# Asymptotic sensitivity analysis for weak nulls with continuous exposures assuming constant effects across matched sets. ```r constant_effects_test( Z, R, index, gamma = 0, theta = 0, X = NA, estimand_function = extract_OLS, gamma_star_vec = NULL ) ``` ## Arguments - `Z`: A length N vector of observed doses. - `R`: A length N vector of observed outcomes. - `index`: A length N vector of indices indicating matched set membership. - `gamma`: The nonnegative sensitivity parameter; gamma = 0 means no unmeasured confounding. - `theta`: The value at which to test the weak null. - `X`: A matrix with I rows and less than I columns that contains covariate information. - `estimand_function`: A function that takes in values z and r and outputs a scalar; this function governs the causal estimand to estimate - `gamma_star_vec`: that contains the maximum ratio of any two probabilities of permutations for each matched set. ## Returns A list containing the deviate, one-sided p-value, observed value of the test statistic in each matched set, and conservative standard deviation estimate. ## Examples ```r # Load the data data <- lead_bmd # prepare data threshold <- log(0.74675) match_info = data |> dplyr::group_by(matched_sets) |> dplyr::summarise(below = sum(log_lead < threshold) > 0, disc = var(log_lead) > 0, above = sum(log_lead > threshold) > 0) below_indices <- match_info$matched_sets[match_info$below] disc_indices <- match_info$matched_sets[match_info$disc] above_indices <- match_info$matched_sets[match_info$above] # outcome analysis using the stochastic intervention statistic, weak null below_nbp <- data |> dplyr::filter(matched_sets %in% below_indices & matched_sets %in% disc_indices) above_below <- below_nbp |> dplyr::filter(matched_sets %in% above_indices) extract_below_threshold_vs_baseline_function <- function(z, r) { extract_below_threshold_vs_baseline(z, r, threshold) } # one-sided test that estimand defined by estimand_function is 0 at gamma = 0 result <- constant_effects_test(Z = above_below$log_lead, R = above_below$lumbar_spine_bmd, index = above_below$matched_sets, gamma = 0, theta = 0, estimand_function = extract_below_threshold_vs_baseline_function) ```

constant_effects_test function