For example, for independent parameter estimates, the naively computed interval g θ ^ l, 1, …, θ ^ l, k ), g ( θ ^ u, 1, …, θ ^ u, k will be too wide.
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Assume that for each parameter θ j, j = 1, …, k, an estimate θ ^ j with an ( 1 - α ) ⋅ 100 % CI is reported.Īn estimate for ϕ is obtained by computing ϕ ^ = g θ ^ 1, …, θ ^ k, but it is less obvious how to derive a CI for ϕ ^ with correct coverage ( 1 - α ) ⋅ 100 %. parameters θ = ( θ 1, …, θ k ) using a function g: ϕ = g ( θ 1, …, θ k ). While in both examples above all parameters are probability parameters, the algorithm is general: it can be used for arbitrarily complex functions to combine an arbitrary number of parameters, each with an arbitrary distribution (provided it can be sampled from).Īssume that a parameter of interest ϕ is computed from k = 2,3.
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Given recent guidelines 4 for nuanced discussion of the full range of values within estimated CIs rather than just a focus on point estimates and p-values, there is a large need for CIs with correct coverage and this is where bootComb provides a simple-to-use tool to propagate uncertainty from all estimates. CIs are needed for the adjusted incidence or prevalence parameters, not for the raw, unadjusted estimates. In public health applications, CIs are as important for policy makers than the central point estimates. However, it was not evident how to derive a corresponding CI. In both applications, the parameter of interest was the unconditional (HDV example) or the adjusted (SARS-CoV-2 example) prevalence, not the raw, directly measured estimate and in each case, multiple independently estimated parameters had to be combined via a known mathematical function. 2Īdjusting the seroprevalence estimate obtained from a novel antibody test for SARS-CoV-2 for the estimated sensitivity and specificity of this test.
Obtaining a 95% CI for hepatitis D virus (HDV) prevalence from the reported estimates and 95% CIs for the conditional prevalence of hepatitis D among hepatitis B surface antigen (HBsAg) positive patients and the prevalence of HBsAg. The development of bootComb was motivated by two real-world examples: While usually easy to combine point estimates, it is often difficult to obtain a valid confidence interval (CI) for the combined parameter. A recent example includes the estimation of typhoid incidence 1 where a Bayesian model was used to derive adjustment factors. The impact of study or facility-based limitations on parameter estimates is well-known 1 and common adjustment factors include the probability of seeking healthcare or of receiving a diagnostic test (both in the case of facility-based estimates), the incidence or prevalence of a related condition (in the case of a conditional disease prevalence/incidence), or the operational characteristics of the diagnostic test (in the case of imperfect diagnostic tests). In epidemiological research, the need to combine several estimated parameters is not unusual.