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PharmaceuticalIntelligence.com Journal – Projecting the Annual Rate of Article Views

Hanoch Lev-Ari, PhD and Aviva Lev-Ari, PhD, RN

Total number of articles viewed in any given year depends on:

1. The overall Average Article-Viewing Profile (AAVP)
2. The number of articles published in the year of interest, and in each one of the preceding years.

In statistics, the article viewing process is known as a “marked point process”: the time-instants of article publication are the events described by the point process, while the “mark” is the subsequent process of viewing each particular article, ongoing from the moment of publication into the future over many years. The article viewing process is assumed to be statistically-independent from the publication time-instants.

Construction of the AAVP

• Each article has its own viewing profile (a.k.a. the “mark”), aggregated by year (available from WordPress stats).
• Article viewing statistics were used to generate an average article-viewing profile (AAVP) for the entire population of articles.
• The population of all articles has a “long-tailed” distribution: a few often-viewed vs. very many with only a few views. Consequently, we sorted all articles into nine non-uniform strata, based on the total number (2012-2020) of views per article.

• For prediction purposes, we constructed a single continuous-time stratum-specific article viewing profile (SSAVP) for each stratum.

• This stratum-specific article-viewing profile was extended smoothly into the future to provide a prediction of total article views for each article over a period of 15 years, starting from the year of publication: the horizontal axis, marked “Age”, indicates the age of an article, i.e., the time elapsed since its publication.
• We combined the stratum-specific profiles into a single average article-viewing profile (AAVP) for the entire population of articles.

Construction of stratum-specific article-viewing profiles

• We arranged the population of articles in nine strata, based on the total number (2012-2020) of views per article. The size of each stratum decreases (exponentially) with the number of views. The four highest ranking strata represent 1%, 2%, 4% and 8% of the total population of articles (and, approximately, 25%, 16%, 16% and 16% of the number of views).

• We selected samples from each stratum, and aligned all sample profiles within a single stratum according to their “age” (= time from moment of publication).
• We normalized each individual article-viewing profile, then constructed a single (normalized) representative profile by averaging over the entire stratum): see Appendix for details.
• A continuous (3^rd order) polynomial curve was fitted to the normalized stratum-averaged profile.
• The publication process is a continuous-time point process. The curve aims to recover this information from aggregated (annual) data.
• We used smoothness constraints to extend the fitted polynomial curve into the future (years 10-15): see Appendix for details.
• The detailed profiles for each one of the nine strata are provided in the Appendix, along with the viewing profile for the home page.

Predicting the Annual Number of Future Article Publications

• Publication of articles is a “random point process”.
• The rate of this process has changed continuously over the 9-year period 2012-2020 (see below)

• The reasons behind the rate change are difficult to model in a quantitative fashion. This makes projection of future publication rates rather challenging.
• One possible prediction: use the average publication rate of 2017-2019 (= a “stable” recent rate of publication of 281 articles per year).
• This prediction was used to determine the projected total number of article views in 2020-2025.

Projecting the Annual Rate of Article-Views

• We generated a stratum-specific article-viewing profile (SSAVP) for each stratum by scaling the fitted and extended curve: we multiplied it by the average number of views for the stratum: see Appendix for details.
• We combined individual SSAVPs to obtain the average article-viewing profile (AAVP) for the entire article population, based on the proportions of individual strata in the 2012-2019 record (= “stratum size (%)” from the Table on p. 3).
• We generated a prediction of the total number of article views in each one of the next five years, under two distinct scenarios: (a) no new articles published after 2020, and (b) the projected annual number of article publication after 2020 is the average publication rate of 2017-2019 (= 281 new articles per year)

• Notice: the statistical model we used for predicting the number of future article views cannot be used to determine the number of home page views in the absence of new publications. Hence the same profile of home page views was used under both scenarios.

Projected Potential Annual Revenue

• Calculation of potential revenue is based on an assumed $5 revenue on every view of the home page, and $30 revenue on every view of a published article.
• The profile-based projections consider two scenarios: (a) continued publication of new articles in 2021-2025, and (b) no publication of new articles beyond 2020.
• The schema-based projections, which were proposed by Dr. Shertok, use the annual 2020 potential revenue as a starting point, and also consider two scenarios: (a) 12.5% annual decline in revenue, assuming continued publication of new articles in 2021-2025, and (b) 25% annual decline in revenue, assuming no publication of new articles beyond 2020.

Projected potential cumulative revenue

Appendix

Construction of stratum-specific article-viewing profiles (SSAVP)

For each individual stratum:

• We selected samples and aligned all sample profiles according to their “age” (= time from moment of publication).
• We normalized each individual article-viewing profile by its average over the period 2012-2019.
• A single normalized stratum-specific profile was constructed by averaging over the entire set of (normalized and aligned) sample profiles.
• A continuous (3^rd order) polynomial curve was fitted to the normalized stratum-averaged profile over the age range 1 ≤ Age ≤ 9.
• The fitted curve was extended using the function f(t) = A exp(-at^½), where “t” indicated age, and the coefficients “A” and “a” were adjusted to provide a continuous and smooth (i.e., continuous-derivative) extension of the polynomial curve to the age range 10 ≤ Age ≤ 15.
• The resulting extended curve was multiplied by the stratum average (evaluated over the period 2012-2019) to obtain the un-normalized Stratum-Specific Article Viewing Profile (SSAVP).

The specific choice we made for the extension function can be justified by considering the logarithmic-scale version of the stratum-profile (examples shown below).

Plots of all nine stratum-specific article-viewing profiles

Home page viewing profile

The actual data for the home viewing profile (shown below by the “x” symbols) was converted to a continuous extended profile curve over the complete age range (1 ≤ Age ≤ 15), using the same technique as in the construction of the SSAVP, except that no normalization is involved.

• Notice that home page views change significantly over the period 2012-2019. There is some correlation with the rate of article publication, but not enough information to make an explicit statement about how the article publication rate affects the home page viewing profile.

Projection of potential annual revenue

• Calculation of potential revenue is based on an assumed $5 revenue on every view of the home page, and $30 revenue on every view of a published article.
• The profile-based projections consider two scenarios: (a) continued publication of new articles in 2021-2025, and (b) no publication of new articles beyond 2020.
• The schema-based projections, which were proposed by Dr. Shertok, use the annual 2020 potential revenue as a starting point, and also consider two scenarios: (a) 12.5% annual decline in revenue, assuming continued publication of new articles in 2021-2025, and (b) 25% annual decline in revenue, assuming no publication of new articles beyond 2020.