Directly calculated growth (#610)

* switch to directly calculated growth rate * remove superseded function * add news item * avoid conversion * add skips * add test for exp(r)==R with fixed gt of 1 day * fix typo and add reviewer Co-authored-by: Sam Abbott <s.e.abbott12@gmail.com> --------- Co-authored-by: seabbs <s.e.abbott12@gmail.com>
epiforecasts · Mar 22, 2024 · 02fd017 · 02fd017
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diff --git a/NEWS.md b/NEWS.md
@@ -40,6 +40,7 @@
 
 * Updated the parameterisation of the dispersion term `phi` to be `phi = 1 / sqrt_phi ^ 2` rather than the previous parameterisation `phi = 1 / sqrt(sqrt_phi)` based on the suggested prior [here](https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations#story-when-the-generic-prior-fails-the-case-of-the-negative-binomial) and the performance benefits seen in the `epinowcast` package (see [here](https://github.com/epinowcast/epinowcast/blob/8eff560d1fd8305f5fb26c21324b2bfca1f002b4/inst/stan/epinowcast.stan#L314)). By @seabbs in #487 and reviewed by @sbfnk.
 * Added an `na` argument to `obs_opts()` that allows the user to specify whether NA values in the data should be interpreted as missing or accumulated in the next non-NA data point. By @sbfnk in #534 and reviewed by @seabbs.
+* Growth rates are now calculated directly from the infection trajectory as `log I(t) - log I(t - 1)`. Originally by @seabbs in #213, finished by @sbfnk in #610 and reviewed by @seabbs.
 
 # EpiNow2 1.4.0
 

diff --git a/R/extract.R b/R/extract.R
@@ -207,7 +207,7 @@ extract_parameter_samples <- function(stan_fit, data, reported_dates,
   out$growth_rate <- extract_parameter(
     "r",
     samples,
-    reported_dates
+    reported_dates[-1]
   )
   if (data$week_effect > 1) {
     out$day_of_week <- extract_parameter(

diff --git a/inst/stan/estimate_infections.stan b/inst/stan/estimate_infections.stan
@@ -195,17 +195,12 @@ model {
 generated quantities {
   array[ot_h] int imputed_reports;
   vector[estimate_r > 0 ? 0: ot_h] gen_R;
-  array[ot_h] real r;
+  vector[ot_h - 1] r;
   real gt_mean;
   real gt_var;
   vector[return_likelihood ? ot : 0] log_lik;
   profile("generated quantities") {
-    if (estimate_r){
-      // estimate growth from estimated Rt
-      gt_mean = rev_pmf_mean(gt_rev_pmf, 1);
-      gt_var = rev_pmf_var(gt_rev_pmf, 1, gt_mean);
-      r = R_to_growth(R, gt_mean, gt_var);
-    } else {
+    if (estimate_r == 0){
       // sample generation time
       vector[delay_params_length] delay_params_sample = to_vector(normal_lb_rng(
         delay_params_mean, delay_params_sd, delay_params_lower
@@ -222,9 +217,9 @@ generated quantities {
       gen_R = calculate_Rt(
         infections, seeding_time, sampled_gt_rev_pmf, rt_half_window
       );
-      // estimate growth from calculated Rt
-      r = R_to_growth(gen_R, gt_mean, gt_var);
     }
+    // estimate growth from infections
+    r = calculate_growth(infections, seeding_time + 1);
     // simulate reported cases
     imputed_reports = report_rng(reports, rep_phi, model_type);
     // log likelihood of model

diff --git a/inst/stan/functions/generated_quantities.stan b/inst/stan/functions/generated_quantities.stan
@@ -28,20 +28,12 @@ vector calculate_Rt(vector infections, int seeding_time,
   }
   return(sR);
 }
-// Convert an estimate of Rt to growth
-array[] real R_to_growth(vector R, real gt_mean, real gt_var) {
-  int t = num_elements(R);
-  array[t] real r;
-  if (gt_var > 0) {
-    real k = gt_var * inv_square(gt_mean);
-    for (s in 1:t) {
-      r[s] = (pow(R[s], k) - 1) / (k * gt_mean);
-    }
-  } else {
-    // limit as gt_sd -> 0
-    for (s in 1:t) {
-      r[s] = log(R[s]) / gt_mean;
-    }
-  }
-  return(r);
+
+// Calculate growth rate
+vector calculate_growth(vector infections, int seeding_time) {
+  int t = num_elements(infections);
+  int ot = t - seeding_time;
+  vector[t] log_inf = log(infections);
+  vector[ot] growth = log_inf[(seeding_time + 1):t] - log_inf[seeding_time:(t - 1)];
+  return(growth);
 }
diff --git a/inst/stan/simulate_infections.stan b/inst/stan/simulate_infections.stan
@@ -35,7 +35,7 @@ generated quantities {
   matrix[n, t] infections; //latent infections
   matrix[n, t - seeding_time] reports; // observed cases
   array[n, t - seeding_time] int imputed_reports;
-  array[n, t - seeding_time] real r;
+  matrix[n, t - seeding_time - 1] r;
   for (i in 1:n) {
     // generate infections from Rt trace
     vector[delay_type_max[gt_id] + 1] gt_rev_pmf;
@@ -94,10 +94,8 @@ generated quantities {
     imputed_reports[i] = report_rng(
       to_vector(reports[i]), rep_phi[i], model_type
     );
-  {
-    real gt_mean = rev_pmf_mean(gt_rev_pmf, 0);
-    real gt_var = rev_pmf_var(gt_rev_pmf, 0, gt_mean);
-    r[i] = R_to_growth(to_vector(R[i]), gt_mean, gt_var);
-  }
+    r[i] = to_row_vector(
+      calculate_growth(to_vector(infections[i]), seeding_time + 1)
+    );
   }
 }
diff --git a/tests/testthat/setup.R b/tests/testthat/setup.R
@@ -4,7 +4,7 @@ library("lifecycle")
 if (identical(Sys.getenv("NOT_CRAN"), "true")) {
   files <- c(
     "convolve.stan", "pmfs.stan", "observation_model.stan", "secondary.stan",
-    "rt.stan", "infections.stan", "delays.stan"
+    "rt.stan", "infections.stan", "delays.stan", "generated_quantities.stan"
   )
   if (!(tolower(Sys.info()[["sysname"]]) %in% "windows")) {
     suppressMessages(

diff --git a/tests/testthat/test-estimate_infections.R b/tests/testthat/test-estimate_infections.R
@@ -4,7 +4,8 @@ futile.logger::flog.threshold("FATAL")
 
 reported_cases <- EpiNow2::example_confirmed[1:30]
 
-default_estimate_infections <- function(..., add_stan = list(), delay = TRUE) {
+default_estimate_infections <- function(..., add_stan = list(), gt = TRUE,
+                                        delay = TRUE) {
   futile.logger::flog.threshold("FATAL")
 
   def_stan <- list(
@@ -15,7 +16,9 @@ default_estimate_infections <- function(..., add_stan = list(), delay = TRUE) {
   stan_args <- do.call(stan_opts, def_stan)
 
   suppressWarnings(estimate_infections(...,
-    generation_time = generation_time_opts(example_generation_time),
+    generation_time = fifelse(
+      gt, generation_time_opts(example_generation_time), generation_time_opts()
+    ),
     delays = ifelse(delay, list(delay_opts(example_reporting_delay)), list(delay_opts()))[[1]],
     stan = stan_args, verbose = FALSE
   ))
@@ -27,6 +30,7 @@ test_estimate_infections <- function(...) {
   expect_true(nrow(out$samples) > 0)
   expect_true(nrow(out$summarised) > 0)
   expect_true(nrow(out$observations) > 0)
+  invisible(out)
 }
 
 # Test functionality ------------------------------------------------------
@@ -89,6 +93,20 @@ test_that("estimate_infections successfully returns estimates using a random wal
   test_estimate_infections(reported_cases, gp = NULL, rt = rt_opts(rw = 7))
 })
 
+test_that("estimate_infections works without setting a generation time", {
+  skip_on_cran()
+  df <- test_estimate_infections(reported_cases, gt = FALSE, delay = FALSE)
+  ## check exp(r) == R
+  growth_rate <- df$samples[variable == "growth_rate"][,
+    list(date, sample, growth_rate = value)
+  ]
+  R <- df$samples[variable == "R"][,
+    list(date, sample, R = value)
+  ]
+  combined <- merge(growth_rate, R, by = c("date", "sample"), all = FALSE)
+  expect_equal(exp(combined$growth_rate), combined$R)
+})
+
 test_that("estimate_infections fails as expected when given a very short timeout", {
   skip_on_cran()
   expect_error(output <- capture.output(suppressMessages(

diff --git a/tests/testthat/test-stan-generated_quantities.R b/tests/testthat/test-stan-generated_quantities.R
@@ -0,0 +1,11 @@
+skip_on_cran()
+skip_on_os("windows")
+
+test_that("calculate_growth works as expected", {
+  skip_on_cran()
+  expect_equal(calculate_growth(rep(1, 5), 1), rep(0, 4))
+  expect_equal(round(calculate_growth(1:5, 2), 2), c(0.41, 0.29, 0.22))
+  expect_equal(round(calculate_growth(exp(0.4*1:5), 2), 2), rep(0.4, 3))
+  expect_error(calculate_growth(1:5, 6))
+  expect_error(calculate_growth(1:5, 0))
+})