For each article provide a one paragraph critique addressing the following below: For each article critique the study (how was it a good or bad study)Provide suggestions on how each study could be imp

By identifying the significant changes in mobility across the continental United States, a baseline can be established in order to evaluate upon the efficacy of government-imposed restrictions and extend to further implementation of policies to minimize mobility and disease spread simultaneously.

Additionally, with increasing concerns about a second wave or outbreak of COVID-19, this study will seek to establish inferences to re-evaluate and improve upon the existing regulations, control measures, and disease mitigation tech- niques used to combat the spread of COVID-19 and the potential for any other similar diseases or epidemics in the future.

Keywords COVID-19, Coronavirus, Linear regression model, Mobility Index OriGinal articlE *Corresponding author:

BM Golam Kibria, Department of Mathematics and Statistics, Florida International University, Miami, Florida, USA Check for updates Introduction The COVID-19 disease (Coronavirus 2019) is caused by and attributable to the virus known as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). The first instance of the disease introduced itself in late De- cember 2019 in the Hubei province of China and ever since has drastically proliferated to reach a pandem - ic status accruing over 10 million cases and 500,000 deaths globally as of present-day. The United States alone accounts for over 2.5 million of those cases and over 125,000 deaths [1]. While the origins of COVID-19 are unknown, it is presumed to have ties with the form of a human to animal (zoonotic) interaction; possibly identified as chiropteran origin [2]. COVID-19 continues to pose a severe public health catastrophe with far more significant consequences, like the ability to damage and halt economic growth permanently. Juxtaposed with a second wave or outbreak on the near horizon, the motive of this study was to use publicly available and anonymous cell phone GPS data as a direct measure of human mobility for the period of March 10, 2020, to May 28, 2020, to form a basis on evaluating the govern - mental restrictions that took place in the United States in mid to late March 2020. The scope of this study was narrowed down to the five most populous states (Cal - ifornia, Florida, New York, Pennsylvania, and Texas) as we believe these states would comprise the majority influence in decision making and changes in future reg - ulations for imposed restrictions for individual states as well on the national scale.

International Journal of Clinical Biostatistics and Biometrics Flor et al. Int J Clin Biostat Biom 2020, 6:032 ISSN: 2469-5831 Volume 6 | Issue 2 Open Access Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 2 of 8 • Unlike defined physical processes, the evaluation of human psychological behavior in this context spanning human responses to imposed government mandates is challenging to analyze due to a lack of a quantifiable metric. For this reason, it was hypothesized that the ide- al metric to investigate in terms of evaluating the over - all response of such restrictions would be in the form of a distance measure or Mobility Index as defined in the context of this study. The mobility data originates from the anonymous and commercial collection of cel- lular GPS data and is publicly available from Descartes Labs. As a result of GPS data collection, several metrics or mobility measures can be defined such as the maxi- mum mobility from the initial location of an individual for a given day (M max ), bounding mobility (M bb) and the convex hull (M ch) all in terms of distance traveled [3]. To investigate the validity of imposed restrictions, the de- cided metric of interest to represent as the Mobility In- dex was the maximum distance traveled on a given day (M max ), as the fundamental notion behind any COVID-19 related restriction is to minimize the distance people typically travel. Due to anonymity restrictions of per- sonal data, the direct data values of maximum distance are not accessible; thus, the median of the maximum distance produced over a random set of individuals that reside in the same county is used instead; hence for the capital M in the naming convention of all mobility-re - lated metrics. Using the median values for mobility will also provide a more accurate depiction of the actual val- ues as compensation for abnormalities taking place in errors that can manifest as GPS malfunctioning, GPS in - consistencies, and the accidental capture of abnormally high or low traveling distances in individuals ( Figure 1).To the best of our knowledge, the published litera- ture on the fitting of Mobility data for COVID-19 is not available yet. The objective of this paper is to fit several regression models on mobility index of the five states and investigate the effect of Government restriction on mobility index during the COVID-19 pandemic. In addi - tion, we have developed a combined regression model using data of the top five populous states.

The organization of this paper is as follows: The data sources, data descriptions, data cleaning and processing are given in section 2. The statistical models and data analysis are provided in section 3. Finally, some con - cluding remarks are added in section 4. Materials and Data The primary source of data used in this experiment to collect mobility information was made publicly avail - able by Descartes Labs, a founded company from re - searchers and scientists from Los Alamos National Lab - oratory, and focuses on large-scale computing, artificial intelligence, and satellite imagery and create solutions targeting Data Modeling and Analytics [4]. The hosting and online access of the data utilized www.data.world, a Public Benefit Corporation that provides a cloud-na - tive solution for hosting publicly available and open- source data repositories along with API and software integration for tools such as Python, R, SQL, and Excel.

To visit and explore the direct data source, navigate to https://github.com/descarteslabs/DL-COVID-19 , and for more information on Descartes Labs, please visit https://www.descarteslabs.com/company/#about . Ad- ditional secondary data sources were used to compile detailed information relating to the statewide data of Figure 1: Visualization of anonymous mobility metrics obtained from GPS data and Mobility Index illustrated as M max as from Figure 1 of Warren M, et al. [ 3].

ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 3 of 8 • daily confirmed cases and deaths. These secondary data sources originated from the Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE) [1], Worldometer [5], and lastly from the Institute of Health Metrics and Evaluation (IHME) [6] and were re - spectively combined into further columns of Cases and Deaths for each date in the time period between March 10, 2020, and May 28, 2020.

The overall process of extracting the primary data (State, Date, and Mobility) involved utilizing SQL que- ries to filter out the Descartes Labs data set in group- ings for the individual states of California, Florida, New York, Pennsylvania, and Texas. Additionally, another partition was applied on the date in the form of a range in order to maintain consistent statewide data from March 10, 2020, to May 28, 2020. Once completed and initially filtered under the above two constraints, an API call was created from www.data.world to be read and manipulated further via the Python programming language (Python 3.8.1). Likewise, a Python script was created to preprocess the dataset by managing and or- ganizing the filtered data into data frames, which will be combined with the data from the secondary sources and represented as the remaining variables (Daily Cases and Daily Deaths). Additionally, to construct a variable for the effect or contribution of government-imposed restrictions, a logical comparison was implemented to make a binary coded variable that would take assigned values of 0 (No Restriction present) or 1 (Restriction present) based upon the respected date values from the data found in the Tracking Involuntary Government Restrictions (TIGR) Dataset [7]. The Cases and Deaths data were compiled from JHU CSSE [1], Worldometer [5], and IHME [6] and integrated into the same Python script, adding on to the initial data frame. At this point, the dataset for analysis is completed and requires trans- formation for analysis and migration to R. As a result, a random subset of the data was taken for each of the individual states (20%) via Python’s random sample() function and flattened as averages to yield distinctive data records for each date in the range as depicted be- low in Figure 2. Finally, a conversion of the data's for- mat (DataFrame to CSV) took place, which enabled the migration directly to RStudio (Version 3.6.3) for per- Figure 2: Final stage of data preprocessing before appending external data.

ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 4 of 8 • Figure 3: Initial data format and manipulation process leading to the reduced dat\ aset.

Table 1: Example of final data (random 5% subset from 395 records total) with appended external data after preprocessing and manipulation stages. Date Mobility Index RestrictionCasesDeaths State 2020-04-23 3.094429 11945104 California 2020-03-11 15.197200 050 Texas 2020-04-09 3.085364 1112848 Florida 2020-03-13 19.293300 0170 Texas 2020-04-21 8.616700 177427 Texas 2020-04-10 3.462533 1114248 Florida 2020-03-25 5.687200 15103 Florida 2020-04-22 1.142000 15713661 New York 2020-03-25 0.541833 12764 Pennsylvania 2020-04-05 0.064750 1138828 California 2020-04-15 6.579100 199626 Texas 2020-03-10 5.646600 050 Pennsylvania 2020-04-23 6.227700 1107260 Florida 2020-04-24 10.093500 177727 Texas 2020-04-12 1.331300 143524 Texas 2020-03-14 11.411000 0263 Florida 2020-03-17 3.032273 0330 Pennsylvania file, dpylr [ 11] for data manipulation, lindia [12] for cre - ating regression diagnostic plots along with verifying lin - ear model assumptions, and knitr [13] for printing and exporting the results of our analyses. A sample of the forming statistical modeling and analysis. A variety of packages were utilized in RStudio namely broom [8] for summarizing the model results, ggplot2 [9] as a graphi - cal visualization tool, readr [10] to process the CSV data ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 5 of 8 • finalized data after the preprocessing and manipulation stage is depicted in below in Table 1.

The above Figure 2 and Figure 3 serve as an example of the data processing stages for an individual state for graphical purposes. It is important to note that this pro- cess is repeated for each of the states (California, Flori - da, New York, Pennsylvania, and Texas). Once the data processing stage was completed, external data of Cases, Deaths, and Restriction were appended to the data for final use. An example of the finalized data is shown be- low in Table 1 .

Statistical Models and Data Analysis To analyze the data, we consider the following multi - ple linear regression models: 0 11 2 2 3 3 Y XX X ββ β β ε=++ + + (3.1) where Y = Mobility Index, 1X = Restriction, 2X = Cases and 3X = Deaths. We assume that ε has a nor- mal distribution with zero mean and unit variance. We also assume that the regressors, 12, XX and 3X are in - dependent. The five implemented models for the five individual states follow equation 3.1.

Before proceeding in performing analysis on any of the models, baseline evaluations were conducted on each of the models and included Shapiro-Wilk normality tests, calculations of Variance Inflation Factors, as well as exploratory plots of Standardized residuals to investi- gate the validity of the normality assumptions and ver - ify multicollinearity was not present in the model itself.

Based on these results, each state model, except for Florida, underwent a square root transformation in the dependent variable (Mobility Index) to satisfy the Shap - iro-Wilk normality test or removal of an insignificant re - gressor(s). A recurring theme displayed that the Deaths regressor proved statistically insignificant in several of the models (under α = 0.05), and hence, was removed from the model where necessary. As a result, all model descriptions in the following sections will refer to the revised versions of the regression models. Individual state models In the final fitted multiple linear regression models of California, New York, and Texas the associated re - gressors of Restriction and Cases show statistical signif - icance at α = 0.05. It is important to note that the ad- justed R-squared values (0.42, 0.59, 0.34) demonstrate a weak, moderate, and weak fit respectively. For the re - maining final fitted multiple linear regression models of Florida and Pennsylvania, all the associated regressors of Restriction, Cases, and Deaths show statistical signif - icance at α = 0.05. Similarly, it is important to note that the adjusted R-squared value (0.48, 0.35) demonstrate a moderate and weak fit respectively for the models. Table 2: Final individual state linear models (summary output). State Model Summary CoefficientsStandard Error t StatP valueR 2 adj California 0.42 (Intercept) 2.08422130.125291 16.6350440.000000 Restriction -1.2576390.166272 -7.5637540.000000 Cases 0.0002970.000074 4.0404770.000127 Florida 0.48 (Intercept) 10.2528860.715398 14.3317320.000000 Restriction -3.7013720.916664 -4.0378730.000129 Cases -0.0037100.000747 -4.9668050.000004 Deaths 0.0444320.010651 4.1714970.000081 New York 0.59 (Intercept) 2.2477810.178481 12.5939650.000000 Restriction -0.9542150.223721 -4.2652050.000058 Cases -0.0002740.000115 -2.3853300.019590 Pennsylvania 0.35 (Intercept) 2.2477810.178481 12.5939650.000000 Restriction -0.9542150.223721 -4.2652050.000058 Cases -0.0002740.000115 -2.3853300.019590 Deaths 0.0038970.000914 4.2613070.000058 Texas 0.34 (Intercept) 13.7385010.932479 14.7333100.000000 Restriction -7.6856141.197682 -6.4170760.000000 Cases 0.0026270.000804 3.2685790.001625 ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 6 of 8 • R-squared value (0.69) demonstrates a moderate fit for the model. Additionally, government restriction proves to be a significant factor for Mobility Index in both the individual state models and combined model.

The importance of the imposed government restric - tion factor may possibly benefit and stem from the in - clusion of two main effects: The direct restrictions on personal mobility and the restrictions in place on social distancing. The CDC recommends social distancing to control COVID-19 spread and government restrictions are one of the most influential factors in controlling the implementation of social distancing standards which in effect explains the limited mobility of individuals. The performance of the categorical state factors can be partly explained as Texas and Florida have an overall higher mobility compared to the other three states of California, New York, and Pennsylvania. Both Texas and Florida have shown cases spiking only recently, while An important observation from the results as seen in Table 2 are the consistent negative coefficient values for the Restriction variable across all individual state mod - els which serves as an indicator that a negative linear re - lationship exists between the factors of Mobility Index and governmental restrictions. This finding supports and extends on the primary basis that government re - strictions play a critical role in reducing the typical mo- bility of individuals. Combined state model (All states) In this section, we will investigate a combined mod - el using the State as a categorical variable. The regres - sion analyses for all states are presented in Table 3. It is observed that the associated regressors of restriction, cases and in part components of the categorical state factor (Florida and Texas) show statistical significance at α = 0.05. It is important to note that the adjusted Figure 4: Final combined state linear model (Normal QQ Plot).Table 3: Final combined state linear model (summary output). Term Model Summary (R 2 adj = 0.69) Coefficients Standard Error t StatP value (Intercept) 2.16617390.0942412 22.98541780.0000000 Restriction -0.76297980.0888960 -8.58283270.0000000 Cases -0.00010790.0000170 -6.33826700.0000000 Florida 0.92141050.0814441 11.31340520.0000000 New York 0.17672990.0989717 1.78566010.0749352 Pennsylvania 0.02087300.0808681 0.25811190.7964574 Texas 1.51917840.0811243 18.72655270.0000000 ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 7 of 8 • results. The issue could be further exacerbated due to the dependencies on a variety of factors such as the varying duration of the incubation period for an individ - ual, age of the individual, and any pre-existing comor- bidities [14]. Additionally, the models created for this project involved at most four regressors to estimate the Mobility Index value, and in further research, additional regressor variables can be explored to better the fit of the model and explain more in the overall variability.

It is also important to note that each state has varying population densities and geographic sizes; as a result, the descriptive statistics and current data for these individual states may not be the best for direct use or judgment in analysis and a method for standardization or normalization of the Mobility Index distance can im- prove upon the validity of the models and may remove the need of transformation in the model entirely. An- other consideration involves the decreased or decay - ing effect of restrictions as time progresses. Due to the implementation of policies and related logistics to poli - cymaking, restrictions have not been officially deemed as lifted and are instead related to an “easing” state, in which case it would be beneficial to consider this effect.

Acknowledgements Authors are grateful to the anonymous referees and the Editor-in-Chief for their valuable comments and suggestions, which certainly improved the quality and presentation of the paper. We wish to dedicate this pa- per to all of those who have been lost or greatly affect- ed by the COVID-19 pandemic . References 1. Dong E, Du H, Gardner L (2020) An interactive web-based New York and Pennsylvania had a significantly higher number of cases from the very beginning. On the other hand, California has many IT companies and Hollywood film industries for which employees are either transi - tioning to work remotely, already working from home, or the industry closed completely due to COVID-19.

It is evident from Figures 4 and 5 that the normality and constant variance assumptions have been met to some extent.

Summary and Concluding Remarks Upon constructing and identifying the ideal model out of the initial and final models for each of the individ - ual states of California, Florida, New York, Pennsylvania, and Texas, it is clear that the overall trend for mobility is decreasing as government restrictions came to imple - mentation; hindering on social gatherings, personal mo- bility, restaurant capacity/usage, as well as in the gener - al business domain whether it be entertainment or the retail industry. The model that demonstrated the most success was the Combined State model which displays a relatively high adjusted R-squared value compared to all of the individual models.

Some of the limitations and challenges identified during this study were the repeated insignificance of the deaths regressor, the lack of additional regressor variables, and biased comparison of statewide mobility without normalization. The possible cause in the pattern of the insignificant deaths regressor could have an asso - ciation with a delay in the number of confirmed deaths from the instance of infection to the reporting stage as no exact method or central guidelines have been estab- lished in reporting death data, leading to inconsistent Figure 5: Final combined state linear model (Residuals vs. Fitted Plot).

ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032 DOI: 10.23937/2469-5831/1510032 • Page 8 of 8 • 9. H Wickham (2016) ggplot2: Elegant graphics for data anal - ysis. Springer-Verlag, New York.

10. Hadley Wickham, Jim Hester, Romain Francois, R Core Team, R Studio, et al. (2018) readr: Read rectangular text data.

11. Hadley Wickham, Romain François, Lionel Henry, Kirill Müller, R Studio (2020) dplyr: A grammar of data manip - ulation.

12. Yeuk Yu Lee, Samuel Ventura (2017) lindia: Automated lin- ear regression diagnostic.

13. Xie Yihui (2014) Knitr: A comprehensive tool for reproduc - ible research in R. In: Victoria Stodden, Friedrich Leisch, Roger D Peng, Implementing Reproducible Computational Research. Chapman & Hall/CRC.

14. Teodoro Alamo, DG Reina, Pablo Millán (2020) Data-driven methods to monitor, model, forecast and control Covid-19 pandemic: Leveraging data science, epidemiology and control theory.

dashboard to track COVID-19 in real time. Lancet Infect Dis.

2. Lu R, Zhao X, Li J, Niu P, Yang B, et al. (2020) Genomic characterisation and epidemiology of 2019 novel coronavi - rus: Implications for virus origins and receptor binding. The Lancet 395: P565-P574.

3. Warren Michael S, Skillman Samuel W (2020) Mobility changes in response to COVID-19. arXiv.

4. Hao Zhu, Thomas Travison, Timothy Tsai, Will Beasley, Yihui Xie, et al. (2020) kableExtra: Construct complex table with 'kable' and pipe syntax.

5. https://www.worldometers.info/ 6. Institute for Health Metrics and Evaluation (IHME) (2020) COVID-19 Projections. University of Washington, Seattle, WA.

7. Rex W Douglass (2020) Crowd-sourced COVID-19 dataset Tracking Involuntary Government Restrictions (TIGR).

8. David Robinson, Alex Hayes, Simon Couch, Indrajeet Patil, Derek Chiu, et al. (2020) broom: Convert statistical objects into tidy tibbles.

ISSN: 2469-5831 Flor et al. Int J Clin Biostat Biom 2020, 6:032