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Zero-Inflated and Hurdle Count Models

Statistical count models — zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and hurdle models — that handle a zero frequency far exceeding what a plain negative binomial predicts by positing a second, separate zero-generating process: either a latent subgroup that structurally cannot produce the event (ZIP/ZINB mixture) or a logistic gate determining whether the patient engages at all (hurdle), with a zero-truncated count distribution for those who cross it; the correct choice between these and a plain negative binomial depends on subject-matter knowledge about structural versus sampling zeros, not on automated tests, because interpretation of two-component models is substantially more complex than a single-coefficient incidence rate ratio.

Inferential Statisticsstatisticscount-datazero-inflationhurdle-modelexcess-zerosstructural-zerossampling-zerosZIP
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Methods reference only. Use primary source citations and local policy before applying this in a study protocol, regulatory submission, payer dossier, or clinical decision.
In plain language

Zero-inflated and hurdle count models are used when a dataset has far more zero-event patients than a standard negative binomial model can explain — for example, when 70% of patients had zero hospitalizations but the model predicts only 50%. These models handle zeros by positing two separate groups: patients who structurally cannot have the event (like a non-smoker in a smoking-cessation study) and patients who could but did not during the study window. The price of this richer model is two sets of coefficients that must be interpreted separately and combined to get a population-average estimate, which is why a simpler negative binomial model is usually the right starting point and should only be replaced when there is a genuine subject-matter reason to believe in a separate zero-generating process.

When to use it
—Use plain NB first; escalate to ZI/hurdle only when (a) the NB rootogram shows material underprediction of zeros and (b) a scientific case for a separate zero-generating process can be articulated for the study...
—Use ZI/hurdle count models for discrete utilization volume (number of visits, fills, admissions); use two-part cost models for the dollar amounts.
Watch out for
—Produces two coefficient sets that are harder to communicate; requires the marginal expected count to be computed separately; vulnerable to the Vuong test's inflated false- positive rate if used for automated model...
—Two-part models for semicontinuous costs are the appropriate approach when the outcome is continuous (dollars), not discrete counts; the structural-zero logic is the same but the cost-part model uses a gamma or...

Excess zeros versus overdispersion: not the same problem

Two problems can create elevated zero counts in healthcare data, and they require fundamentally different solutions. Overdispersion — the condition where Var(Y) > E(Y) — arises when patients have heterogeneous underlying event rates. The negative binomial distribution handles overdispersion correctly: patients with very low rates will produce zero-count observations frequently by chance, and the NB dispersion parameter absorbs that extra mass at zero through its variance function. This entry does not re-teach NB regression; see negative-binomial-distribution and poisson-negative-binomial-count-models for that foundation.

Zero-inflation addresses a categorically different situation: a subgroup of patients that structurally cannot generate the event of interest, regardless of follow-up length or model specification. These patients' zeros are not probabilistic outcomes of a count process — they are certainties from a separate data-generating mechanism entirely.

A plain NB model treats all zeros as draws from a single continuous count distribution. When a structural-zero subgroup genuinely exists, the NB consistently underpredicts the observed zero frequency even after alpha is estimated, and its coefficients average over two scientifically distinct groups in a way that obscures both.

The key diagnostic: after fitting an NB model, compare its predicted P(Y=0) to the observed zero proportion. If the NB predicts 50% zeros but you observe 70%, and there is a credible subject-matter reason to believe a true never-user subgroup exists, zero-inflated or hurdle models deserve consideration. If the NB tracks the zero rate well, the additional complexity is unjustified. Most of the time, plain NB suffices — this is the most important sentence in this entry.

Structural zeros versus sampling zeros

A structural zero is a zero that cannot be anything else. A patient who has undergone a hysterectomy contributes a structural zero to any study of uterine procedures. A patient who is physiologically incapable of addiction, or who is enrolled in a claims database but has never sought care for the relevant condition, may be a structural zero for drug fills or specialist visits. The defining feature: no amount of time in the at-risk window can change the count from zero, because the generating mechanism is absent.

A sampling zero is probabilistic. A patient who fills opioid prescriptions occasionally might have zero fills in any given year simply because no refill fell within the observation window. A low-frequency hospitalizer will frequently have zero hospitalizations in a one-year window. These zeros are fully explained by the count distribution at low event rates; the negative binomial handles them without special treatment.

The clinical distinction determines the entire modeling strategy. In administrative claims, structural zeros are rarely directly observable: a claims record for a patient with zero fills looks identical whether the patient is a structural never-user or a sampling zero from a sporadic user.

Subject-matter knowledge must therefore drive the decision. If every patient in your cohort definition can plausibly generate the event — for example, elderly patients who can be hospitalized, diabetic patients who can fill glucose-lowering drugs — the structural-zero hypothesis has no support and zero-inflation adds a scientifically meaningless latent class.

ZIP and ZINB: mixture model mechanics and two coefficient sets

A zero-inflated model is a finite mixture of two components. Let pi (π) denote the probability that a given patient belongs to the structural-zero class. With probability π the patient contributes a guaranteed zero. With probability (1 − π) the patient is in the active-count class and their count follows a Poisson distribution (for ZIP) or a negative binomial distribution (for ZINB).

The observed probability of a zero count is therefore:

P(Y = 0) = π + (1 − π) × P(Y_count = 0)

and the probability of a positive count k > 0 is:

P(Y = k) = (1 − π) × P(Y_count = k)

The inflation term π is itself modeled as a function of patient covariates via a logistic regression: log(π/(1−π)) = γ₀ + γ₁Z₁ + ... where Z variables may differ from the count-model predictors. This produces two distinct coefficient sets that must be interpreted separately:

First, the inflation logistic coefficients (γ): these predict belonging to the structural-zero class. A positive γ coefficient means higher covariate values increase the probability of being a structural never-user. Exponentiated, they are odds ratios for the latent structural-zero state.

Second, the count-model coefficients (β): these predict the expected count for the active-count subgroup only. Exponentiated, they are incidence rate ratios (IRRs) conditional on the patient not being a structural zero. A treatment-arm IRR from the count component does not apply to all patients in the study — it applies only to the estimated (1 − π) fraction who are active-count patients.

The marginal expected count for any patient, combining both components, is:

E(Y) = (1 − π) × mu_count

where mu_count is the count-component mean. This marginal quantity — not the count-model IRR alone — is the right input to a budget-impact analysis, because it averages over the probability of being in each class.

Hurdle count models: a distinct data-generating story

A hurdle model is architecturally similar to a zero-inflated model — two components, two coefficient sets — but embodies a different causal story. In a hurdle model, there is no latent structural-zero class. All zeros have a single origin: the patient did not cross the utilization hurdle. A logistic model determines whether the count is zero (no event) or positive (any event). If positive, the count follows a zero-truncated count distribution, meaning the Poisson or NB probability mass function is renormalized to exclude zero.

Under this story:

P(Y = 0) = 1 − p_hurdle P(Y = k | k > 0) = p_hurdle × P(Y_truncated = k)

The hurdle is more natural for many utilization questions. Consider a study of specialty visits: some patients never seek the specialist at all (did not cross the hurdle), and among those who do, the number of visits follows a right-skewed count distribution. Every zero is explained by the logistic component alone; there is no latent-class ambiguity. The logistic hurdle coefficient is directly interpretable as a predictor of any engagement with care, which is itself a policy-relevant outcome separable from the volume question.

The practical difference between ZIP/ZINB and hurdle: for a given observed dataset, both models may produce similar predicted distributions and pass goodness-of-fit checks similarly. The difference is in interpretation and in the scientific commitment being made. Under ZIP, some patients are asserted to be structural zeros who cannot respond to treatment through the count channel; under hurdle, those same patients simply did not engage, and an intervention could move them across the hurdle. The choice should be grounded in the scientific question, not in model-selection statistics.

Model choice: theory first, Vuong test controversies, rootogram checks

The Vuong test has been widely applied to compare ZIP and plain Poisson (or ZINB and plain NB) in practice, but it is a poor gating criterion. The standard Vuong statistic does not follow the assumed standard-normal null distribution for non-nested model comparison in finite samples; simulation evidence shows that it generates inflated false-positive rates, recommending zero-inflation even when none exists. A correction term (Vuong-Clarke) restores proper calibration but is rarely implemented in standard software outputs. Because of these properties, automated Vuong-based model selection produces unreliable conclusions and encourages treating a scientific modeling decision as a mechanical test.

The recommended workflow:

  1. Before looking at the data, ask whether structural zeros are scientifically plausible in this cohort. If the cohort definition requires the patient to be capable of the event, there are no structural zeros by design and the ZIP story is inappropriate.
  2. Fit a plain negative binomial model and compute the predicted zero probability from the fitted model: P_NB(Y=0) = (1/(1+alpha*mu))^(1/alpha). Compare to the observed zero fraction. A rootogram (hanging rootogram from the countreg R package) displays this comparison visually for all count values simultaneously, making underfitting at zero obvious.
  3. Only if a meaningful gap remains and subject matter supports a two-process story, fit ZINB or hurdle. Examine whether the inflation (or hurdle) coefficient estimates are interpretable and stable. A very large inflation probability with huge standard errors suggests the model cannot identify the latent class reliably.
  4. Report the marginal expected count from the chosen model alongside the component-specific coefficients to give decision-makers the population-average quantity they actually need.

When plain negative binomial suffices — and that is usually the right answer

Analysts routinely reach for zero-inflated models upon seeing a high zero rate, but the NB distribution already produces substantial zero probability when mean rates are low and dispersion is high. The NB mass at zero is P_NB(Y=0) = (1/(1+alpha*mu))^(1/alpha), which can be 0.6 or higher at low mu with moderate alpha.

Before adding model complexity, confirm quantitatively that the NB underpredicts the zero fraction by a practically meaningful margin — not just a margin that is statistically detectable at large sample sizes. In pharmacoepidemiology studies with 50,000-patient claims cohorts, even a 2-percentage-point underprediction of zeros will produce a "significant" Vuong test result without any scientific justification for structural zeros. The default should remain plain NB unless there is a specific, articulated scientific reason to believe in a separate zero-generating process.

Pros, cons, and trade-offs

Zero-inflated models (ZIP/ZINB):

  • Pros: correctly models a structural-zero subgroup when one genuinely exists; separates the probability of being a never-utilizer from the count rate among active users; can substantially improve predicted zero fit when the latent-class story is scientifically supported.
  • Cons: two coefficient sets required for every inference question; structural-zero class is latent and unverifiable from data alone; Vuong test for selection is unreliable; marginal expected counts require combining both components; overfitting is a real risk when the zero excess is ordinary overdispersion that NB would absorb; interpretation for payer and HTA audiences is substantially more complex.
  • When to prefer: population-based cohorts where genuine never-users are included by design; when the NB systematically underpredicts the zero frequency by more than ten percentage points and subject matter supports a structural-zero story.

Hurdle models:

  • Pros: cleaner data-generating story with all zeros from one source; logistic hurdle coefficient directly interpretable as a predictor of any utilization; avoids the unverifiable latent-class interpretation of ZIP/ZINB; separable scientific questions (any engagement vs how much engagement) map naturally to the two components.
  • Cons: the two-part structure still requires reporting and interpreting two models; forces all zeros into the logistic part even if some are sampling zeros from a low-rate count process; zero-truncated count distribution is less familiar and less commonly implemented in standard software.
  • When to prefer: the scientific question naturally divides into any-event versus how-many-given- event; specialty utilization, medication initiation, or referral studies where "crossing the hurdle" of first engagement is itself a meaningful outcome.

Plain negative binomial (the usual right answer):

  • Pros: single interpretable coefficient set; marginal IRR applicable to the full patient population; handles overdispersion and much of the zero excess without any latent-class assumption; computationally simpler and results are immediately communicable to non-technical stakeholders; the correct model in the vast majority of HCRU count analyses.
  • Cons: will underfit genuine structural zero processes; predicted zero probability from the fitted model should always be compared to the observed rate as a diagnostic.
  • When to prefer: almost always — specifically when the NB-predicted zero probability matches the observed zero fraction and when no subject-matter case for structural zeros can be made.

When NOT to use

  • When the NB fits the zero distribution well: if the predicted NB zero probability closely matches the observed zero fraction, adding a zero-inflated or hurdle layer introduces model complexity without scientific benefit, and the Vuong test alone does not justify the additional latent-class assumption.
  • When the cohort is restricted to event-experiencing patients: inclusion criteria requiring at least one event (e.g., patients with at least one hospitalization in the lookback) remove structural zeros by design. A plain NB or zero-truncated model is correct; zero-inflation would estimate a structural-zero probability near zero while degrading estimation precision.
  • When every patient can plausibly have the event: for endpoints that any enrolled patient can experience (hospitalizations among the elderly, drug fills among an established user cohort), structural zeros are scientifically implausible and the inflation logit will fit a latent class with no real-world meaning.
  • As a mechanical response to a high zero rate: high zero rates are common in claims data and usually reflect low event rates among some patients, not structural impossibility. Fit NB first; resort to ZI models only after confirming material underprediction and providing a scientific rationale.
  • When a single marginal rate ratio is required for communication or downstream modeling: the count-model IRR from a ZINB is conditional on the active-count subgroup and cannot be applied to the full population directly. If the audience needs one interpretable IRR, the plain NB provides it; if ZI is used, the marginal E(Y) = (1-π) × mu_count must be computed and reported for both arms to give the population-level contrast.

Interpreting the output

Using the worked example: a ZIP model for opioid prescription fills in 100 chronic pain patients produces two sets of estimated parameters. The inflation logistic component estimates π = 0.40 (40% are structural never-users). The count-component mean is μ_count with the Poisson zero probability for the active subgroup at 0.50.

(1) Formal interpretation. The ZIP model estimates two simultaneous processes. The logistic inflation component estimates that 40 out of 100 patients (π = 0.40) belong to a latent structural-zero class — patients who would produce zero opioid fills under any length of follow-up. These patients are not draws from the Poisson count distribution; their zero contributions are certain rather than probabilistic. Among the remaining 60% of patients (the active-count class, probability 1 − π = 0.60), the Poisson count component governs the fill distribution.

The count-model IRR for a treatment indicator applies only within this active subgroup, not to all 100 patients. The marginal predicted zero rate for the full population is π + (1 − π) × P_count(Y=0) = 0.4 + 0.6 × 0.5 = 0.4 + 0.3 = 0.7, matching the observed 70/100 = 0.7. Any treatment-effect comparison that uses only the count-model IRR implicitly conditions on the patient not being a structural zero — an assumption that must be stated explicitly and is typically not what a budget-impact model requires.

(2) Practical interpretation. For a payer or clinical decision-maker: the model estimates that roughly 4 in 10 patients in this chronic pain population do not fill opioid prescriptions at all — a structural behavioral or clinical state the count model alone cannot explain.

Among the 6 in 10 who do fill at least occasionally, the count model describes how often they fill and how a treatment or policy affects that rate. For a budget-impact calculation, the population-average expected fills per patient is E(Y) = (1 − 0.40) × μ_count, not μ_count alone — using μ_count directly would overestimate the cost burden for the full population by nearly 67%.

This is the interpretive price of the richer model: two sets of coefficients, a marginal calculation to reach a population-level quantity, and a latent-class story that must be defended to a non-technical audience. When that price is not worth paying because the plain NB fits well, do not pay it.

Decision diagram

flowchart TD
  Start[Count outcome with high zero frequency] --> NB[Fit plain negative binomial]
  NB --> Root{Compare NB-predicted vs<br/>observed zero proportion<br/>rootogram or direct check}
  Root -->|NB matches zeros well| UseNB[Use plain NB: single IRR<br/>interpretable for full population]
  Root -->|NB materially underpredicts zeros| Theory{Scientific case for<br/>structural-zero subgroup?}
  Theory -->|No credible story| UseNB
  Theory -->|Cohort includes true never-users| Story{Story: latent structural zeros<br/>vs non-engagement?}
  Story -->|Latent never-user class| ZINB[Zero-Inflated NB<br/>pscl::zeroinfl dist=negbin<br/>PROC GENMOD DIST=ZINB]
  Story -->|All zeros = non-engagement| Hurdle[Hurdle NB<br/>pscl::hurdle dist=negbin<br/>Logistic + truncated NB]
  ZINB --> Interp[Report: inflation logit OR<br/>count-model IRR AND<br/>marginal E-Y = 1-pi times mu]
  Hurdle --> Interp
  UseNB --> Single[Report: single adjusted IRR<br/>with 95% CI for full population]
Model-selection decision tree for excess-zero count outcomes. Plain NB is the default; ZI and hurdle models require both a statistical gap (rootogram) and a scientific rationale. Automated Vuong tests should not be the sole criterion for escalating to ZI/hurdle models.

Worked example

Scenario

A pharmacy analyst studies opioid prescription fills among 100 patients diagnosed with chronic pain over one year. Seventy patients had zero fills. After fitting a negative binomial model, the predicted proportion of zero-fill patients is approximately 50 percent — substantially below the observed 70 percent. With subject-matter justification (some patients decline opioids entirely on behavioral or cultural grounds), the analyst fits a zero-inflated Poisson model. The inflation logistic component estimates that 40 percent of patients are structural never-users (π = 0.40). The Poisson count component for the active-user group yields a zero probability of 0.50 at the estimated mean. The analyst verifies that these ZIP parameters reproduce the observed zero rate.

Dataset

Observed count distribution of opioid fills in one year for 100 chronic pain patients. Seventy patients had zero fills; the remaining 30 had one or more fills, creating a zero proportion of 0.70 that a plain NB model cannot match.

count_valueobserved_patients
070
112
28
35
43
52

Steps

1Observed zero count = 70 patients out of 100 total. Observed zero rate: 70/100 = 0.7.
2A fitted negative binomial model predicts approximately 50 patients with zero fills (observed rate 0.70 vs NB-predicted rate approximately 0.50) — a gap suggesting a zero-generating process beyond ordinary overdispersion.
3Fit a ZIP model. The logistic inflation component estimates pi = 0.40: 40 percent of patients are classified as structural never-users who contribute a guaranteed zero.
4The Poisson count component for the remaining active-user group (probability 0.60) estimates a mean fill rate such that the count-part zero probability is 0.50 for an active-user with average characteristics.
5Compute the ZIP-predicted proportion of zeros. Structural-zero share contributes 0.40. Active-user sampling-zero share: 0.6*0.5 = 0.3. Total ZIP-predicted zero rate: 0.4 + 0.3 = 0.7.
6The ZIP prediction matches the observed rate: 0.4 + 0.3 = 0.7, which equals observed 70/100 = 0.7. The model successfully reproduces the excess zero rate by attributing 40 of the 70 zero-fill patients to the structural-zero class and 30 to sampling zeros from the active-user Poisson distribution.

Result

Observed zero rate: 70/100 = 0.7. ZIP-predicted zero rate: 0.4 + 0.3 = 0.7, matching observed. Of the 70 zero-fill patients, approximately 40 are attributed to the structural never-user class (pi = 0.40) and 30 to sampling zeros from the active-user group (0.6*0.5 = 0.3). The marginal expected fill count for the full population is (1 - 0.40) times the active-user mean — not the active-user mean alone — because 40 percent of patients are expected to contribute zero fills regardless of follow-up.

Trade-offs

vs. Poisson and Negative Binomial Count Models for HCRU and Utilization
Pros of this
—Correctly models datasets where NB underpredicts zeros due to a genuine structural-zero or non-engagement subgroup; separates the "who ever uses" question from the "how much among users" question; can substantially improve model fit and avoid biased marginal effect estimates when structural zeros exist.
vs. Two-Part and Hurdle Models for Semicontinuous Costs
Pros of this
—Count outcomes have a natural integer structure that ZI/hurdle count models handle exactly; the count-part component produces an interpretable IRR on the same event-count scale as the plain NB; the inflation probability has a direct clinical interpretation as the proportion of never-utilizers.

Runnable example

Zero-inflated Poisson and zero-inflated negative binomial models using statsmodels ZeroInflatedPoisson and ZeroInflatedNegativeBinomialP. Demonstrates the NB-versus-ZIP diagnostic workflow (predicted vs observed zero comparison), followed by ZINB fitting with separate inflation predictors and extraction of the...

requires: numpy · pandas · statsmodels · scipy
import numpy as np
import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf
from scipy import stats

rng = np.random.default_rng(42)
n = 200

# ── Synthetic dataset: 200 patients, structural-zero subgroup (~40%) ──
# Structural zeros: 80 patients who never fill opioids
# Active users: 120 patients; fill count ~ NegBin(mu=2.5, alpha=0.8)
structural_zero = rng.binomial(1, 0.4, n).astype(bool)
mu_active = 2.5
alpha_nb   = 0.8
p_nb = 1.0 / (1.0 + alpha_nb * mu_active)         # NB prob param for scipy
r_nb = 1.0 / alpha_nb

active_counts = rng.negative_binomial(r_nb, p_nb, n)
counts = np.where(structural_zero, 0, active_counts).astype(int)

age = rng.normal(55, 12, n)
df = pd.DataFrame({
    "count":           counts,
    "age":             age,
    "pain_severity":   rng.uniform(0, 10, n).round(1),
    "person_years":    np.ones(n),
})
df["log_pt"] = np.log(df["person_years"])

obs_zero_rate = (df["count"] == 0).mean()
print(f"Observed zero rate: {obs_zero_rate:.3f}")

# ── Step 1: Fit plain NB and compare predicted vs observed zeros ──
nb_mle = sm.NegativeBinomial.from_formula(
    "count ~ age + pain_severity", data=df, offset=df["log_pt"]
).fit(disp=0)
alpha_est = float(nb_mle.params["alpha"])
mu_hat    = nb_mle.predict()

# P_NB(Y=0) = (1/(1 + alpha*mu))^(1/alpha) for each patient
p_zero_nb = (1.0 / (1.0 + alpha_est * mu_hat)) ** (1.0 / alpha_est)
nb_pred_zero_rate = p_zero_nb.mean()
print(f"NB predicted zero rate: {nb_pred_zero_rate:.3f}")
print(f"Gap (observed - NB): {obs_zero_rate - nb_pred_zero_rate:.3f}")
print("NB underpredicts zeros by more than 10 pp -> investigate zero-inflation")

# ── Step 2: Fit ZIP (as a diagnostic, count component is Poisson) ──
zip_res = sm.ZeroInflatedPoisson.from_formula(
    "count ~ age + pain_severity",      # count-model predictors
    exog_infl=df[["age"]].assign(const=1.0),   # inflation predictors
    data=df,
    offset=df["log_pt"]
).fit(method="bfgs", maxiter=400, disp=False)
print("\nZIP model summary (count component):")
print(zip_res.summary2().tables[1].round(3))

# ── Step 3: Fit ZINB (NB count component + inflation logit) ──
zinb_res = sm.ZeroInflatedNegativeBinomialP.from_formula(
    "count ~ age + pain_severity",
    exog_infl=df[["age"]].assign(const=1.0),
    data=df,
    offset=df["log_pt"]
).fit(method="bfgs", maxiter=400, disp=False)

# ── Step 4: Extract the structural-zero probability (pi) ──
# Inflation logit -> sigmoid -> pi for each patient
pi_hat = zinb_res.predict(which="prob-zero")  # or which="mean-main"
pi_mean = float(pi_hat.mean()) if hasattr(pi_hat, "mean") else float(pi_hat)
print(f"\nEstimated mean structural-zero probability (pi): {pi_mean:.3f}")

# ── Step 5: Compute marginal expected count E(Y) = (1 - pi) * mu_count ──
mu_count_hat = zinb_res.predict(which="mean-main")
marginal_mean = (1.0 - pi_mean) * float(mu_count_hat.mean())
raw_count_mean = float(mu_count_hat.mean())
print(f"Active-user mean (count component): {raw_count_mean:.3f}")
print(f"Marginal expected count E(Y):        {marginal_mean:.3f}")
print(f"Using count-component mean for full population would overstate by "
      f"{100 * (raw_count_mean / marginal_mean - 1):.0f}%")

# ── Step 6: Verify ZIP arithmetic from worked example ──
pi_ex     = 0.4       # structural-zero share
p_count_0 = 0.5       # count-part zero probability for active group
zip_pred_zero = pi_ex + (1 - pi_ex) * p_count_0
obs_ex        = 70 / 100
print(f"\nWorked-example verification:")
print(f"ZIP predicted zeros: {pi_ex} + {1-pi_ex}*{p_count_0} = {zip_pred_zero:.1f}")
print(f"Observed:            {obs_ex:.1f}")
print(f"Match: {abs(zip_pred_zero - obs_ex) < 1e-9}")

Citations

FOUNDATIONAL / METHODS
  1. [1]Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics. 1992;34(1):1-14.
  2. [2]Rose CE, Martin SW, Wannemuehler KA, Plikaytis BD. On the use of zero-inflated and hurdle models for modeling vaccine adverse event count data. Journal of Biopharmaceutical Statistics. 2006;16(4):463-481.
APPLIED EXAMPLES
  1. [3]Zeileis A, Kleiber C, Jackman S. Regression models for count data in R. Journal of Statistical Software. 2008;27(8):1-25.
REPORTING & GUIDANCE
  1. [4]Diehr P, Yanez D, Ash A, Hornbrook M, Lin DY. Methods for analyzing health care utilization and costs. Annual Review of Public Health. 1999;20:125-144.