Questions & explanations
1. How do you handle a situation where the outcome is rare in logistic regression?
When the outcome is rare (e.g., disease occurs in <5% of animals), logistic regression can still be used, but odds ratios may overestimate relative risk. In such cases, exact logistic regression or Firth's penalized likelihood can reduce bias. Alternatively, you can use Poisson regression with robust variance to estimate relative risk directly. Another approach is to oversample cases (case-control design) and then adjust the intercept. The key is that standard logistic regression may have convergence issues or inflated coefficients. It is important to check the number of events per variable; a rule of thumb is at least 10 events per predictor. If events are very few, simpler methods or Bayesian approaches may be better.
2. What is multilevel modeling and why is it needed in veterinary data?
Multilevel modeling (also called hierarchical modeling) is used when data has a nested structure, such as animals within herds, or herds within regions. In veterinary studies, animals from the same herd are more similar than animals from different herds, so they are not independent. Ordinary logistic regression ignores this and can give wrong standard errors. Multilevel models include random effects to account for the clustering. For example, a model might include a random intercept for each herd, capturing herd-level variation. This gives correct confidence intervals and allows studying both animal-level and herd-level factors. It is essential for properly analyzing field data where animals are grouped.
3. What are the limitations of simple compartmental models like SIR?
Simple compartmental models assume homogeneous mixing, constant parameters, and no demographic changes. They ignore individual variation in susceptibility, infectiousness, and behavior. For example, they cannot capture superspreading events or age-specific contact patterns. They also assume that all recovered individuals are immune, which may not be true for some diseases. Additionally, they do not account for spatial spread or stochastic effects (randomness) that are important in small populations. Despite these limitations, they are useful for understanding general dynamics and comparing interventions. More complex models (e.g., age-structured, stochastic) can address some of these issues.
4. Compare Bayesian inference with frequentist methods for estimating test accuracy when a gold standard is missing.
Frequentist methods often require a gold standard or strong assumptions like conditional independence between tests. Bayesian methods can incorporate prior information and handle missing gold standards more naturally. For example, a frequentist latent class model might assume the two tests are independent given disease status, which may be unrealistic. Bayesian methods can include prior knowledge about dependence. Also, Bayesian results are intuitive: a 95% credible interval means there is a 95% probability the true value lies in that interval, given the data. Frequentist confidence intervals have a different interpretation. Bayesian methods are more flexible but require specifying priors.
5. Give an example of a Bayesian model for estimating sensitivity and specificity of a new test without a gold standard.
Suppose you have a new test and an old test, both imperfect. You test 200 animals with both tests. You set prior distributions: sensitivity of new test ~ Beta(10,2) (mean ~83%), specificity ~ Beta(20,1) (mean ~95%), and similarly for old test. The disease prevalence prior is Beta(5,20) (mean 20%). Using the observed counts (e.g., both positive: 30, both negative: 140, new positive/old negative: 10, new negative/old positive: 20), a Bayesian model (e.g., using Markov chain Monte Carlo) estimates posterior distributions. The posterior might show new test sensitivity 85% (credible interval 78-91%) and specificity 96% (92-99%). This gives accuracy estimates without a gold standard.
6. What factors can make the actual herd immunity threshold different from the simple formula?
The simple formula assumes a homogeneous population where everyone mixes randomly. In reality, people have different contact patterns (e.g., children have more contacts). If a disease spreads more among certain groups, the threshold may be higher or lower. Also, if immunity wanes over time, the threshold increases. Another factor is that vaccines may not provide perfect protection or may not be taken up uniformly. For example, if a vaccine is 80% effective, you need more vaccinated people. Spatial clustering of unvaccinated individuals can also allow outbreaks even if overall coverage is above the threshold. So the formula gives a rough guide, not an exact number.
7. What is publication bias and how can it affect a meta-analysis?
Publication bias occurs when studies with positive or significant results are more likely to be published than those with null or negative results. This can make the meta-analysis overestimate the true effect. For example, if only successful vaccine trials are published, the pooled effect looks larger than it really is. To detect publication bias, a funnel plot is used: it plots effect size against study size. If the plot is asymmetric, bias may be present. Statistical tests like Egger's test can check asymmetry. Methods like trim-and-fill can adjust for missing studies. It is important to search for unpublished studies and register reviews to reduce this bias.
8. How do you check if a logistic regression model fits the data well?
Model fit can be assessed using the Hosmer-Lemeshow test, which compares observed and predicted outcomes across groups. A non-significant p-value (e.g., >0.05) suggests good fit. Also, the area under the ROC curve (AUC) measures discrimination; values above 0.7 indicate acceptable ability to separate events from non-events. Residual plots can reveal patterns, but for binary data they are less informative. Overdispersion (more variation than expected) can be checked by comparing deviance to degrees of freedom. It is also important to check for influential points and multicollinearity among predictors. No single test is perfect; multiple checks are recommended.
9. Compare spatial scan statistics with traditional disease mapping methods like kernel density estimation.
Spatial scan statistics are designed to formally test for clusters and give a p-value, while kernel density estimation (KDE) creates a smooth surface of disease risk without formal testing. KDE uses a bandwidth to spread each case over a small area, producing a continuous map. Scan statistics, on the other hand, search for specific circular clusters and report their significance. KDE is better for visualizing overall risk patterns, but it does not tell you if a hotspot is real or random. Scan statistics are more rigorous for hypothesis testing, while KDE is exploratory. Both can be used together: KDE to see patterns, then scan statistics to confirm clusters.
10. How do you compare survival curves between two groups of animals?
To compare survival curves from two groups, such as treated vs. untreated animals, you can use the log-rank test. This test checks if the observed differences between curves are likely due to chance. It compares the number of events observed in each group to the number expected if the groups had the same survival. A small p-value (e.g., less than 0.05) suggests a real difference. The Kaplan-Meier curves can be plotted together for visual comparison. If the curves cross, the proportional hazards assumption may be violated, and other methods like restricted mean survival time might be used. The log-rank test is the most common way to formally compare survival.
11. What is the main idea behind capture-recapture methods?
Capture-recapture methods estimate the size of a hidden population, like the number of sick animals in a region. First, you capture and mark a sample of animals (first capture). Later, you capture another sample and count how many are marked (recapture). The proportion of marked animals in the second sample tells you roughly how big the whole population is. For example, if you mark 50 deer and later catch 100 deer including 10 marked, you estimate the total population as 500. This method assumes the population is closed (no births, deaths, or movement) and marks are not lost. It is used in wildlife biology and epidemiology to estimate disease prevalence.
12. How does probe design differ between RNAscope and a standard DNA ISH assay?
RNAscope uses a set of 20-40 short probes (about 20-25 bases each) that target a specific RNA sequence. These probes are designed to avoid secondary structure and are paired with a preamplifier and amplifier system to create a tree-like signal. In contrast, DNA ISH typically uses a single long probe (100-1000 bases) that binds to complementary DNA. The long probe may require blocking of repetitive sequences to reduce background. RNAscope probes are designed for high specificity and signal amplification, while DNA probes often rely on direct labeling with enzymes or fluorophores. The RNAscope system also includes a target retrieval step to expose RNA.