FINAL EXAM ISyE6420 solution

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1. Revisiting Jane, Michael, and Melissa from Homework 1. Logistic regression
is a superb ML tool for classification tasks when covariates are present. Recall the question
from HW1 where the probabilities that Jane, Michael, and Melissa will go to the beach were
calculated.

Using Bayesian Logistic Regression predict the probability classes for Jane, Michael, and
Melissa. Data are available in starter file jmmatbeach0.odc. Compare the results with their
counterparts from HW1. Do the results for the three probabilities from HW1 fall in the 95%
Credible Set?

Hint: Since sample size (n = 100) is modest for a regression with 5 predictors, the priors for
coefficients for logit term should not be very flat. Normal priors with 0 mean and precision
0.5 for all coefficients in the linear part are recommended.

2. Regression to Predict Acute Aquatic Toxicity Towards Daphnia Magna. This
dataset was used to develop quantitative regression in order to predict acute aquatic toxicity
towards Daphnia Magna in a set of chemicals. The LC50 data, which is the concentration
that causes death in 50% of test D. magna over a test duration of 48 hours, was used as model
response.

The model comprised 8 molecular descriptors: TPSA(Tot) (Molecular properties),
SAacc (Molecular properties), H-050 (Atom-centred fragments), MLOGP (Molecular properties), RDCHI (Connectivity indices), GATS1p (2D autocorrelations), nN (Constitutional
indices), C-040 (Atom-centred fragments). Details can be found in Cassotti et al. (2014)1

Figure 1: Daphnia Magna (Photo courtesy of Norwegian Institute for Water Research)
Attribute Information: Table below provides 8 molecular descriptors and 1 quantitative experimental response for 546 experiments. The WinBUGS starter file is DaphniaMagna0.odc.

1M. Cassotti, D. Ballabio, V. Consonni, A. Mauri, I. V. Tetko, R. Todeschini (2014). Prediction of
acute aquatic toxicity towards daphnia magna using GA-kNN method, Alternatives to Laboratory Animals
(ATLA), 42,31:41; doi: 10.1177/026119291404200106.
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Molecular Descriptor Predictors
1 TPSA(Tot)
2 SAacc
3 H-050
4 MLOGP
5 RDCHI
6 GATS1p
7 nN
8 C-040

9 Quantitative response, LC50 [-LOG(mol/L)]
(a) Predict LC50 for variables TPSA = 12.5, H-050 = 0.4, MLOGP = 1.5, and RDCHI
= 1. The other four predictors are equal to 0. Give both prediction for a mean response and
prediction for a new observation.

(b) Can any of the predictors be excluded? Use 95% Credible Set Argument.
(c) Find Bayesian R-square. Comment.

3. Meta Analysis of Amantadine for Treatment of Influenza A. The flu (influenza) can be caused by many different viruses. One type is influenza A, with headaches,
coughs and runny noses that can last for many days and lead to serious illnesses such as
pneumonia.

Drug amantadine is FDA-approved for treatment and chemoprophylaxis of influenza A virus infections among adults and children aged one year and older. The review
of trials found that amantadine is helpful in preventing the flu, but only when there is a
high probability that the cause of the flu is influenza A (a known epidemic, for example).

However, this drug has adverse gastrointestinal (stomach and gut) effects, and in rare cases
can also have serious effects on the nervous system.
Trial Drug (n/N) Placebo (n/N)
Oker-Blom (1970) 16/141 41/152
Muldoon (1986) 1/53 8/52
Monto (1979) 8/136 28/139
Kantor (1980) 9/59 9/51
Pettersson (1980) 32/95 59/97
Quarless (1981) 15/107 20/99
Dolin (1982) 2/113 27/132
Reuman (1989) 3/317 5/159

Table 1: Eight trials of amantadine for prevention of influenza. Outcome is proportion of
cases of influenza n, out of N subjects.

In the meta-analysis of randomised controlled trials of amantadine for preventing influenza (Table 1)2
the treatment effects in the eight trials are variable: the reduction in
2Jefferson, T. O., Demicheli, V., Deeks, J. J., Rivetti, D. (2002).

Amantadine and rimantadine for
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odds of influenza vary from 16% to 93%, with some of the confidence intervals not overlapping. Classical methods are often poor at detecting true heterogeneity, important for finding
ultimate summary of the studies.

(a) Conduct Bayesian meta analysis of these eight studies. Use WinBUGS. Explain how
Bayesian analysis accounts for heterogeneity of studies.

(b) Find in the literature how meta analyses are graphically presented. Construct a plot
for your meta analysis from (a).

Hint: Consult the Blocker example from WinBUGS Examples Vol I. For the plot in (b)
export results from WinBUGS to your favorite plotting program.

preventing and treating influenza A in adults. Cochrane Database Syst Rev 2002;(4): CD001169. [PubMed]
Higgins, J. P. T., Thompson, S. G., Deeks, J, J., and Altman, D. G. (2003). Measuring inconsistency
in meta-analyses http://www.ncbi.nlm.nih.gov/pmc/articles/PMC192859/ BMJ, 6, 327(7414): 557560.
doi:10.1136/bmj.327.7414.557, PMCID: PMC192859
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