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positively

positively provides diagnostics for positivity violations and extrapolation in causal inference. Causal effect estimates rest on the positivity assumption: every unit must have a non-zero probability of receiving each level of the exposure within every stratum of the covariates. Where that probability is zero, or close to it, you face one of two problems: 1) for an exposure-based model, like Inverse Probability Weighting, you get a biased and unstable estimate or 2) for an outcome-based model, like a regression model, an estimate comes from the model extrapolating rather than from observed comparisons.

Installation

positively is not yet on CRAN. You can install the development version from GitHub with:

# install.packages("pak")
pak::pak("r-causal/positively")

Example

check_positivity() detects the exposure type, or uses the one you declare in exposure_type, and runs the diagnostics appropriate to that type. The bundled pos_violations dataset has two positivity problems planted in it: a structural subgroup that is never exposed, and a practical near-violation where the fitted propensity approaches zero or one in the tails of x1.

library(positively)

check <- check_positivity(pos_violations, exposure, c(x1, x2, region))
#> ℹ Treating `.exposure` as binary
check
#> 
#> ── Positivity check ────────────────────────────────────────────────────────────
#> Exposure: "exposure" (binary); 1000 observations; covariates x1, x2, and region
#> 
#> ── port ────────────────────────────────────────────────────────────────────────
#> 231 subgroups reported, 3 with low support
#> Rule: prevalence outside [0.05, 0.95] among subgroups of at least 5% of the
#> sample
#> 
#> ── extrapolation ───────────────────────────────────────────────────────────────
#> Geometric variability 0.144
#> 999 of 1000 have an opposite-exposure unit within one geometric variability;
#> 784 of 1000 fall in the opposite hull
#> 
#> ── edp ─────────────────────────────────────────────────────────────────────────
#> Data variant over 2 intervention values; edp 0.013 to 144.662
#> 
#> ℹ `sniff_violations()` for what was found, `$port` to extract a diagnostic,
#> `summary()` for every statistic.

sniff_violations() gathers what the run found into one table, across every diagnostic, with the number behind each row in the threshold column where there is one.

sniff_violations(check)
#> # A tibble: 5 × 7
#>   diagnostic    scope    label                      n statistic  value threshold
#>   <chr>         <chr>    <chr>                  <int> <chr>      <dbl>     <dbl>
#> 1 port          subgroup x1<-0.5027               305 prevalen… 0.0459     0.05 
#> 2 port          subgroup x1>=0.9626 & x1<1.154     53 prevalen… 0.962      0.05 
#> 3 port          subgroup x2>=1.063 & region=b      69 prevalen… 0          0.05 
#> 4 extrapolation overall  beyond one geometric …     1 prop_sup… 0.999      0.144
#> 5 extrapolation overall  outside the opposite-…   216 prop_in_… 0.784     NA

The positivity regression tree (port) reports each problem as a rule over the covariates. Pull that diagnostic out with $ and read its full results with tidy(), one row per reported subgroup. The low_support column marks those whose exposure prevalence falls below beta or above 1 - beta among subgroups at least alpha of the sample.

library(dplyr)

check$port |>
  tidy() |>
  filter(low_support)
#> # A tibble: 3 × 7
#>   subgroup   description  exposure_level     n proportion prevalence low_support
#>   <chr>      <chr>        <chr>          <int>      <dbl>      <dbl> <lgl>      
#> 1 x1         x1<-0.5027   1                305      0.305     0.0459 TRUE       
#> 2 x1         x1>=0.9626 … 1                 53      0.053     0.962  TRUE       
#> 3 x2, region x2>=1.063 &… 1                 69      0.069     0      TRUE

The three low-support subgroups match the planted ground truth. One rule combining region and x2 has an exposure prevalence of zero, the structural violation, and two x1 rules in the lower and upper tails have prevalence near zero and one, the practical near-violation.

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