm (MCMC) explains the long running time. 12

13 Bayesian methodology (very) briefly Modelling using survival data and Simulation experiment We generated randomly one data from the model we use. Model appears to be able to restore the original trends from the data. 13

14 Trend estimates for the simulated data: North Karelia men North Karelia women proportion of smokers participants only true trends 95 % credible interval proportion of smokers Northern Savonia men Northern Savonia women proportion of smokers proportion of smokers

15 Trend estimates for the FINRISK data: North Karelia men North Karelia women proportion of smokers participants only 95 % credible interval proportion of smokers Northern Savonia men Northern Savonia women proportion of smokers proportion of smokers

16 Follow-up data can be used in to estimate the prevalence of smoking although the survey data suffer from selective non-participation. Long register-based follow-up is required. For the later years, which do not have lengthy follow-up, modelling assumptions can be made to provide different scenarios. (2007 and 2012 luckily have re-contact data) Bayesian model fitting requires informative prior and is computationally very demanding with large absolute amount of missing values. 16

17 THANKS 17

18 References Bayesian models for data missing not at random in health examination surveys. Juho Kopra, Juha Karvanen and Tommi Härkänen. Accepted for publication in Statistical Modelling. Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing. 124, p Wien, Austria: Technische Universit at Wien. 18