GATE Bioassay, Survival & Epidemiological Statistics: practice questions

GATE - Statistics (ST) · India · IITs and IISc on rotation (2026: IIT Guwahati)

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

10worked here, free

62written 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

What GATE asks from it

GATE Statistics and Data Science (related items)

Survival and hazard functions, censoring and the exponential likelihood, and ROC/AUC concepts.

Where the 62 questions fall

How our questions for GATE spread across the units of Bioassay, Survival & Epidemiological Statistics. Difficulty: 11 easy, 41 medium, 10 hard.

Kaplan-Meier estimator and the log-rank test	10
Parametric survival models: exponential and Weibull	9
Diagnostic-test evaluation: sensitivity, specificity and ROC curves	8
Survival data: censoring and truncation	7
Cox proportional hazards model	7
Parallel-line and slope-ratio assays; Fieller's theorem	5
Study designs: cohort, case-control and cross-sectional	4
Disease progress curves and the area under the disease progress curve	4
Quantal response: probit and logit analysis, LD50 and LC50	3
Measures of disease frequency and association: risk ratio and odds ratio	3
Direct and indirect bioassays	2

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 · Direct and indirect bioassays · medium

Why are direct assays rare in agricultural work?

They are not valid for insecticides by law
Dosing until response is impractical
They require quantal responses
They give no estimate of relative potency

Answer and working

B. Dosing until response is impractical

A direct assay needs continuous dosing of the same subject until response, which is impractical for insects, plants or field animals.

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 · medium

Why are doses giving 0% or 100% mortality of little use in estimating a probit line?

They cause the LD50 to equal zero
Little information on the line
They make the probit undefined in software
They are always excluded by regulation

Answer and working

B. Little information on the line

Binomial information np(1 − p) and the probit weights vanish as p approaches 0 or 1, so such groups barely constrain the fit; design should target 10-90% responses.

3 · Survival data: censoring and truncation · medium

Seeds are checked daily and one first shows germination on day 5. Strictly, how is its germination time observed?

Exactly 5 days
Left-truncated at 5 days
Interval-censored
Right-censored at 5 days

Answer and working

C. Interval-censored

Germination happened sometime after the day-4 check and before the day-5 check: interval censoring, often treated as exact when checks are frequent.

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 · easy

How is the median survival time read from a Kaplan-Meier curve?

The time of the middle censoring
The value of Ŝ at the median follow-up
The smallest t with Ŝ(t) ≤ 0.5
The mean of the observed event times (deaths)

Answer and working

C. The smallest t with Ŝ(t) ≤ 0.5

The median is where the estimated survival first falls to 0.5 or below; it may be undefined if Ŝ never drops that low.

6 · 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.

7 · Parametric survival models: exponential and Weibull · medium

An exponential survival model has hazard 0.02 per day. What is the median survival time?

25.0 days
0.0139 days
50.0 days
34.7 days

Answer and working

D. 34.7 days

Median = (log 2)/λ = 0.693/0.02 = 34.7 days; 50 days is the mean.

8 · Measures of disease frequency and association: risk ratio and odds ratio · medium

In plant pathology, what does disease 'incidence' usually measure?

The rate of new infections per day
The proportion of plant units showing disease
The proportion of tissue area affected
The yield loss per infected plant

Answer and working

B. The proportion of plant units showing disease

Plant-pathology incidence counts diseased units (plants, leaves) — a prevalence in the epidemiological sense; severity measures tissue affected.

9 · Diagnostic-test evaluation: sensitivity, specificity and ROC curves · medium

Positives from a screening test are confirmed by a second test before culling. Which property increases?

Prevalence
Sensitivity
Apparent prevalence
Specificity

Answer and working

D. Specificity

Serial interpretation (positive only if both positive) raises specificity and lowers sensitivity.

10 · Diagnostic-test evaluation: sensitivity, specificity and ROC curves · medium

A test has sensitivity 0.95 and specificity 0.98, and prevalence is 2%. What is the negative predictive value?

0.9500
0.9990
0.9604
0.9800

Answer and working

B. 0.9990

NPV = Sp(1 − p)/[Sp(1 − p) + (1 − Se)p] = 0.9604/(0.9604 + 0.001) = 0.9990: negatives are very reliable at low prevalence.

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