Sentence:
“Mortality research for phytosanitary treatments typically pursues two distinct focus areas.”
Literature:
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Follett (2006) explicitly distinguishes between dose–response treatment development and large-scale confirmatory tests aimed at quarantine security in postharvest entomology.
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NAPPO RSPM 34 (2011) separates “treatment development” (dose–response / biology-heavy) from “treatment verification” (large-scale efficacy trials vs targets like probit-9).
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Schortemeyer et al. (2011) also contrast dose–response modeling and verification trials for probit-9 in timber pests, arguing that verification often dominates regulatory practice.
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van Klinken et al. (2020) go further and argue for systems/risk-based approaches that integrate these strands, so they partly “defy” a hard dichotomy by adding a third, risk-framework layer.
Sentence:
“The first is dose-response studies, which focus on biological modeling and the underlying relationship between treatments and the average mortality of a population.”
Literature:
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Finney’s Probit Analysis (1971) is the classical reference for modeling dose–mortality relationships as population averages (median and slope in probit space).
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Predictive microbiology reviews (e.g., Fakruddin 2011; Bevilacqua 2015) describe time/temperature/concentration → survival models explicitly as population-average responses to process variables.
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Corradini, Hassani and co-authors show exactly this for non-isothermal heat inactivation: fit isothermal models, then predict mean survival under arbitrary treatments.
Sentence:
“The second is quarantine-security studies, which aim to determine, with statistical confidence, if a treatment falls within a regulatory threshold.”
Literature:
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Couey & Chew (1986) develop the binomial sample-size / confidence-limit framework for quarantine research, explicitly to show treatments meet specified security levels (e.g., probit-9 with 95% confidence).
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Follett & McQuate (2001) and Follett (2006) frame probit-9 and related standards as quarantine security targets, not just biological endpoints.
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Schortemeyer et al. (2011) discuss how international standards require verification to specific “efficacy thresholds” and associated confidence levels.
Sentence:
“For example, using a hazard (killing rate) integral over a time-temperature profile to calculate cold treatment survival.”
Literature:
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In predictive microbiology, Corradini & Peleg (2004, 2007) and Hassani et al. (2007) derive survival under non-isothermal treatments by integrating a temperature-dependent inactivation rate over the time–temperature history.
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The “cumulated lethal time” model for codling moth (thermal quarantine treatment in cherries) is exactly a hazard/inactivation-rate integral over measured time–temperature profiles.
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The USDA PMP (Predictive Microbiology Program) tutorial describes computing F-values / lethal equivalents by integrating time–temperature-dependent rates, which is the same mathematical object.
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For cold treatments in fruit flies, newer statistical models (e.g., Ratnayake et al. 2024) don’t always call it a “hazard integral” but effectively estimate time–temperature-dependent mortality, some explicitly connecting to probit-9 thresholds.
Sentence:
“For example, the probit-9 standard, where a mortality of at least 99.9968% is achieved with 95% confidence.”
Literature:
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Baker (1939) first proposed probit-9 as a quarantine-security level for fruit fly treatments.
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Couey & Chew (1986) and later summaries (e.g., Follett & Neven 2006; Follett 2007; Schortemeyer et al. 2011; RSPM 34) all describe probit-9 as 99.9968% mortality with verification typically at 95% confidence.
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Wright et al. (2023) and Haack et al. (2011) explicitly contrast probit-9 (99.9968% at 95% confidence) with alternatives like 99.99% (probit ~8.7).
Sentence:
“The dose-response framework underlies survival analysis, toxicological dose-response, and predictive microbiology.”
Literature:
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Classical survival analysis texts (Clark & Altman 2003; Bewick et al. 2004; Jenkins 2005) define survival and hazard in the same way as toxicology and reliability.
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Finney’s probit analysis and Bliss (1934) are the foundational dose–response references in toxicology/entomology.
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Predictive-microbiology reviews (Fakruddin 2011; Bevilacqua 2015; Cebrián 2017) explicitly present microbial inactivation as a dose–response / survival modeling problem with the same machinery.
Sentence:
“Time-temperature or time-concentration inactivation is modeled via hazard with biologically interpretable parameters.”
Literature:
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Bevilacqua (2015) and Cebrián (2017) summarise microbial inactivation models where temperature (and other factors) modulate a rate or hazard term with parameters like D-value, z-value, activation energy, etc.
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Bigelow-type models (see Soni 2022; Muramatsu 2019; Peñalver-Soto 2019) use D- and z-values as biologically interpretable parameters linking time–temperature profiles to inactivation rates.
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USDA PMP documentation and many non-isothermal modeling papers treat the temperature-dependent inactivation rate as a hazard-like function.
Sentence:
“Hazard in terms of mortality h(t) is the instantaneous risk of death conditional on survival.”
Literature:
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Standard survival-analysis definitions:
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Clark & Altman (2003): hazard is the “instantaneous event rate” conditional on survival to time t.
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Bewick et al. (2004) and multiple lecture notes (e.g., Jenkins 2005; University of Washington notes) give the same interpretation.
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Sentence:
“Survival, on the other hand, is defined by the cumulative hazard.”
Literature:
- Survival-analysis basics:
$S(t)=\exp{-H(t)}$ with$H(t)=\int_0^t h(u),du$ is standard in textbooks and notes (e.g., Jenkins 2005; Clark & Altman 2003; UW lecture notes).
Sentence:
“This type of recursion is called a Volterra integral, where the survival function (the quantity to be solved for) appears inside the integral on the right-hand side and is therefore defined in terms of its own past values.”
Literature:
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In many applied papers, the relationship is usually written as the differential equation
$dS/dt = -h(t)S(t)$ , with solution$S(t)=\exp{-\int_0^t h(u),du}$ ; the “Volterra integral equation” language is more mathematical than what most applied entomology/microbiology papers use. -
Non-isothermal inactivation papers (Corradini 2004, 2007; Hassani 2007) indeed derive integral equations where the inactivation rate depends on temperature and sometimes on survival itself; these are first-order linear ODEs or Volterra equations in mathematical terms, even if not called that.
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So: supportive at the math level, but you might want a footnote that this is a mathematical characterization rather than a standard applied term of art.
Sentence:
“Most literature resolves this by choosing a parametric transformation for the time–mortality data that yields an approximately linear relationship over time at each temperature (options include log survival, log time, Arrhenius temperature, etc.).”
Literature:
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Classical first-order (log-linear) models: microbial and insect thermal-death work often uses log survivor vs time linearity at each temperature (Bigelow 1921-type); this is documented in many reviews (e.g., Soni 2022; Bevilacqua 2015).
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Many predictive-microbiology papers apply Arrhenius-type or log D vs T relationships to linearize temperature effects (e.g., Muramatsu 2019; Peñalver-Soto 2019; Corradini 2008; Xu 2020).
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Nonlinear models (Weibull, Geeraerd-type) have become common, so “most literature” is somewhat strong; but the statement is broadly accurate for traditional and regulatory-facing models. Bevilacqua (2015) and Cebrián (2017) discuss the contrast between log-linear and nonlinear approaches.
Sentence:
“Integration in this domain resolves to a closed-form expression for arbitrary non-isothermal profiles, which can then be transformed back to obtain the survival response.”
Literature:
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For simple log-linear + Arrhenius / Bigelow models, many authors derive either closed-form or straightforward numerical integrals for non-isothermal treatments (Corradini 2004; Hassani 2007; USDA PMP documentation).
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Some models (e.g., cumulated lethal time for codling moth; certain microbial models) do give analytic forms for cumulative lethal effect under arbitrary temperature histories.
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However, more complex models (with shoulders/tails, piecewise kinetics) often require numerical integration rather than tidy closed forms. Corradini (2007) and Bevilacqua (2015) discuss these limitations, so you might nuance “closed-form” to “integral that can be evaluated (analytically or numerically)”.
Sentence:
“The result is a mean population response as a function of dose; larger sample sizes mainly tighten uncertainty around the hazard parameters, rather than directly guaranteeing extremely small survival probabilities as in quarantine-security studies.”
Literature:
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Predictive-microbiology and survival-analysis papers are mostly concerned with parameter estimation and uncertainty (confidence intervals on rate parameters, D/z values, etc.), not with guaranteeing ultra-low survival probabilities per se (Bevilacqua 2015; Soni 2022).
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In contrast, Couey & Chew (1986), Follett (2001, 2006), Haack et al. (2011) explicitly design sample sizes to drive lower confidence bounds on survival to very small values (probit-9 or probit-8.7), which is conceptually different from just tightening parameter CIs.
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Wright et al. (2023) and van Klinken et al. (2020) contrast parameter-focused modeling with quarantine-security criteria and show how the same data can be used in both ways.
Sentence:
“The quarantine-security framework operates on a simple binomial view: expose n individuals to a fixed treatment, observe y survivors, and use binomial or probit models to estimate the underlying survival probability p.”
Literature:
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Couey & Chew (1986) are the classic reference: they treat numbers of survivors as binomial outcomes and show how to invert this to obtain bounds on p.
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RSPM 34 (NAPPO 2011) and IPPC treatment guidance formalize the same binomial/probit-based estimation of efficacy in postharvest quarantine tests.
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Numerous applied quarantine papers (e.g., Hallman 2000; Follett 2007; Ware 2006; Platt 2024) implement exactly this experimental structure: fixed schedule, large n, count survivors, analyse via probit/binomial.
Sentence:
“Benchmarks such as Baker’s probit-9 standard require that true mortality is at least 99.9968% with 95% confidence.”
Literature:
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Baker (1939) proposed probit-9 as the “satisfactory level of quarantine security” for fruit fly treatments.
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Couey & Chew (1986) quantified that probit-9 (99.9968% mortality) at 95% confidence requires ~93,613 treated insects with zero survivors; this is repeated in many later reviews and standards.
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Follett & Neven (2006), Follett (2007), Schortemeyer et al. (2011), NAPPO RSPM 34 and IPPC documents all restate probit-9 as 99.9968% mortality with 95% confidence as the de facto benchmark.
Sentence:
“In practice this confidence is obtained through very large sample sizes and zero survivors.”
Literature:
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Couey & Chew’s tables (and later reproductions by Follett, RSPM 34, Schortemeyer) show how extremely large n with zero survivors delivers 95% confidence at probit-9 (or probit-8.7, etc.).
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Experimental quarantine papers routinely report designs like “>30,000 insects treated, 0 survivors” for 99.99% (probit-8.7) and “>90,000 insects, 0 survivors” for probit-9. Examples include Wade/Jessup/De Lima cold treatments, Western cherry fruit fly, and various fruit fly/quarantine studies.
Sentence:
“Here, sample size is the main lever: larger n pushes the lower confidence bound on mortality upward, while the detailed dose–response shape is mostly ignored.”
Literature:
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Couey & Chew (1986) derive lower confidence bounds solely from n, y, and assumed binomial structure; dose–response curve shape only enters if you do additional modeling.
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Schortemeyer et al. (2011) and Haack et al. (2011) stress that probit-9 verification is dominated by sample-size requirements and that detailed dose–response structure is typically bypassed in verification experiments.
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Wright et al. (2023) show, via simulation, how increasing n at fixed y=0 shifts lower confidence bounds on mortality, which supports your “main lever” language.
Sentence:
“The result is a conservative pass–fail framework aimed at meeting quarantine-security regulations.”
Literature:
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Follett (2006), Follett & Neven (2006) and Haack et al. (2011) explicitly frame probit-9-type standards as conservative, easily communicable “pass/fail” criteria chosen to satisfy importing-country regulators rather than optimize biological realism.
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NAPPO RSPM 34 and IPPC treatment standards also implement efficacy criteria as thresholds (e.g., probit-9, probit-8.7) for regulatory decision-making.
Sentence:
“The focus is on confidence in very high mortality, with little attention to the underlying biological dose–response model.”
Literature:
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Haack et al. (2011) and Schortemeyer et al. (2011) criticise probit-9 for focusing on extreme mortality with limited attention to realistic pest prevalence, biology, or heterogeneity—exactly your point.
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Follett & Neven (2006) and Follett (2001) discuss alternatives (e.g., maximum pest limit, systems approaches) precisely because strict probit-9 verification is only loosely connected to underlying biology.
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Risk-based frameworks like van Klinken et al. (2020) explicitly argue that quarantine decisions should combine biology, prevalence, and trade volume, not just confidence in a very high mortality figure—supporting your “little attention” contrast.