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Adam Howes edited this page Apr 20, 2022 · 17 revisions

Improving the estimates for FSW

  • Biases and variation in methodology for key population data which vary by country. Survey estimates have more comparable methodology but depending on KP features (for example proportion in households included in survey sampling frame) may have varying bias. See working paper "Laga - Mapping the population size of female sex worker in countries across sub-Saharan Africa"
  • Survey question "did you have sex in exchange for money or goods" has been critisied. Likely too broad with regard to key population of female sex workers
    • Only the most recent round of DHS has this survey question (change was made in 2013 and started to be implemented in 2015, although this may vary by country with some countries still not using this question). Alternative question regards last three sexual partners
  • Other sources of data about key populations
    • The UNAIDS Key Population Atlas
    • Johnston et al. (2021, preprint) Deriving and interpreting population size estimates for adolescent and young key populations at higher risk of HIV transmission: men who have sex with men, female sex workers and transgender persons
      • Disaggregates the UNAIDS published population size estimates by age using proportion of sexually active adults
      • Kinh is a coauthor
        • Warns that the estimates should be seen as expert opinion rather than based on data
        • Several countries had no data
        • Rounding up when the number is too small
    • Laga et al. (2021, preprint) Mapping female sex worker prevalence (aged 15-49 years) in sub-Saharan Africa
      • Has code and data
      • Jeff is a coauthor
        • Variation across countries may be implausibly large
        • Uses study type random effects but implementation differences even within studies belonging to the same group likely to be large
  • Possible approaches
    • Move all sexpaid12m into sexnonreg, then get the FSW estimates from other data sources. Is there a way to integrate this data in a coherent way?
    • Use the sexpaid12m data to learn the spatial pattern and the other data sources to learn the level
  • Is there a coherent way to use existing estimates? Penalise distance from existing estimates equivalent to placing a prior on estimate?
    • Sounds similar to Bayesian melding, but implementing Bayesian melding is intractable for all but the simplest models
    • Can we get distributions or standard errors on the existing estimates? Not for Johnston
    • Work of Jon Wakefield / Taylor Okonek on calibration of estimates?
  • Other possible data source on men who paid for sex
    • See Hodgkins et al. (2021, preprint)
    • The proportion of men who pay for sex (CFSW) can be estimated from the data, and then this can be linked to the proportion of FSW by some model like p_{CFSW} = B * p_{FSW} where a strongly informative prior is placed on B (around 10 say)
  • Fully Bayesian benchmarking of small area estimation models (Zhang and Bryant, 2020)
    • Zhang and Bryant have quite a few papers which look interesting

Resources

Gaussian Markov Kronecker random fields

R-INLA's group argument allows specifying Gaussian Kronecker product random fields with covariance given as the Kronecker product of between group and within group covariance matrices. If A (m x n) and B (p x q) are matrices then their Kronecker product C (pm x qn) is the block matrix

C = [a_11 B ... a_1n B]
    [...    ...    ...]
    [a_m1 B ... a_mn B]

Within-group is controlled by f(), and between group is controlled by the control.group argument. See https://becarioprecario.bitbucket.io/inla-gitbook/ch-temporal.html#sec:spacetime.

Often the group argument is used to define (separable) spatiotemporal covariance structures. Following e.g. Blangiardo and Cameletti (2015), let delta_it be spatio-temporal interaction random effects. Knorr-Held (2000) present four ways to specify the structure matrix R_delta, where in the following R_space and R_time refer to spatially or temporally structured random effects and I_space and I_time unstructured random effects:

  • Type I: I_space (x) I_time f(spacetime, model = "iid")
  • Type II: I_space (x) R_time f(space, model = "iid", group = time, control.group = list(model = "rw1"))
  • Type III: R_space (x) I_time f(time, model = "iid", group = space, control.group = list(model = "besag"))
  • Type IV: R_space (x) R_time f(space, model = "besag", group = time, control.group = list(model = "rw1"))

We use the group option to define random effects for each of the multinomial categories. For example, setting f(sur_idx) with group = cat_idx gives the grouped survey random effects for each category.

Additional constraints

Interaction random effects should be constrained such that the sum over the non-category index is zero. For example, in each category the sum over ages of \alpha_{ak} should be zero:

\sum_a \alpha_{ak} = 0 \forall k = 1, ..., K

Intuition for this constraint is as follows. Suppose that the sum over age groups in category k is non-zero.

\sum_a \alpha_{a1} = C_1,
...
\sum_a \alpha_{ak} = C_k,
...
\sum_a \alpha_{aK} = C_K,

If C_1 =/= C_k =/= C_K, then the age x category interactions have the effect of increasing the likelihood of a particular category. This isn't the desired effect: increasing the likelihood of any of the categories relative to the others should be left to the category random effects \beta_k.

Additional linear constraints may be enforced on random effects in R-INLA using extraconstr = list(A = A, e = e) See https://becarioprecario.bitbucket.io/inla-gitbook/ch-INLAfeatures.html#sec:constraints. A should be a matrix which has ncol(A) = length(u) and nrow(A) equal to the number of constraints required. e should have length equal to the number of constraints required.

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