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ICAR AICE-JRF/SRF Bioassay, Survival & Epidemiological Statistics: practice questions

ICAR AICE-JRF/SRF - Agricultural Statistics, Computer Application, Bioinformatics (PhD admission and fellowship) · India · National Testing Agency for ICAR

Original practice questions written to the published syllabus · not past papers
10worked here, free
54written to this exam in this subject
11syllabus units

What this subject covers

Dose and response, time to event and disease in populations: direct and indirect assays, probit and logit analysis of LD50 and LC50, parallel-line and slope-ratio assays, Kaplan-Meier and Cox models, and the statistical side of plant and animal epidemiology. Introductory veterinary epidemiology lives in the Veterinary track; this is the statistics behind it.

In the exams: Light in AICE-JRF Ag Stat; ICAR MSc/PhD elective; plant-protection and veterinary research (applied); UPSC ISS (light)

Where the 54 questions fall

How our questions for ICAR AICE-JRF/SRF spread across the units of Bioassay, Survival & Epidemiological Statistics. Difficulty: 8 easy, 22 medium, 24 hard.

Parallel-line and slope-ratio assays; Fieller's theorem9
Quantal response: probit and logit analysis, LD50 and LC508
Direct and indirect bioassays6
Cox proportional hazards model6
Parametric survival models: exponential and Weibull6
Disease progress curves and the area under the disease progress curve5
Survival data: censoring and truncation4
Kaplan-Meier estimator and the log-rank test4
Measures of disease frequency and association: risk ratio and odds ratio2
Study designs: cohort, case-control and cross-sectional2
Diagnostic-test evaluation: sensitivity, specificity and ROC curves2

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Quantal response: probit and logit analysis, LD50 and LC50 · easy

A logit fit gives logit P = −4.6 + 2.3 log₁₀(concentration in mg/L). What is the LC50?

  1. 10.58 mg/L
  2. 2 mg/L
  3. 100 mg/L
  4. 10 mg/L
Answer and working

C. 100 mg/L

log₁₀ LC50 = −α/β = 4.6/2.3 = 2, so LC50 = 10² = 100 mg/L. 2 is the log concentration.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

2 · Quantal response: probit and logit analysis, LD50 and LC50 · hard

If log tolerances are normal with mean μ and SD σ, what is the slope of the probit line against log dose?

  1. 1/σ
  2. 1/μ
  3. μ/σ
  4. σ
Answer and working

A. 1/σ

Φ⁻¹(P) = (x − μ)/σ, so the slope is 1/σ: a steep line means homogeneous tolerances. The LD50 is at x = μ.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

3 · Quantal response: probit and logit analysis, LD50 and LC50 · medium

A field aphid population has LC50 = 120 mg/L and a susceptible strain 8 mg/L. What is the resistance ratio?

  1. 15
  2. 128
  3. 112
  4. 0.067
Answer and working

A. 15

Resistance ratio = LC50(field)/LC50(susceptible) = 120/8 = 15. 112 is a difference, not a ratio.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

4 · Survival data: censoring and truncation · easy

How are the survival function S(t) and the cumulative hazard H(t) related?

  1. S(t) = exp[−H(t)]
  2. S(t) = 1 − H(t)
  3. S(t) = −log H(t)
  4. S(t) = H(t)/t
Answer and working

A. S(t) = exp[−H(t)]

H(t) = −log S(t), since h = f/S = −d log S/dt.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

5 · Survival data: censoring and truncation · hard

For a hazard function h(t), what is the density f(t)?

  1. h(t)/S(t)
  2. 1 − exp[−h(t)]
  3. ∫₀ᵗ h(u)du
  4. h(t) exp[−∫₀ᵗ h(u)du]
Answer and working

D. h(t) exp[−∫₀ᵗ h(u)du]

f = hS and S = exp(−H), so f(t) = h(t)exp[−H(t)].

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

6 · Kaplan-Meier estimator and the log-rank test · hard

Which formula estimates the variance of the Kaplan-Meier estimator?

  1. Σ dⱼ/nⱼ²
  2. Ŝ²/n
  3. Ŝ(1 − Ŝ)/n
  4. Greenwood's: Ŝ² Σ dⱼ/[nⱼ(nⱼ − dⱼ)]
Answer and working

D. Greenwood's: Ŝ² Σ dⱼ/[nⱼ(nⱼ − dⱼ)]

Greenwood's formula accounts for the shrinking risk sets; Ŝ(1 − Ŝ)/n is the binomial variance without censoring.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

7 · Cox proportional hazards model · hard

A covariate measured during follow-up and depending on survival itself is included as a fixed baseline covariate. What bias results?

  1. Length bias
  2. Regression dilution only
  3. Immortal-time bias
  4. Recall bias
Answer and working

C. Immortal-time bias

Subjects must survive long enough to acquire the covariate value, which falsely makes it look protective; time-dependent coding avoids this.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

8 · Diagnostic-test evaluation: sensitivity, specificity and ROC curves · hard

No gold standard exists for a new kit. How can its sensitivity and specificity be estimated?

  1. Latent-class models
  2. From the kit's apparent prevalence
  3. By assuming the older test is perfect
  4. From the ROC curve of the kit alone
Answer and working

A. Latent-class models

Latent-class models treat true status as unobserved and use differing prevalences to identify Se and Sp of both tests, under stated assumptions.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

9 · Disease progress curves and the area under the disease progress curve · medium

An AUDPC of 315 %-days covers 14 days. What is the standardised AUDPC?

  1. 22.5%
  2. 45%
  3. 4.4%
  4. 315%
Answer and working

A. 22.5%

Standardised AUDPC = AUDPC/duration = 315/14 = 22.5%, the average severity over the period.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

10 · Disease progress curves and the area under the disease progress curve · medium

Which model suits a monocyclic soil-borne disease whose inoculum does not increase in the season?

  1. Gompertz
  2. Logistic
  3. Monomolecular
  4. Exponential
Answer and working

C. Monomolecular

Monomolecular growth dy/dt = r(1 − y) reflects infection from a fixed inoculum; logistic growth suits polycyclic spread.

Further reading: Finney, Statistical Method in Biological Assay; Klein and Moeschberger, Survival Analysis; Dohoo, Martin and Stryhn, Veterinary Epidemiologic Research; Madden, Hughes and van den Bosch, The Study of Plant Disease Epidemics

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Bioassay, Survival & Epidemiological StatisticsThe full study manual, free ICAR AICE-JRF/SRFFormat, sections and how it has changed

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