Green S

A funnel plot is a scatterplot of the study effect size versus some measure of its precision, often its inverted standard error. It is the most common tool used to assess the presence of small-study effects in a meta-analysis [34] (link). A funnel plot which is asymmetrical with respect to the line of the summary effect implies that there are differences between the estimates derived from small and large studies.
Extending the use of funnel plots into network meta-analysis needs to account for the fact that studies estimate effects for different comparisons. As a result, there is not a single reference line against which symmetry can be judged. To account for the fact that each set of studies estimates a different summary effect we suggest the ‘comparison-adjusted’ funnel plot. Before using this plot, investigators should order the treatments in a meaningful way and make assumptions about how small studies differ from large ones. For example, if they anticipate that newer treatments are favored in small trials, then they could name the treatments from oldest to newest so that all comparisons refer to ‘old versus new intervention’. Other possibilities include defining the comparisons so that all refer to an active treatment versus placebo or sponsored versus non-sponsored intervention.
In the ‘comparison-adjusted’ funnel plot the horizontal axis presents the difference between the study-specific effect sizes from the corresponding comparison-specific summary effect [35] . For example, in a triangle , we get the three direct summary estimates from simple pairwise meta-analyses. The treatments have been named, say, from the oldest to newest. Then, for studies that compare treatments and (providing and observed effect ) the horizontal axis represents the difference . Similarly, it represents and for studies comparing XZ and YZ respectively. In the absence of small study effects the ‘comparison-adjusted’ funnel plot should be symmetric around the zero line.
To produce a comparison-adjusted funnel plot in STATA our command netfunnel can be used:
. netfunnel lnOR selnOR t1 t2, bycomparison(assuming that effect size lnOR has been estimated as t1 vs. t2)
The option bycomparison adds comparison-specific colors to the studies.
The routine netfunnel plots the comparisons as ‘treatment alphabetically or numerically earlier versus later treatment' (e.g. A vs. B or 1 vs. 2) for string or numerical treatment identifiers. Therefore, missing (small) studies lying on the right side of zero line suggest that small studies tend to exaggerate the effectiveness of treatments named earlier in alphabet compared to those later for a harmful outcome. If the outcome is beneficial such asymmetry would indicate that small-study effects favor treatments later in the alphabetical or numerical order. A ‘comparison-adjusted’ funnel plot is meaningless unless the treatments are named in an order that represents a characteristic potentially associated with small study effects. Consequently, we recommend its use only when specific assumptions about the directions of small study effects can be made.
Figure 5 shows the funnel plot for the rheumatoid arthritis network which provides an indication for the presence of small-study effects. The plot indicates that small studies tend to show that the active treatments are more effective than their respective comparison-specific weighted average effect.
The options fixed and random in netfunnel command specify whether the summaries will be derived from a fixed- or random-effects model. A linear regression line of the comparison-specific differences on the standard error of can be fitted to the plot using the addplot option, e.g. addplot(lfit selnOR _ES_CEN) (see the green line in Figure 5).
After running netfunnel a new variable is added to the dataset named _ES_CEN that includes the differences between study-specific effect sizes and comparison-specific summary estimates.
As with the conventional funnel plot, caution is needed in interpretation. Asymmetry should not be interpreted as evidence of publication bias. If the funnel plot suggests the presence of small-study effects, investigators can explore this further by employing appropriate network meta-regression or selection models [36] , [37] (link).

All considered systems have been described using a single Π-band tight binding Hamiltonian, taking into account only the nearest neighbour interactions with a hopping γ₀ = 2.75eV[24 (link)]. We have described the heterostructures using surface Green’s function formalism within a renormalization scheme
[16 (link),17 (link),25 (link)]. In the linear response approach, the conductance is calculated using the Landauer formula. In terms of the conductor Green’s function, it can be written as
[26 ]:
$G=\frac{2e^2}{h}\overline{T}\left(E\right)=\frac{2e^2}{h}\text{Tr}\left[{\mathrm{\Gamma }}_L{G}_C^R{\mathrm{\Gamma }}_R{G}_C^A\right],$
where
$\overline{T}\left(E\right)$ , is the transmission function of an electron crossing the conductor region,
${\mathrm{\Gamma }}_{L/R}=i[{\mathrm{\Sigma }}_{L/R}-{\mathrm{\Sigma }}_{L/R}^{†}]$ is the coupling between the conductor and the respective lead, given in terms of the self-energy of each lead: Σ_L/R= V_C,L/Rg_L/RV_L/R,C. Here, V_C,L/R are the coupling matrix elements and g_L/R is the surface Green’s function of the corresponding lead
[16 (link)]. The retarded (advanced) conductor Green’s function is determined by
[26 ]:
$G_C^{R,A}={[E-H_C-{\mathrm{\Sigma }}_L^{R,A}-{\mathrm{\Sigma }}_R^{R,A}]}^{-1}$ , where H_C is the hamiltonian of the conductor. Finally, the magnetic field is included by the Peierls phase approximation
[27 (link)-31 ]. In this scheme, the magnetic field changes the unperturbed hopping integral
${\gamma }_{n,m}^0$ to
${\gamma }_{n,m}^B={\gamma }_{n,m}^0{e}^{2\Pi i\mathrm{\Delta }{\mathrm{\Phi }}_{n,m}}$ , where the phase factor is determined by a line integral of the vector potential A by:
$\mathrm{\Delta }{\mathrm{\Phi }}_{n,m}=\frac{e}{h}\underset{{\mathbf{R}}_n}{\overset{{\mathbf{R}}_m}{\int }}d\mathbf{l}·\mathbf{A}.$
Using the vectors exhibited in Figure
1, R₁ = (1,0)a,
${\mathbf{R}}_2=-\left(1,\sqrt{3}\right)a/2$ and
${\mathbf{R}}_3=\left(-1,\sqrt{3}\right)a/2$ , where a = |R_n,m| = 1.42 Å, the phase factors for the armchair configuration in the Landau gauge A = (0,Bx) are given by:
$\begin{array}{l}\mathrm{\Delta }{\mathrm{\Phi }}_{n,m}\left({\mathbf{R}}_{n,m}={\mathbf{R}}_1\right)=-\mathit{\text{aB}}{y}_n,\\ \mathrm{\Delta }{\mathrm{\Phi }}_{n,m}\left({\mathbf{R}}_{n,m}={\mathbf{R}}_2\right)=-\frac{\mathit{\text{aB}}}{2}\left(y_n+\frac{a\sqrt{3}}{4}\right),\\ \mathrm{\Delta }{\mathrm{\Phi }}_{n,m}\left({\mathbf{R}}_{n,m}={\mathbf{R}}_3\right)=\frac{\mathit{\text{aB}}}{2}\left(y_n+\frac{a\sqrt{3}}{4}\right),\end{array}$
where y_n is the carbon atom position in the transverse direction of the ribbons. In what follows, the Fermi energy is taken as the zero energy level, and all energies are written in units of γ₀.

NORT was performed to evaluate short-term memory retention. It was done by a slight modification of previously published literature [51 (link)]. For habituation, each mouse was placed in a wooden box without any object for 10 min, 24 h before the test. On the testing day, mouse was placed in that same box containing two identical green round blocks for 5 min for the familiarization phase. After a 30 min interval, during the test phase one of the objects was replaced with an orange rectangular shaped object. The time spent by the mice exploring each object was recorded by video capture and analyzed. The results are presented as the discrimination index which is calculated by: (time exploring the novel object—time exploring the familiar object)/(time exploring the novel object + time exploring the familiar object). It is common rodent behavior for a mouse to explore a novel object over a familiar one. The premise for this test is that a mouse with a cognitive deficit will not be able to remember the old object during the test phase, therefore will spend a similar amount of time exploring each object. All experiments were performed between 10 a.m. and 12 p.m.

For the identified cohort, we have considered demographics, body mass index (BMI), comorbidities [15 (link)], treatment with pressors, the quarter of COVID-19 diagnosis, patient severity at the time of diagnosis, and prescribed treatments as input features for model development.
To measure patient severity, we used an Ordinal Scale (OS) developed for use with EHR data [16 (link)]. Specifically, this was a 6-point ordinal scale assigned with odd integers from 1 to 11, devised explicitly for patients diagnosed with COVID-19 based on discrete EHR data elements. In this context, a level of 1 represents an outpatient or patient discharged from the hospital, level 3 indicates hospitalization, while being hospitalized on Oxygen or Mechanical Ventilator is an indicator of levels 5 and 7, respectively, with level 9 representing patients hospitalized on ECMO and level 11 representing death.
Fig 2 shows the lookback period used for determining the patient’s comorbidities in green with a minimum of 2 years, while highlighted in blue are the considered treatments’ duration within up to 28 days after the diagnosis, followed by the recorded patient’s outcome as of the last day of treatment.
Prescribed therapeutics on each day after the diagnosis were categorized and considered in eight distinct groups, defined as anticoagulants (Coag), steroid preparations (Ster), unproven antiviral therapies (ViralUnp), targeted antivirals (ViralTrgt), spike protein monoclonal antibodies (MonoSP), monoclonal antibody Immunomodulators (MonoI), macrolide and quinolone antibiotics (BiotMQ), and a miscellaneous treatments (Misc) category that included other treatments presumed to be administered for treatment of COVID-19. Medications in each category are shown in Table 1.
The model considered the proportion of days on treatment combinations, any direct correlations between the treatment values and duration of treatment are removed, preventing the ML algorithm from leveraging this information directly for prediction. By using the proportion of days on treatment combinations, the modeling algorithm is forced to find the effect of different treatment distributions rather than attributing days on treatments to the outcome of interest.