Two alternative models of human papillomavirus and cervical cancer.

<p>Pre-cancerous states are designated as cervical intraepithelial neoplasia (CIN) stages 1, 2, and 3.</p

An illustration of the danger of overfitting a model to data in a theoretical demonstration.

<p>We first generated data describing the prevalence of all cervical intraepithelial neoplasia (CIN) lesions over a 30-year period among a fictional cohort of young women. To do so, we used the more “realistic” (complex) model in <a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001540#pmed-1001540-g002" target="_blank">Figure 2</a> and assigned typical parameter values for the rates of progression and regression between states (a 5% rate of progression to the next state and 50% rate of regression per year to the prior state), then added noise to the data by drawing randomly from a normal distribution with mean equal to average prevalence and standard deviation corresponding to the prevalence rate's standard deviation. We performed a common model “calibration” approach in which both the simple and complex model shown in <a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001540#pmed-1001540-g002" target="_blank">Figure 2</a> were fitted to the first 20 years of the data (solid red dots), starting from standard parameter uncertainty ranges for progression and regression of disease <a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001540#pmed.1001540-Basu3" target="_blank">[29]</a>. Despite being the “real” model, the more complex model had numerous alternative parameter values fit the data, since there are so many uncertainties about the progression and regression rates that many combinations of parameters were able to produce reasonable fits. As shown, one of these fits (green) produced a pattern that poorly forecast future prevalence (hollow red dots) despite fitting the earlier prevalence data (solid red dots). The more complex model (in green) actually has a better “fit” to the early prevalence data when judged by standard reduced chi-squared criteria than does the simpler model (in blue); but as illustrated here, it has substantially poorer performance in forecasting prevalence in future years. The more complex model did not perform poorly simply by chance; it did so because there was insufficient prior knowledge to inform the parameter values describing the process of progression and regression through pre-cancerous states, hence the model was susceptible to fitting too tightly to the noisy prevalence data (overfitting).</p

An illustration of the identifiability problem, using an example from HIV policy.

<p>Both a 1-month duration of acute infection with six secondary infections per month (top graph) and a 3-month duration of acute infection with two secondary infections per month (bottom graph) produce the same result of six infections per person during the acute infectious period. But the implications of the two different parameter sets are very different, as early treatment (red dashed line) would be effective in preventing secondary infections only in the latter case.</p

Countries and territories with the fewest publications in medicine (1996–2010) in absolute numbers.

<p>Note: The term “United States Minor Outlying Islands" encompasses a group of Pacific atolls with no permanent population. While featured in only six publications, it has a high proportion of scientists among the 300 or so temporary visitors, incidentally, making it the territory with the highest number of publications per head of population in the world.</p

Association between publication output (1996–2010) and total health expenditure per capita (2008), Africa.

<p>Association between publication output (1996–2010) and total health expenditure per capita (2008), Africa.</p

Association between publication output (1996–2010) and gross national product per capita (2008), Africa.

<p>Association between publication output (1996–2010) and gross national product per capita (2008), Africa.</p

Countries and territories with the fewest publications in medicine (1996–2010) per capita.

<p>Countries and territories with the fewest publications in medicine (1996–2010) per capita.</p

Dietary Salt Reduction and Cardiovascular Disease Rates in India: A Mathematical Model

<div><h3>Background</h3><p>Reducing salt intake has been proposed to prevent cardiovascular disease in India. We sought to determine whether salt reductions would be beneficial or feasible, given the worry that unrealistically large reductions would be required, worsening iodine deficiency and benefiting only urban subpopulations.</p> <h3>Methods and Results</h3><p>Future myocardial infarctions (MI) and strokes in India were predicted with a Markov model simulating men and women aged 40 to 69 in both urban and rural locations, incorporating the risk reduction from lower salt intake. If salt intake does not change, we expect ∼8.3 million MIs (95% CI: 6.9–9.6 million), 830,000 strokes (690,000–960,000) and 2.0 million associated deaths (1.5–2.4 million) per year among Indian adults aged 40 to 69 over the next three decades. Reducing intake by 3 g/day over 30 years (−0.1 g/year, 25% reduction) would reduce annual MIs by 350,000 (a 4.6% reduction; 95% CI: 320,000–380,000), strokes by 48,000 (−6.5%; 13,000–83,000) and deaths by 81,000 (−4.9%; 59,000–100,000) among this group. The largest decline in MIs would be among younger urban men, but the greatest number of averted strokes would be among rural men, and nearly one-third of averted strokes and one-fifth of averted MIs would be among rural women. Only under a highly pessimistic scenario would iodine deficiency increase (by <0.0001%, ∼1600 persons), since inadequate iodized salt access—not low intake of iodized salt—is the major cause of deficiency and would be unaffected by dietary salt reduction.</p> <h3>Conclusions</h3><p>Modest reductions in salt intake could substantially reduce cardiovascular disease throughout India.</p> </div

Overall mortality trend for myocardial infarctions in India over the period 2013–2022.

<p>“Meds” simulates the cumulative effects of aspirin, antihypertensive drugs, and statins. “Tobacco control” refers to a combination of smoke-free legislation, brief cessation advice by clinicians, a mass media campaign, a ban on advertising, and a 300% tax rate increase on both bidis and cigarettes with a cumulative impact equal to 1−([1−risk reduction from intervention A]×[1−risk reduction from intervention B], etc.). “TC+meds” refers to the combination of all medications and tobacco control measures, also assuming cumulative impact. MI, myocardial infarction.</p

Model diagram.

<p>Health states are further divided into age-, gender- and location-specific (urban and rural) submodels. Deaths from non-cardiovascular events are calculated from each compartment of the model at each time point in the simulation (not drawn). The transition probabilities between health states in the model are detailed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0044037#pone.0044037.s008" target="_blank">Tables S1</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0044037#pone.0044037.s009" target="_blank">S2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0044037#pone.0044037.s010" target="_blank">S3</a>. Dietary salt reduction in the model lowers the risk of incident and recurrent myocardial infarction and stroke events. MI: myocardial infarction.</p