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

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

Additional file 1: of The association of county-level socioeconomic factors with individual tobacco and alcohol use: a longitudinal study of U.S. adults

Table S1. Ordinary Least Squares Analysis of the Association between Lagged County-Level Characteristics and Individual Health Behaviors, U.S. National Longitudinal Study of Youth, 1992–2012. (DOCX 23 kb

Additional file 2: of The association of county-level socioeconomic factors with individual tobacco and alcohol use: a longitudinal study of U.S. adults

Table S2. Fixed Effects Analysis of the Association between Lagged County-Level Characteristics and Individual Health Behaviors, U.S. National Longitudinal Study of Youth, 1992–2012. (DOCX 23 kb

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

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

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

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

Appendix_1_online_supp – Supplemental material for Personalizing Medical Treatment Decisions: Integrating Meta-Analytic Treatment Comparisons with Patient-Specific Risks and Preferences

Supplemental material, Appendix_1_online_supp for Personalizing Medical Treatment Decisions: Integrating Meta-Analytic Treatment Comparisons with Patient-Specific Risks and Preferences by Christopher Weyant, Margaret L. Brandeau and Sanjay Basu in Medical Decision Making</p