Workshop on Adjusting for Non-Ignorable Missing Data using Heckman-Type Selection Models

Workshop on Adjusting for Non-Ignorable Missing Data using Heckman-Type Selection Models

Harvard University, September 8^th 2015 0900 – 1800

Background

Missing data is common problem in survey data, and standard approaches for dealing with this issue rely on the strong and generally untestable assumption that data are ignorable (missing at random) once we condition on the observed characteristics of respondents. The assumption of missing at random is often implausible, including in contexts where the outcome itself may be a predictor of survey participation. For example, estimates of HIV prevalence which rely on data collected from blood tests taken from respondents in nationally representative household surveys may be affected by selection bias if those who are HIV positive are less likely to participate in testing. Then, conventional adjustments for missing data, such as using imputation or inverse-probability weighting, will result in biased estimates because of an incorrect assumption of missing at random. Standard approaches are also likely to result in confidence intervals which are too narrow because they ignore the uncertainty surrounding the unknown relationship between participation and the outcome, which needs to be estimated.    

Workshop

This workshop will introduce the use of Heckman-type Selection models for adjusting for non-ignorable missing data with the goal of making this approach easily accessible to researchers working with survey data affected by non-participation. A non-technical introduction to different approaches for dealing with missing data will be provided, and we will discuss the implications of not correctly adjusting for missing data which are not missing at random. We will provide an overview of the statistical rationale for the use of selection models, and the R package SemiParBIVProbit will be presented. This software allows researchers to implement this approach in a straightforward and transparent manner in a variety of different contexts affected by missing data. A simulation study will also be used to demonstrate the properties of the model. The final session will be interactive where participants are invited to bring their own datasets, and the audience and presenters will work together on implementing this approach in their own research. Alternatively, the organizers will provide example data. Throughout, we will illustrate the key concepts using data from HIV research.

Invitation

The workshop is free and open to all interested parties, however space is limited so if you would like to attend please register with Mark McGovern (mcgovern@hsph.harvard.edu). The workshop will take place at Harvard on September 8^th, exact location to be confirmed. Unfortunately we do not have the funds to cover expenses of participants.

Organizers

Harvard University: Till Bärnighausen, Guy Harling, Mark McGovern

University College London: Giampiero Marra

University of London Birbeck: Rosalba Radice

Agenda

Time	Topic
0900-0930	Introductions and Background
0930-1015	Implications of Non-Ignorable Missing Data for Parameter Estimates
1015-1030	Break
1030-1130	Introduction to Selection Models
1130-1230	Overview of Applications of Selection Models
1230-1300	Lunch
1300-1330	Optional Session on Getting Started with R
1330-1415	Introduction to R Package SemiParBIVProbit
1415-1445	Simulation Studies
1445-1500	Break
1500-1800	Interactive session with Data from Participants or Data Provided by Organizers

Key References

Bärnighausen, T., Bor, J., Wandira-Kazibwe, S., & Canning, D. (2011). Correcting HIV Prevalence Estimates for Survey Nonparticipation using Heckman-type Selection Models. Epidemiology, 22(1), 27-35. http://www.ncbi.nlm.nih.gov/pubmed/21150352

 

Marra, G., Radice, R., Till, B., Wood, S., McGovern, M., 2015. A Unified Modeling Approach to Estimating HIV Prevalence in Sub-Saharan African Countries. Research Report 324, Department of Statistical Science, University College London. http://www.ucl.ac.uk/statistics/research/pdfs/rr324.pdf

McGovern, M., Bärnighausen, T., Marra, G., Radice, R., 2015. On the Assumption of Bivariate Normality in Selection Models: A Copula Approach Applied to Estimating HIV Prevalence. Epidemiology 26, 229–327. http://www.ncbi.nlm.nih.gov/pubmed/25643102

 

Marra, Giampiero, and Rosalba Radice, 2015. A Regression Modeling Framework for Analyzing Bivariate Binary Data: The R Package SemiParBIVProbit. http://www.homepages.ucl.ac.uk/~ucakgm0/SemiParB.pdf

 

McGovern, M. E., Bärnighausen, T., Salomon, J. A., & Canning, D. (2015). Using Interviewer Random Effects to Remove Selection Bias from HIV Prevalence Estimates. BMC Medical Research Methodology, 15(1), 8. http://www.biomedcentral.com/1471-2288/15/8/

On the Assumption of Bivariate Normality in Selection Models: A Copula Approach Applied to Estimating HIV Prevalence

On the Assumption of Bivariate Normality in Selection Models: A Copula Approach Applied to Estimating HIV Prevalence

McGovern, Mark E.; Bärnighausen, Till; Marra, Giampiero; Radice, Rosalba, Epidemiology. 26(2):229-237, March 2015.

Abstract

Background: Heckman-type selection models have been used to control HIV prevalence estimates for selection bias when participation in HIV testing and HIV status are associated after controlling for observed variables. These models typically rely on the strong assumption that the error terms in the participation and the outcome equations that comprise the model are distributed as bivariate normal.

Methods: We introduce a novel approach for relaxing the bivariate normality assumption in selection models using copula functions. We apply this method to estimating HIV prevalence and new confidence intervals (CI) in the 2007 Zambia Demographic and Health Survey (DHS) by using interviewer identity as the selection variable that predicts participation (consent to test) but not the outcome (HIV status).

Results: We show in a simulation study that selection models can generate biased results when the bivariate normality assumption is violated. In the 2007 Zambia DHS, HIV prevalence estimates are similar irrespective of the structure of the association assumed between participation and outcome. For men, we estimate a population HIV prevalence of 21% (95% CI = 16%–25%) compared with 12% (11%–13%) among those who consented to be tested; for women, the corresponding figures are 19% (13%–24%) and 16% (15%–17%).

Conclusions: Copula approaches to Heckman-type selection models are a useful addition to the methodological toolkit of HIV epidemiology and of epidemiology in general. We develop the use of this approach to systematically evaluate the robustness of HIV prevalence estimates based on selection models, both empirically and in a simulation study.

http://journals.lww.com/epidem/Abstract/2015/03000/On_the_Assumption_of_Bivariate_Normality_in.16.aspx

The Economics of HIV/AIDS in Low-Income Countries: The Case for Prevention

The Economics of HIV/AIDS in Low-Income Countries: The Case for Prevention

David Canning

Journal of Economic Perspectives, 2006, 20(3): 121–142.
DOI:10.1257/jep.20.3.121


Abstract
There are two approaches to reducing the burden of sickness and death associated with the human immunodeficiency virus (HIV), which leads to acquired immunodeficiency syndrome (AIDS): treatment and prevention. Despite large international aid flows for HIV/AIDS, the needs for prevention and treatment in low- and middle-income countries outstrip the resources available. Thus, it becomes necessary to set priorities. With limited resources, should the focus of efforts to combat HIV/AIDS be on prevention or treatment? I discuss the range of prevention and treatment alternatives and examine their cost effectiveness. I consider various arguments that have been raised against the use of cost-effectiveness analysis in setting public policy priorities for the response to HIV/AIDS in developing countries. I conclude that promoting AIDS treatment using antiretrovirals in resource-constrained countries comes at a huge cost in terms of avoidable deaths that could be prevented through interventions that would substantially lower the scale of the epidemic.

http://www.aeaweb.org/articles.php?doi=10.1257/jep.20.3.121

Criminal Prosecution and HIV-related Risky Behavior

There has been a serious debate in the UK about whether the transmission of HIV should be a prosecutable offence. This is especially the case after a couple of high profile cases resulted in prosecution, in Scotland in '01 for 'reckless injury' and soon after in England and Wales for 'reckless transmission'. This has led to a lot of speculation in the UK about what the public health consequences of taking a stringent or lenient view of HIV transmission may be. The main concern being that taking a hard line may discourage both disclosure to partners and also people coming forward for testing or voicing their potential concerns to GP's and psychologists.

Delavande,Goldman and Sood (2008) are the first to empirically investigate the potential consequences of prosecutions for HIV transmission. They use U.S. inter-state variation in prosecution rate, from a limited sample of just 316 prosecutions for this crime and categorise states into those with 'strict' or 'non-strict' enforcement of laws which would permit prosecution. They then use a nationally representative survey of the sexual risk behaviours of 1,400 people with HIV to see is there a relationship between state type and risk behaviour. Interestingly, they find that in 'strict' states safe sex is practiced more often by those with HIV as is abstinence. They go on to claim that transmission rates should be 'responsive to agressive prosecution' and if the prosectution rate for HIV is doubled then the number of new infections will be reduced by a third in 10 years.

Looking at the figures I don't think it can control fully for the effects of the 'elephant in the room' in this paper which is that those in stict states are more likely to visit prostitutes and more than twice as likely not to disclose their HIV status to any of their last 5 partners. It is very difficult to know the extent of the knock on effects this can have on new infections and it may indeed wipe out the potential effects of more safe sex and more abstinence, the latter which probably shouldn't be the goal for a HIV intervention anyway. However, we have to be very careful before advocating criminalisation in the case of HIV transmission and framing the argument in term of a welfare enhancing 'tax on risky behaviour' could have some dangerous consequences down the line both in terms of the welfare of those with HIV and the number of new infections criminalisation may cause. Because criminalisation may disincentivise testing it is also difficult to separate this effect from the potential effect it may have on reducing new infections. More work on this is definitely needed but it is worth noting that WHO and European Commission guidelines going back three decades have stated that it is an ethical obligation on the part of those with HIV to disclose to potential or existing partners, but that this should not translate into a legal obligation as such legislation would be 'inappropriate ad impractical'.