CSIR-UGC NET Bioassay, Survival & Epidemiological Statistics: practice questions

CSIR-UGC NET - Mathematical Sciences (statistics option) · India · National Testing Agency for CSIR

Original practice questions written to the published syllabus · not past papers

9worked here, free

35written 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)

Direct and indirect bioassays
Quantal response: probit and logit analysis, LD50 and LC50
Parallel-line and slope-ratio assays; Fieller's theorem
Survival data: censoring and truncation
Kaplan-Meier estimator and the log-rank test
Cox proportional hazards model
Parametric survival models: exponential and Weibull
Measures of disease frequency and association: risk ratio and odds ratio
Study designs: cohort, case-control and cross-sectional
Diagnostic-test evaluation: sensitivity, specificity and ROC curves
Disease progress curves and the area under the disease progress curve

Where the 35 questions fall

How our questions for CSIR-UGC NET spread across the units of Bioassay, Survival & Epidemiological Statistics. Difficulty: 1 easy, 11 medium, 23 hard.

Cox proportional hazards model	6
Parametric survival models: exponential and Weibull	5
Parallel-line and slope-ratio assays; Fieller's theorem	4
Survival data: censoring and truncation	4
Kaplan-Meier estimator and the log-rank test	4
Quantal response: probit and logit analysis, LD50 and LC50	3
Direct and indirect bioassays	2
Measures of disease frequency and association: risk ratio and odds ratio	2
Study designs: cohort, case-control and cross-sectional	2
Diagnostic-test evaluation: sensitivity, specificity and ROC curves	2
Disease progress curves and the area under the disease progress curve	1

9 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 · hard

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

1/σ
1/μ
μ/σ
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

2 · Parallel-line and slope-ratio assays; Fieller's theorem · medium

A slope estimate is 2.0 with standard error 0.4 and t = 2.0. What is Fieller's g?

0.20
0.64
0.16
0.40

Answer and working

C. 0.16

g = t²v₂₂/b² = 4 × 0.16/4 = 0.16, large enough for Fieller limits to differ noticeably from delta-method limits. 0.40 is t × SE/b; 0.64 omits division by b².

3 · Survival data: censoring and truncation · easy

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

S(t) = exp[−H(t)]
S(t) = 1 − H(t)
S(t) = −log H(t)
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.

4 · Survival data: censoring and truncation · hard

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

h(t)/S(t)
1 − exp[−h(t)]
∫₀ᵗ h(u)du
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)].

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

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

Σ dⱼ/nⱼ²
Ŝ²/n
Ŝ(1 − Ŝ)/n
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.

6 · Cox proportional hazards model · medium

Many event times are tied in a Cox analysis. Which approximation is generally more accurate?

Greenwood's
Breslow's
Efron's
Kaplan's

Answer and working

C. Efron's

Efron's method approximates the exact partial likelihood better than Breslow's when ties are frequent; Greenwood's formula concerns KM variances.

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?

Length bias
Regression dilution only
Immortal-time bias
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.

8 · Parametric survival models: exponential and Weibull · hard

Which survival distribution is both a proportional-hazards and an accelerated-failure-time model?

The log-logistic
The log-normal
The gamma
The Weibull

Answer and working

D. The Weibull

Only the Weibull family (including the exponential) has both properties.

9 · 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?

Latent-class models
From the kit's apparent prevalence
By assuming the older test is perfect
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.

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