Assessing outcomes of large-scale public health interventions in the absence of baseline data using a mixture of Cox and binomial regressions

Large-scale public health interventions with rapid scale-up are increasingly being implemented worldwide. Such implementation allows for a large target population to be reached in a short period of time. But when the time comes to investigate the effectiveness of these interventions, the rapid scale-up creates several methodological challenges, such as the lack of baseline data and the absence of control groups. One example of such an intervention is Avahan, the India HIV/AIDS initiative of the Bill & Melinda Gates Foundation. One question of interest is the effect of Avahan on condom use by female sex workers with their clients. By retrospectively reconstructing condom use and sex work history from survey data, it is possible to estimate how condom use rates evolve over time. However formal inference about how this rate changes at a given point in calendar time remains challenging.

We propose a new statistical procedure based on a mixture of binomial regression and Cox regression. We compare this new method to an existing approach based on generalized estimating equations through simulations and application to Indian data.

Both methods are unbiased, but the proposed method is more powerful than the existing method, especially when initial condom use is high. When applied to the Indian data, the new method mostly agrees with the existing method, but seems to have corrected some implausible results of the latter in a few districts. We also show how the new method can be used to analyze the data of all districts combined.

The use of both methods can be recommended for exploratory data analysis. However for formal statistical inference, the new method has better power.