Objectives To evaluate the impact of treatments for overdose of heroin on mortality a prospective cohort study was carried out for 18 months in Italy. A total of 10,258 heroin users were recruited and detailed information on each treatment episode was collected. Within a year from the end of the study, the number of deaths of the study subjects almost doubled. These deaths were not included in the original analysis, because their treatment at the time of death was unknown. To incorporate this extra information on mortality into the analysis, we used a multiple imputation scheme. Methods We estimate a matrix of transition probabilities using the empirical treatment distribution from the first 18 months of the study to create 600 datasets in which the missing data are imputed. At the last step we apply a Cox model to each of the completed datasets in which we adjust for severity of drug-dependence. We summarise the results to get the overall estimates for the treatment effects on mortality. To validate the multiple imputation approach we use three different strategies: (i) we adopt a more complex probabilistic model, (ii) we use the model to impute “observed data”, and (iii) we compare results from the model to those collected on a sub-cohort for which a complete follow-up was available. Results The average percentage of imputed person years in “out of treatment” time is larger compared to the observed one (over the first 18 months), while the average percentage of imputed person years in “methadone maintenance” and “methadone detoxification” is reduced. These differences are expected, since these two treatments are mostly used in new patients that enter the study, and in our case we imputed data for the existing patients. The Cox model applied to the completed data set produces similar estimates to the ones reported in the original analysis. The three used validation models show the robustness of the adopted one. Conclusions The imputation model produced similar results to the listwise-deletion analysis, while reducing the risk of bias. We show multiple imputations to be an easily applicable choice in the treatment of missing values in epidemiological studies.
Using multiple imputations to handle missing data: a national multicenter study of heroin dependents to evaluate the impact of treatments on mortality
VIGNA-TAGLIANTI, Federica
2007-01-01
Abstract
Objectives To evaluate the impact of treatments for overdose of heroin on mortality a prospective cohort study was carried out for 18 months in Italy. A total of 10,258 heroin users were recruited and detailed information on each treatment episode was collected. Within a year from the end of the study, the number of deaths of the study subjects almost doubled. These deaths were not included in the original analysis, because their treatment at the time of death was unknown. To incorporate this extra information on mortality into the analysis, we used a multiple imputation scheme. Methods We estimate a matrix of transition probabilities using the empirical treatment distribution from the first 18 months of the study to create 600 datasets in which the missing data are imputed. At the last step we apply a Cox model to each of the completed datasets in which we adjust for severity of drug-dependence. We summarise the results to get the overall estimates for the treatment effects on mortality. To validate the multiple imputation approach we use three different strategies: (i) we adopt a more complex probabilistic model, (ii) we use the model to impute “observed data”, and (iii) we compare results from the model to those collected on a sub-cohort for which a complete follow-up was available. Results The average percentage of imputed person years in “out of treatment” time is larger compared to the observed one (over the first 18 months), while the average percentage of imputed person years in “methadone maintenance” and “methadone detoxification” is reduced. These differences are expected, since these two treatments are mostly used in new patients that enter the study, and in our case we imputed data for the existing patients. The Cox model applied to the completed data set produces similar estimates to the ones reported in the original analysis. The three used validation models show the robustness of the adopted one. Conclusions The imputation model produced similar results to the listwise-deletion analysis, while reducing the risk of bias. We show multiple imputations to be an easily applicable choice in the treatment of missing values in epidemiological studies.
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