Count data with excess zeros arise frequently in health economics and epidemiology. The standard Poisson Hurdle Model (PHM) parametrises the underlying Poisson rate directly, so its count-component coefficients are log-rate ratios rather than log-ratios of the marginal mean. Consequently, the incidence density ratio (IDR) from the PHM is neither exact nor constant across covariate profiles, complicating applied reporting. We propose the Marginalised Poisson Hurdle Model (MPHM), which reparametrises the count component so that the coefficient vector beta directly governs the marginal mean E[Y]. A nonlinear connector equation links the structural Poisson rate to this parametrised mean. We prove existence and uniqueness of the connector solution, develop a vectorised Brent's-method solver, derive the score equations and block-diagonal Fisher information, establish asymptotic normality, and prove that exp(beta) is exactly constant across all covariate values. A simulation study with n in {100, 250, 500, 1000}, zero proportion pi in {0.2, 0.4, 0.6, 0.8}, and R = 200 replications confirms consistency, near-zero bias, and 95% Wald coverage of 0.905-0.975 across all 16 scenarios. Applied to the NMES1988 physician visit data (n = 4,406), the MPHM yields IDR = 1.163 (95% CI: 1.150-1.177) per additional chronic condition - an exact, population-wide effect not derivable from the PHM. The MPHM resolves the non-constant IDR problem by directly parametrising E[Y]. The resulting IDR holds for every individual and the whole population without further marginalisation, substantially simplifying the reporting of covariate effects in health utilisation research.

翻译：含过量零值的计数数据在健康经济学与流行病学中频繁出现。标准泊松障碍模型（PHM）直接参数化潜在泊松率，其计数分量的系数为对数率比而非边际均值的对数比，导致PHM的发病密度比（IDR）既不精确也不随协变量分布恒定，给应用报告带来困难。我们提出边际化泊松障碍模型（MPHM），通过重新参数化计数分量，使系数向量β直接控制边际均值E[Y]，并借助非线性连接方程将结构泊松率与该参数化均值关联。我们证明了连接解的存在唯一性，开发了向量化Brent法求解器，推导了得分方程与块对角Fisher信息矩阵，建立了渐近正态性，并证明exp(β)对所有协变量取值严格恒定。基于n∈{100,250,500,1000}、零比例π∈{0.2,0.4,0.6,0.8}及R=200次重复的模拟研究证实：在全部16种场景下，模型具有一致性、近零偏差，且95% Wald覆盖率介于0.905-0.975。应用于NMES1988医生就诊数据（n=4,406）时，MPHM显示每增加一种慢性病，IDR=1.163（95%CI: 1.150-1.177）——该精确且具群体普适性的效应无法通过PHM推导。MPHM通过直接参数化E[Y]解决了非恒定IDR问题，所得IDR对每个个体及全体人群均成立且无需额外边际化，显著简化了健康利用研究中协变量效应的报告。