OBJECTIVES: This study sought to determine the rate of emergency department use among the elderly and examined whether that use is reduced if the patient has a principal-care physician. METHODS: The Health Care Financing Administration's National Claims History File was used to study emergency department use by Medicare patients older than 65 years in Washington State during 1994. RESULTS: A total of 18.1% of patients had 1 or more emergency department visits during the study year; the rate increased with age and illness severity. Patients with principal-care physicians were much less likely to use the emergency department for every category of disease severity. After case mix, Medicaid eligibility, and rural/urban residence were controlled for, the odds ratio for having any emergency department visit was 0.47 for patients with a generalist principal-care physician and 0.58 for patients with a specialist principal-care physician. CONCLUSIONS: The rate of emergency department use among the elderly is substantial, and most visits are for serious medical problems. The presence of a continuous relationship with a physician--regardless of specialty--may reduce emergency department use.

10.2105/AJPH.91.11.1815

${\beta }_{\mathrm{qj}}={\gamma }_{\mathrm{q0}}+{\gamma }_{\mathrm{q1}}{W}_j+u_{\mathrm{qj}}\text{,}$

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10.2105/AJPH.92.1.59

$\mathrm{AF}=\frac{p(\mathrm{RR}-1)}{p(\mathrm{RR}-1)+1}$

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10.2105/AJPH.92.11.1773

$S_i^{*}{*}^{}=\beta ’x_{\mathrm{si}}+{\in }_{\mathrm{si}}\text{,}{S}_i=1\mathrm{if}{S}_i^{*}{*}^{}>0\text{,}0\mathrm{otherwise}$

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$C_i^{*}{*}^{}=\beta ’x_{\mathrm{ci}}+{\in }_{\mathrm{ci}}\text{,}{C}_i=1\mathrm{if}{C}_i^{*}{*}^{}>0\text{,}0\mathrm{otherwise}\text{,}$

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$\partial \mathrm{Prob}(P=1)/\partial x=\varphi \left(\beta ’x\right)\beta \text{,}$

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10.2105/AJPH.92.12.1921

$\mathrm{Ln}\mathrm{Homicide}\mathrm{rate}=\alpha +{\beta }_1\left(\mathrm{Ln}\mathrm{Alcohol}\mathrm{mortality}\mathrm{rate}\right)+{\beta }_2\left(\mathrm{Ln}\mathrm{Poverty}\right)+$

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${\beta }_3\left(\mathrm{Ln}\mathrm{Gini}\mathrm{coefficient}\right)+{\beta }_4\left(\mathrm{Ln}\mathrm{Unemployment}\right)+$

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${\beta }_5\left(\mathrm{Ln}\mathrm{Mobility}\right)+{\beta }_6(\mathrm{Ln}\mathrm{Single}-\mathrm{parent}\mathrm{households})$

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$+{\beta }_7\left(\mathrm{Ln}\mathrm{Population}\mathrm{diversity}\right)+{\beta }_8\left(\mathrm{Ln}\mathrm{Percentage}\mathrm{urban}\right)+{\beta }_9(\mathrm{Ln}\mathrm{Percentage}\mathrm{male}$

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$\mathrm{aged}25\mathrm{to}54\mathrm{years})+{\beta }_{10}(\mathrm{Regional}\mathrm{dummy}\mathrm{variable})+\epsilon$

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10.2105/AJPH.92.2.288

$\mathrm{EFFECT}=\Delta \mathrm{Hb}(\mathrm{Final}-\mathrm{Initial}{)}_{\mathrm{EXPT}}-\Delta \mathrm{Hb}(\mathrm{Final}-\mathrm{Initial}{)}_{\mathrm{COMP}}$

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10.2105/AJPH.92.3.420

${\mathrm{RPRS}}_f=\sum _i^n{C}_i{\mathrm{xT}}_i$

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10.2105/AJPH.92.5.799

$Y_i=\alpha +{\beta }_1{P}_i+{\beta }_2{X}_i+{\epsilon }_i$

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$(Y_{\mathrm{ij}}-Y_j^{*}{*}^{})={\beta }_1(P_{\mathrm{ij}}-P^{*}{j}_{})+{\beta }_2(X_{\mathrm{ij}}-X^{*}{j}_{})+({\epsilon }_{\mathrm{ij}}-{\epsilon }_j^{*}{j}_{})\text{.}$

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10.2105/AJPH.93.11.1820

$\log \mathrm{it}(p_{\mathrm{ijk}}=x_{\mathrm{ijk}}\beta +u_{\mathrm{jk}}+v_k$

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10.2105/AJPH.93.11.1844

10.2105/AJPH.93.12.2055

$\mathrm{AF}=(\mathrm{OR}-1)/\mathrm{OR}\text{,}$

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${\mathrm{AF}}_T=P_E(\mathrm{OR}-1)/\mathrm{OR}=P_E\left(\mathrm{AF}\right)\text{.}$

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10.2105/AJPH.93.12.2099

${\psi }_i=\mu +{\alpha }_i\mathrm{Age}+{\beta }_j\mathrm{Period}+Y_k\mathrm{Cohort}+e_i$

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10.2105/AJPH.93.12.2124

$\mathrm{Eadj}=E/S^{0.73}\text{.}$

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10.2105/AJPH.93.4.635

$\sum _{s=1}^n\sum _{a=1}^m(t·f·n·p)\text{,}$

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$\sum _{s=1}^n$

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$\sum _{a=1}^m$

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10.2105/AJPH.93.6.943

$C=Q_m(\theta {\alpha }_1-{\alpha }_1)+Q_w(\theta {\alpha }_2-{\alpha }_2)+Q_{\mathrm{msm}}(\theta {\alpha }_3-{\alpha }_3)\text{,}$

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$Q_m=\left(\frac{N_w}{1-U}\right)(1-{\lambda }_w)\left(\frac{1}{S}\right)\left[H_m\right(1-\Delta h_w\left)\right]+\left(\frac{N_m}{1-U}\right)(1-{\lambda }_m)\left(\frac{1}{S}\right)\left[h_m\right(1-\Delta H_w\left)\right]\text{,}$

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$Q_w=\left(\frac{N_m}{1-U}\right)(1-{\lambda }_m)\left(\frac{1}{S}\right)\left[H_w\right(1-\Delta h_m\left)\right]+\left(\frac{N_w}{1-U}\right)(1-{\lambda }_w)\left(\frac{1}{S}\right)\left[h_w\right(1-\Delta H_m\left)\right]\text{,}$

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$Q_{\mathrm{msm}}=\left(\frac{N_m}{1-U}\right)\left({\lambda }_m\right)\left(\frac{1}{S}\right)\left[H_{\mathrm{msm}}\right(1-\Delta h_{\mathrm{msm}}\left)\right]+\left(h_{\mathrm{msm}}\right)1-\Delta H_{\mathrm{msm}}\left)\right]\text{,}$

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10.2105/AJPH.93.9.1376-a

$\mathrm{logit}\left(P_{\mathrm{preg}}\right)={\beta }_0+{\beta }_{\mathrm{planned}}\times I_{\mathrm{planned}}+{\beta }_{\mathrm{infected}}\times I_{\mathrm{infected}}$

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$+{\beta }_{\left(}\times I_{\left(}\text{,}$

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$\hat{\beta }{\mathrm{infected}}_{}=\ln \left({\widehat{\mathrm{OR}}}_{\mathrm{infected}}\right)=\ln \left(3.0\right)=1.0986\text{,}$

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$\hat{\beta }{\mathrm{planned}}_{}=\ln \left({\widehat{\mathrm{OR}}}_{\mathrm{planned}}\right)=\ln \left(1.7\right)=0.5306\text{,}$

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$\hat{\beta }{\left(}_{\mathrm{planned}}=\ln \left({\widehat{\mathrm{OR}}}_{\left(}\right)=\ln \left(0.1\right)=-2.3026\text{.}$

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${\widehat{\mathrm{OR}}}_1=\frac{\mathrm{Odds}\mathrm{for}(I_{\mathrm{planned}}=0\mathrm{and}{I}_{\mathrm{infected}}=1)}{\mathrm{Odds}\mathrm{for}\left(I_{\mathrm{planned}}=0\mathrm{and}{I}_{\mathrm{infected}}=0\right)}=\exp \left(\hat{\beta }{\mathrm{infected}}_{}\right)=\exp \left(1.0986\right)=3.0\text{.}$

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${\widehat{\mathrm{OR}}}_2=\frac{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=1\mathrm{and}I{\mathrm{infected}}_{}=1\right)}{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=1\mathrm{and}I{\mathrm{infected}}_{}=0\right)}$

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$=\exp (\hat{\beta }{\mathrm{infected}}_{}+\hat{\beta }{\left(}_{\mathrm{planned}})=\exp (1.0986-2.3026)=0.3\text{.}$

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$\widehat{\mathrm{OR}}{3}_{}=\frac{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=1\mathrm{and}I{\mathrm{infected}}_{}=0\right)}{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=0\mathrm{and}I{\mathrm{infected}}_{}=0\right)}=\exp \left(\hat{\beta }{\mathrm{planned}}_{}\right)=\exp \left(0.5306\right)=1.7\text{.}$

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$\widehat{\mathrm{OR}}{4}_{}=\frac{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=1\mathrm{and}I{\mathrm{infected}}_{}=1\right)}{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=0\mathrm{and}I{\mathrm{infected}}_{}=1\right)}$

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$=\exp (\hat{\beta }{\mathrm{planned}}_{}+\hat{\beta }{\left(}_{\mathrm{planned}})=\exp (0.5306-2.3026)=0.17\text{.}$

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$\widehat{\mathrm{OR}}{5}_{}=\frac{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=1\mathrm{and}I{\mathrm{infected}}_{}=1\right)}{\mathrm{Odds}\mathrm{for}\left(I{\mathrm{planned}}_{}=0\mathrm{and}I{\mathrm{infected}}_{}=0\right)}$

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$=\exp (\hat{\beta }{\mathrm{planned}}_{}+\hat{\beta }{\mathrm{infected}}_{}+\hat{\beta }{\left(}_{\mathrm{planned}})=\exp (0.5306+1.0986-2.3026)=0.51\text{.}$

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$\hat{\beta }{\mathrm{infected}}_{}=\ln \left({\widehat{\mathrm{OR}}}_{\mathrm{infected}}\right)=\ln \left(1.6\right)=0.47\text{,}$

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$\hat{\beta }{\mathrm{planned}}_{}=\ln \left({\widehat{\mathrm{OR}}}_{\mathrm{planned}}\right)=\ln \left(1.2\right)=0.1823\text{,}$

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$\hat{\beta }{\left(}_{\mathrm{planned}}=\ln \left({\widehat{\mathrm{OR}}}_{\left(}\right)=\ln \left(0.5\right)=-0.6931\text{,}$

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$\widehat{\mathrm{OR}}{1}_{}=1.6\text{,}\widehat{\mathrm{OR}}{2}_{}=0.80\text{,}\widehat{\mathrm{OR}}{3}_{}=1.2\text{,}\widehat{\mathrm{OR}}{4}_{}=0.60\text{,}\mathrm{and}\widehat{\mathrm{OR}}{5}_{}=0.47\text{.}$

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10.2105/AJPH.93.9.1478

$$\begin{gathered} P_{\mathrm{niod}}=\exp \left(V_{\mathrm{niod}}\right)/\left[{\sum }_j\exp \right(V_{\mathrm{njod}}\left)\right]\text{,}\forall V_{\mathrm{niod}} \\ \hspace{1em}\hspace{1em}=f\left(I_{\mathrm{od}}\text{,}{\mathrm{PH}}_n\text{,}{\mathrm{BE}}_o\text{,}{\mathrm{BE}}_d\right) \end{gathered}$$

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10.2105/AJPH.93.9.1583

$A_i=\sum _j^{}{m_j}^{\alpha }{S_j}^{\lambda }/{d_{\mathrm{ij}}}^{\beta }\text{,}$

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$\mathrm{Att}=\sum _j^{}{A}_j\times W_j\text{,}$

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10.2105/AJPH.94.1.128

$\log \left(\frac{p_{\mathrm{ijk}}}{1-p_{\mathrm{ijk}}}\right)={\beta }_0+\sum _{i=1}^p{\alpha }_i{x}_{\mathrm{ijk}}+\sum _{j=1}^q{\beta }_j{y}_{\mathrm{jk}}+\sum _{k-1}^r{\gamma }_k{z}_k+v_k+u_{\mathrm{jk}}$

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10.2105/AJPH.94.11.2004

$y_{\mathrm{jt}}=\alpha t_{}+X_{\mathrm{jt}}\beta +E_{\mathrm{jt}}\gamma +C_j+\epsilon {\mathrm{jt}}_{}$

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$y_{\mathrm{jt}}=\alpha t_{}+X_{\mathrm{jt}}\beta +E_{\mathrm{jt}}\gamma +C_j+C_j^{*}{*}^{}T+\epsilon {\mathrm{jt}}_{}$

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10.2105/AJPH.94.2.308

$A_c=N_e\times [(\mathrm{RR}-1)/\mathrm{RR}]\text{,}$

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$\mathrm{RR}=\mathrm{OR}/\left[\right(1-p)+(\mathrm{OR}\times p\left)\right]\text{,}$

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10.2105/AJPH.94.2.314

${\mathrm{ETS}}_{2000}-{\mathrm{ETS}}_{1992}=\Sigma {\beta }_{2000}{X}_{2000}$

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$-\Sigma {\beta }_{1992}{X}_{1992}=\Sigma {\beta }_{1992}(X_{2000}-X_{1992})$

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$+\Sigma X_{2000}({\beta }_{2000}-{\beta }_{1992})$

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10.2105/AJPH.94.3.446

${Y_{\mathrm{ij}}=B}_0{j}_{}+B_1{j}_{}{\mathrm{Female}}_{\mathrm{ij}}+B_2{j}_{}{\mathrm{Race}}_{\mathrm{ij}}+B_6{j}_{}{\mathrm{ESL}}_{\mathrm{ij}}+B_7{j}_{}{\mathrm{Grade}}_{\mathrm{ij}}+e_{\mathrm{ij}}$

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$B_0{j}_{}=G_{00}+G_{01}{\mathrm{Treatment}}_j+U_0{j}_{}$

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10.2105/AJPH.94.3.484

$\frac{\mathrm{Pr}(y=2)}{\mathrm{Pr}(y=1)}=e^X\text{,}$

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$$\begin{gathered} \mathrm{RRR}=\frac{e^{{\beta }_1^{\left(}}}{e^{{\beta }_1^{\left(}}}\text{,} \\ =e^{{\beta }_i^{\left(}} \end{gathered}$$

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${\beta }_i^{\left(}{\left(}^2$

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10.2105/AJPH.94.4.568

$K_{\left(}=\left\{K_{\left(}\right({\mathrm{CFRS}}_{\left(}/{\mathrm{CFRS}}_{\left(}\left)\right\}-K_{\left(}\text{,}$

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$K_{\left(}/K{\left(}_B=V_{\left(}^A{4}^{}/V_{\left(}^B{4}^{}$

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10.2105/AJPH.94.4.582

$\Delta C=N_{\mathrm{new}}{R}_{\mathrm{new}}+N_{\mathrm{old}}{R}_{\mathrm{old}}^{+}{\mathrm{old}}_{}\text{.}$

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$\Delta C\left(T\right)={\sum }_u{\sum }_d{\sum }_g{\sum }_S\Delta C\left(T\text{,}S\text{,}g\text{,}d\text{,}u\right)\text{,}$

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10.2105/AJPH.94.6.1043

$\mathrm{Prob}(H_{\mathrm{ist}}=1)=\Phi (X_{\mathrm{ist}}{\beta }_1+A_{\mathrm{st}}{\beta }_2+{\nu }_t)\text{,}$

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10.2105/AJPH.94.7.1174

$R_{\mathrm{cv}}=(T/M)+1-T$

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$M_{\mathrm{cv}}=T/(R-1+T)$

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$T_{\mathrm{cv}}=\left[M\times \right(R-1\left)\right]/(1-M)$

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10.2105/AJPH.94.8.1341

$p_n=f\{1-(1-b\left)\right[1-\underset{j=1}{\overset{a}{\Pi }}(1-p_n)]-b[1-\underset{k=1}{\overset{i}{\Pi }}(1-p_{n-k})\left]\right\}\text{,}$

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10.2105/AJPH.94.9.1486

$\mathrm{PAF}=P\left(E\right)\times (\mathrm{RR}-1)/[1+P(E\left)\times \right(\mathrm{RR}-1\left)\right]$

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10.2105/AJPH.94.9.1531

$\mathrm{Log}\left(\mathrm{OR}\right)=a+b_1\times x^p+b_2\times x^p\times \log \left(x\right)\text{,}$

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10.2105/AJPH.94.9.1574

${\mathrm{SI}}_i={50\left(\right(S\%}_i-{D\%}_i)+1)\text{,}$

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10.2105/AJPH.2004.054700

$Ŷ=1-e^{(}:Y~\mathrm{binomial}\text{,}$

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$\mathrm{where}\eta ={\alpha }_{\mathrm{gae}}+{\sum }_d{\beta }_{\mathrm{dgae}}{\chi }_d$

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10.2105/AJPH.2004.050617

$\mu =\sum _{i=1}^n{p}_i{y}_i\text{,}$

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$E=\left(\frac{N}{N-1}\right)\times \left[\left(\frac{1}{\mu }\right)\sum _{i=2}^n\sum _{j=1}^{i-1}{p}_i\right|y_i-y_j\left|p_j\right]\text{,}$

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$\mathrm{SDS}=\sqrt{\sum _{i=1}^n{p}_i(y_i-\mu {)}^2}\text{.}$

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10.2105/AJPH.2004.043885

$\sum p_i({\mathrm{RR}}_i-1)/[1+\sum p_i({\mathrm{RR}}_i-1\left)\right]\text{,}$

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10.2105/AJPH.2004.037705

${\eta }_{\mathrm{tijk}}={\pi }_{\mathrm{ojk}}+{\pi }_{\mathrm{ljk}}{d}_{\mathrm{tjk}}+{\pi }_{\mathrm{2jk}}{d}^2{\mathrm{tjk}}_{}+{\alpha }_i$

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$\pi 0_{\mathrm{jk}}=\mu {+X}_{\mathrm{jk}}\beta {+W}_k\gamma$

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$\pi 1_{\mathrm{jk}}={\mu }_1{+X}_{\mathrm{jk}}{\beta }_1{+W}_k{\gamma }_1$

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10.2105/AJPH.2003.031179

$\mathrm{Attributable}\mathrm{Fraction}=p_e(\mathrm{RR}-1)/\left[p_e\right(\mathrm{RR}-1)+1]\text{.}$

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10.2105/AJPH.2004.042150

$d_{\mathrm{ij}}=|x_i-x_j|+|y_i-y_j|$

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10.2105/AJPH.2004.046284

$\left\{\right(x_{\mathrm{ref}}\left)\pm 1.96\right(s_{\mathrm{ref}}\left)\right\}\text{,}$

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$\left\{\right(x_i\left)\pm 3.3\right[(s_{\mathrm{ref}}^2{2}^{}+s_i^2{2}^{}{)}^{0.5}-s_{\mathrm{ref}}]\}\text{,}$

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10.2105/AJPH.2004.053710

$\mathrm{HbA1c}=(60.16+\mathrm{mean}\mathrm{glucose})/30.9$

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10.2105/AJPH.2004.057422

$Y_{\mathrm{ijk}}={\pi }_{\mathrm{ijk}}+{\epsilon }_{\mathrm{ijk}}{Z}_{\mathrm{ijk}}$

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10.2105/AJPH.2004.050872

$\log \mathrm{it}\left(p_{\mathrm{ij}}\right)=x_{\mathrm{ij}}\beta +u_j\text{,}$

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10.2105/AJPH.2004.045823

${\mathrm{Death}}_i=Z_i\beta +m\left({\mathrm{BMI}}_i\right)+{\epsilon }_i$

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10.2105/AJPH.2005.076547

$$\begin{gathered} \mathrm{Ln}\left[\mathrm{Pr}\right(y=\mathrm{1x})/1-\mathrm{Pr}(y=\mathrm{1x}\left)\right]= \\ {\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\text{.}\text{.}\text{.}{\beta }_n{x}_n+\epsilon \end{gathered}$$

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10.2105/AJPH.2005.083352

$$\begin{gathered} {\mathrm{Adstock}}_t={\mathrm{Ad}}_t+\lambda {\mathrm{Ad}}_{(}+{\lambda }^2{\mathrm{Ad}}_{(}+ \\ {\lambda }^3\mathrm{Ad}{(}_t \end{gathered}$$

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10.2105/AJPH.2005.064253

$$\begin{gathered} {\mathrm{Performance}}_i=\beta {\mathrm{System}}_i+ \\ \delta {\mathrm{Community}}_i+ \\ {\mu }_j+{\epsilon }_i \end{gathered}$$

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10.2105/AJPH.2004.048132

$\log {\lambda }_i={\beta }_0+{\beta }_1{x}_i+{\beta }_2{x}_i+\text{.}\text{.}\text{.}+{\beta }_k{x}_{\mathrm{ik}}+{\sigma }_{\epsilon }+\log \left({\mathrm{pop}}_i\right)$

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10.2105/AJPH.2004.060103

$$\begin{gathered} \mathrm{logit}\left(\pi {\mathrm{ijklm}}_{}\right)=\log \left[\frac{\pi {\mathrm{ijklm}}_{}}{(1-\pi {\mathrm{ijklm}}_{})}\right] \\ ={\beta }_0+\beta \left(X\right)+u_{\mathrm{0jklm}} \\ +v_{\mathrm{0klm}}+f_{\mathrm{0lm}}+g_{\mathrm{0m}}\text{.} \end{gathered}$$

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$\frac{\mathrm{AOR}-\mathrm{UOR}}{\mathrm{UOR}-1}\times 100\text{.}$

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10.2105/AJPH.2004.049312

$L_1=\sum _{\mathrm{ij}}^{}\frac{N_{\mathrm{ij}}}{N_{+}}{R}_{\mathrm{ij}}$

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$L_2=\sum _{\mathrm{ij}}^{}\frac{N_{\mathrm{ij}}}{N_{+}}{R}_{\mathrm{ij}}$

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$$\begin{gathered} L_2-L_1=\sum _{\mathrm{ij}}^{}\frac{N_{\mathrm{ij}}}{N_{+}}(R_{\mathrm{ij}}-R_{\mathrm{ij}}) \\ +\sum _{\mathrm{ij}}^{}{R}_{\mathrm{ij}}(\frac{N_{\mathrm{ij}}}{N_{+}}-\frac{N_{\mathrm{ij}}}{N_{+}}) \end{gathered}$$

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$\sum _{\mathrm{ij}}^{}\frac{N_{\mathrm{ij}}}{N_{+}}{R}_{\mathrm{ij}}$

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10.2105/AJPH.2005.064543

$$\begin{gathered} [\mathrm{CES}-D_2-\mathrm{CES}-D_1]=\alpha +{\mathrm{age}}_1+ \\ {\mathrm{education}}_1+{\mathrm{income}}_1+{\mathrm{discrimination}}_1 \\ +[{\mathrm{discrimination}}_2-{\mathrm{discrimination}}_1]+ \\ \mathrm{CES}-D_1+\epsilon \left(a\right) \end{gathered}$$

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$$\begin{gathered} [{\mathrm{GH}}_2-{\mathrm{GH}}_1{]}_j=\alpha +{\mathrm{age}}_1+{\mathrm{education}}_1 \\ +{\mathrm{income}}_1+{\mathrm{discrimination}}_1+[\mathrm{discrimi}- \\ {\mathrm{nation}}_2-{\mathrm{discrimination}}_1]+{\mathrm{GH}}_1+\epsilon (b) \end{gathered}$$

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10.2105/AJPH.2004.056929

$\mathrm{logit}\left(m_{\mathrm{at}}\right)=s\left(a\right)+s\left(t\right)+e_{\mathrm{at}}\text{,}$

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10.2105/AJPH.2005.069617

$$\begin{gathered} \ln \left({\mathrm{Consumption}}_t\right)= \\ {\alpha }_{{\mathrm{Consumption}}_t}\ln \left({\mathrm{Consumption}}_t\right) \\ +{\beta }_{\mathrm{Price}}\ln \left({\mathrm{Price}}_t\right) \\ +{\delta }_{\mathrm{Social}}\ln \left(\mathrm{Social} \\ \mathrm{Unacceptability}\right)\text{.} \end{gathered}$$

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10.2105/AJPH.2004.050575

$\mathrm{Cost}\mathrm{per}\mathrm{Visit}=\$89.69-\$12.986\ln$

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$\left(\mathrm{Current}\mathrm{Client}\mathrm{Count}\right)\text{,}$

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$\mathrm{Cost}\mathrm{per}\mathrm{Day}=\$206.79-\$39.32\ln$

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$\left(\mathrm{Current}\mathrm{Client}\mathrm{Count}\right)\text{,}$

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$\ln \left(\mathrm{Total}\mathrm{Annual}\mathrm{Cost}\right)=9.628+0.649\ln$

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$$\begin{gathered} \left(\mathrm{Current}\mathrm{Client} \\ \mathrm{Count}\right)\text{,} \end{gathered}$$

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$\mathrm{Total}\mathrm{Annual}\mathrm{Cost}=\$321637+\$13212$

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$$\begin{gathered} \left(\mathrm{Current}\mathrm{Client} \\ \mathrm{Count}\right)\text{,} \end{gathered}$$

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10.2105/AJPH.2005.078451

$$\begin{gathered} {\mathrm{Immunization}}_i= \\ {\beta }_0+{\beta }_{1}317{\mathrm{funding}}_i \\ +\gamma X_i \\ +{\theta }_i\mathrm{jurisdiction}+{\epsilon }_i \end{gathered}$$

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$$\begin{gathered} \mathrm{Log}\left[\right(\mathrm{vaccination}\mathrm{coverage}{i}_{\text{,}})/ \\ (1-\mathrm{vaccination}{\mathrm{coverage}}_i\left)\right]= \\ {\beta }_0+{\beta }_{1}317\mathrm{Funding}{i}_{\text{,}} \\ +\beta 2_{}{\mathrm{poverty}}_i+{\beta }_{3}5\times P_i \\ +{\beta }_4\mathrm{unemployment}{i}_{\text{,}} \\ +{\beta }_5\mathrm{NOHI}{i}_{\text{,}}+{\theta }_i\mathrm{jurisdiction} \\ +\lambda \mathrm{jurisdiction}\times {\mathrm{time}}_i \\ +\tau \mathrm{jurisdiction}\times {\mathrm{time}}_i^{\text{,}}{i}_{\text{,}}+{\epsilon }_i \end{gathered}$$

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10.2105/AJPH.2005.068874

$\sum _{x=1}^5{M}_x{e}_x/(1-p_x)$

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$\sum _{x=1}^5{D}_x·L_x$

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$\sum _{x=1}^5(H_{\mathrm{Ax}}-H_{\mathrm{Bx}})·P_x$

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$\sum _{x=1}^5{Q}_{\mathrm{Mx}}+H_x·Y_x$

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10.2105/AJPH.2003.035378

$M_{\mathrm{US}}=(P_{\mathrm{US}N}\hat{M}{N}_{}+P_{\mathrm{US}H}\hat{M}{H}_{})/(P_{\mathrm{US}N}+P_{\mathrm{US}H})$

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$$\begin{gathered} M_{\mathrm{TX}}=(P_{\mathrm{TX}N}\hat{M}{N}_{}+P_{\mathrm{TX}H}\hat{M}{H}_{})/(P_{\mathrm{TX}N}+ \\ {P}_{\mathrm{TX}H}) \end{gathered}$$

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$$\begin{gathered} \hat{M}{H}_{}=(P_{\mathrm{TX}N}{D}_{\mathrm{US}}-P_{\mathrm{US}N}{D}_{\mathrm{TX}})/(P_{\mathrm{US}H}{P}_{\mathrm{TX}N}- \\ {P}_{\mathrm{US}N}{P}_{\mathrm{TX}H}){\mathrm{if}P}_{\mathrm{US}H}{P}_{\mathrm{TX}N}\ne P_{\mathrm{US}N}{P}_{\mathrm{TX}H} \end{gathered}$$

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$\hat{M}{N}_{}=(D_{\mathrm{US}}-P_{\mathrm{US}H}\hat{M}{H}_{})/P_{\mathrm{US}N}{\mathrm{if}P}_{\mathrm{US}N}$

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10.2105/AJPH.2006.090399

$$\begin{gathered} ({\%}_{\mathrm{intervention}}\_{\%}_{\mathrm{intervention}})\_ \\ ({\%}_{\mathrm{comparison}}\_{\%}_{\mathrm{comparison}})\text{.} \end{gathered}$$

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10.2105/AJPH.2006.089169

$\frac{\log ({\mathrm{SA}}_{2002}/{\mathrm{SA}}_{1995})}{\log ({\mathrm{SA}}_{2002}/{\mathrm{SA}}_{1995})+\log \left[\right({\mathrm{CRI}}_{2002})/({\mathrm{CRI}}_{1995}\left)\right]}\times 100\text{,}$

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$\frac{\log \left[\right({\mathrm{CRI}}_{2002})/({\mathrm{CRI}}_{1995}\left)\right]}{\log ({\mathrm{SA}}_{2002}/{\mathrm{SA}}_{1995})+\log \left[\right({\mathrm{CRI}}_{2002})/({\mathrm{CRI}}_{1995}\left)\right]}\times 100\text{.}$

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10.2105/AJPH.2006.105478

$C=c_p+\left(c_h\times p_g\right)+\left(c_c\times p_c\right)\text{,}$

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10.2105/AJPH.2006.102947

$H=(P/100000)\times M\times \mathrm{ERC}\text{,}$

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$\mathrm{ERC}=\exp \left(b\Delta T_{\mathrm{ave}}\right)-1\text{,}$

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10.2105/AJPH.2006.088732

$5_{}{q}_0=1-(1-1_{}{q}_0)(1-4_{}{q}_1)\text{.}$

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$4_{}{q}_1=1-\mathrm{EXP}(-4{\times }_4{m}_1)\times 1000$

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10.2105/AJPH.2005.074542

$\sum _{i=1}^N\left[x_i/X\right]\left[x_i/t_i\right]$

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$\frac{\{\left[\sum _{i=1}^N\right(x_i{a}_i/X\left)\right]/\left[\sum _{i=1}^n\right(y_i{a}_i/Y\left)\right]-1\}}{\{\left[\sum _{i=1}^{n_1}\right({t_i{a}_i/T}_1\left)\right]/\left[\sum _{{i=n}_2}^n\right({t_i{a}_i/T}_2\left)\right]-1\}}$

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10.2105/AJPH.2005.083873

${\mathrm{RATE}}_{\mathrm{it}}={\beta }_0+\sum _{k=1}^n{\beta }_k{\chi }_{\mathrm{kit}}+{\mu }_i+{\lambda }_t+e_{\mathrm{it}}\text{,}$

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10.2105/AJPH.2005.080754

${\mathrm{BMI}}_{\mathrm{mtcs}}={\alpha }_{\mathrm{0cs}}+{\alpha }_{\mathrm{1cs}}{\mathrm{Kindergarten}}_{\mathrm{tcs}}+{\alpha }_{\mathrm{2cs}}{\mathrm{Summer}}_{\mathrm{tcs}}+{\alpha }_{\mathrm{3cs}}\mathrm{First}{\mathrm{Grade}}_{\mathrm{tcs}}+e_{\mathrm{mtcs}}\text{.}$

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${\mathrm{BMI}}_{\mathrm{mtcs}}={\mathrm{Exposures}}_{\mathrm{tcs}}{\alpha }_{\mathrm{cs}}+e_{\mathrm{mtcs}}\text{,}$

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${\alpha }_{\mathrm{cs}}={\gamma }_0+b_s+a_c\text{,}$

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${\alpha }_{\mathrm{cs}}={\gamma }_0+{\gamma }_1{X}_{\mathrm{cs}}+b_s+a_c\text{.}$

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${\mathrm{BMI}}_{\mathrm{mtcs}}={\mathrm{Exposures}}_{\mathrm{tcs}}({\gamma }_0+{\gamma }_1{X}_{\mathrm{cs}}+b_s+a_c)+e_{\mathrm{mtcs}}\text{.}$

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10.2105/AJPH.2005.063644

$Y_2{=a+b}_1{Y}_1{+b}_2{\mathrm{Tx}+b}_3{D}_1{+b}_4{D}_2+e\text{,}$

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$D_2={-}_1+{-}_{11}\mathrm{Tx}{+}_{-}{D}_1+{-}_{13}{Y}_1+e_1\mathrm{and}$

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$Y_2={-}_2+{-}_{21}\mathrm{Tx}{+}_{-}{D}_1{+}_{-}{D}_2+{-}_{24}{Y}_1+e_2\text{,}$

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10.2105/AJPH.2005.071472

$$\begin{gathered} \log \left(\frac{{\varphi }_{\mathrm{ij}}}{1-{\varphi }_{\mathrm{ij}}}\right)={\beta }_0+{\beta }_1(\mathrm{LatForeignBorn}{)}_{\mathrm{ij}}+ \\ {\beta }_2(\mathrm{LatUSborn}{)}_{\mathrm{ij}}+{\beta }_3(\mathrm{Black}{)}_{\mathrm{ij}}+ \\ {\beta }_4(\mathrm{OtherRace}{)}_{\mathrm{ij}}+\sum _{q=5}^Q{\beta }_{\mathrm{qj}}{X}_{\mathrm{qij}} \end{gathered}$$

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$$\begin{gathered} {\beta }_0={\gamma }_{00}+{\gamma }_{01}(\mathrm{ConPov}{)}_j+{\gamma }_{02}(\mathrm{RStab}{)}_j+ \\ {\gamma }_{03}(\mathrm{PercentForBorn}{)}_j+{\gamma }_{04}(\mathrm{CollEff}{)}_j+ \\ {\gamma }_{05}(\mathrm{SocIntEx}{)}_j+u_0 \end{gathered}$$

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$$\begin{gathered} {\beta }_1={\gamma }_{10}+{\gamma }_{11}(\mathrm{PercentForBorn}{)}_j+ \\ {\gamma }_{12}(\mathrm{CollEff}{)}_j+{\gamma }_{13}(\mathrm{SocIntEx}{)}_j+u_1 \end{gathered}$$

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10.2105/AJPH.2006.087551

$$\begin{gathered} \log \left(\mathrm{hiv}\right)=\mathrm{offset}\left[\log \right({\mathrm{pop}}_{\mathrm{yr}}{i}_{\text{,}}{j}_{}\left)\right]+b_0+ \\ {b}_1(\mathrm{yr}-20001)+b_{2}I(\mathrm{yr}>2002)+ \\ {b}_{3}I(\mathrm{yr}>2003)+b_4{\mathrm{age}}_i+b_5{\mathrm{race}}_j+\epsilon \text{,} \end{gathered}$$

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$$\begin{gathered} \log \left(\mathrm{hiv}\right)=\mathrm{offset}\left(\log \right({\mathrm{pop}}_{\mathrm{yr}}{j}_{}\left)\right)+b_0+b_1(\mathrm{yr}-20001)+ \\ {b}_4{\mathrm{age}}_i+b_5{\mathrm{race}}_j+b_6(\mathrm{yr}>2001)\times {\mathrm{age}}_i+ \\ {b}_7{\mathrm{ij}}_{}{\mathrm{age}}_i\times {\mathrm{race}}_j+\epsilon ;i=1\text{,}\text{.}\text{.}\text{.}\text{,}11;j=1\text{,}2\text{,}3\text{.} \end{gathered}$$

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10.2105/AJPH.2005.074609

$$\begin{gathered} Y_{\mathrm{ti}}={\pi }_0+{\pi }_1{a}_1+{\pi }_2{a}^2{1}_{\mathrm{ti}}+{\pi }_3{a}_2+ \\ {\pi }_4{a}^2{2}_{\mathrm{ti}}+\text{.}\text{.}\text{.}+{\pi }_P{a}^P{P}_{\mathrm{ti}}+e_{\mathrm{ti}}\text{.} \end{gathered}$$

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${\pi }_{\mathrm{pi}}=b_p+\sum _{q=1}^{Q_p}{b}_{\mathrm{pq}}{X}_{\mathrm{qi}}+r_{\mathrm{pi}}\text{,}$

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10.2105/AJPH.2005.071522

$Y_{\mathrm{ijk}}={\pi }_{\mathrm{ijk}}+{\epsilon }_{\mathrm{ijk}}{Z}_{\mathrm{ijk}}\text{,}$

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10.2105/AJPH.2006.093708

$$\begin{gathered} \mathrm{Overall}\mathrm{Mortality}\mathrm{Difference}= \\ \sum _i^{}\left(\right(P_{\mathrm{Bi}}-P_{\mathrm{Wi}})*\left(\frac{R_{\mathrm{Bi}}+R_{\mathrm{Wi}}}{2}\right)+(R_{\mathrm{Bi}}-R_{\mathrm{Wi}})*\left(\frac{P_{\mathrm{Bi}}+P_{\mathrm{Wi}}}{2}\right))\text{,} \end{gathered}$$

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10.2105/AJPH.2005.084343

$P\left(\mathrm{Ob}\right)=P\left(\mathrm{Ob}S\right)P\left(S\right)+P\left(\mathrm{Ob}N\right)(1-P[S\left]\right)\text{,}$

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$P(\mathrm{Ob}*)=P\left(\mathrm{ObS}\right)P(S*)+P\left(\mathrm{ObN}\right)(1-P[S*\left]\right)\text{,}$

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$P\left(\mathrm{Ob}\right)-P(\mathrm{Ob}*)=\left(P\right[S*]-P[S\left]\right)\left(P\right[\mathrm{ObS}]-P[\mathrm{ObN}\left]\right)$

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10.2105/AJPH.2006.092692

$\mathrm{FFM}=0.61\times H^2÷R+0.25\times W+1.31$

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10.2105/AJPH.2006.093195

$$\begin{gathered} \ln \left(E\right[Y_t\left]\right)=B+B_1\times t+B_2\times \sin (2\pi t/T)+ \\ {B}_3\times \cos (2\pi t/T)+B_4\times X_t\text{,} \end{gathered}$$

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10.2105/AJPH.2006.087320

$\mathrm{ID}=\left\{\right({\sum }_i|Q_{\mathrm{ri}}-Q_{\mathrm{r5}}|/I)/Q_{\mathrm{r5}}\}\times 100\text{,}$

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10.2105/AJPH.2005.063669

$\frac{1}{n}\sum _{i=1}^n{s}_i{t}_i=d\equiv 0.1\text{,}0.15\text{.}$

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10.2105/AJPH.2005.079418

$$\begin{gathered} \mathrm{BMR}=655+\left(9.6\times \mathrm{weight}\mathrm{in}\mathrm{kilograms}\right)+ \\ \left(1.8\times \mathrm{height}\mathrm{in}\mathrm{centimeters}\right)- \\ \left(4.7\times \mathrm{age}\mathrm{in}\mathrm{years}\right) \end{gathered}$$

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$Y=X\beta +Z\gamma +\epsilon \text{,}$

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10.2105/AJPH.2006.095844

$\left[D÷\right(D+S\left)\right]\times 100\text{,}$

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10.2105/AJPH.2007.114769

$\mathrm{PD}=\left[\right(\mathrm{kg}-D)/\mathrm{kg}]\times 100\%$

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$$\begin{gathered} U={\beta }_0+{\beta }_1\mathrm{age}+{\beta }_2{\mathrm{age}}^2+{\beta }_3\mathrm{BMI} \\ +{\beta }_4\mathrm{PD}+{\beta }_5{\mathrm{PD}}^2+{\beta }_{6}C+e\text{,} \end{gathered}$$

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10.2105/AJPH.2007.113738

${\pi }_{\mathrm{ijkl}}:y_{\mathrm{ijkl}}~\mathrm{Bernoulli}\left(1\text{,}{\pi }_{\mathrm{ijkl}}\right)$

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$$\begin{gathered} \mathrm{logit}\left({\pi }_{\mathrm{ijkl}}\right)=\log [{\pi }_{\mathrm{ijkl}}/(1-{\pi }_{\mathrm{ijkl}}\left)\right]={\beta }_0 \\ +\beta X+u_{\mathrm{0jkl}}+v_{\mathrm{0kl}}+f_{\mathrm{0l}} \end{gathered}$$

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10.2105/AJPH.2007.110080

$E_c=(P_{\mathrm{t2}}/P_{\mathrm{t1}})H_{\mathrm{t1}}\text{,}$

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10.2105/AJPH.2007.114454

$h\left(t\right)=\exp \{a+b_i{x}_i+\gamma t\}\text{,}$

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$h\left(t\right)=\underset{s\to 0}{\overset{}{\lim }}P(t\text{,}t+s)/s\text{,}$

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10.2105/AJPH.2007.123075

$$\begin{gathered} \mathrm{RRR}\left(\mathrm{health}\mathrm{limitation}\right)=\mathrm{probability}[\mathrm{pre}-\mathrm{contemplation}]/\mathrm{probability}\left[\mathrm{maintenance}\right]\mathrm{with}a\mathrm{health}\mathrm{limitation}\text{.} \\ \mathrm{or}\mathrm{probability}\left[\mathrm{precontemplation}\right]/\mathrm{probability}\left[\mathrm{maintenance}\right]\mathrm{without}a\mathrm{health}\mathrm{limitation}=1.83;95\%\mathrm{CI}=1.29\text{,}2.59\text{.} \end{gathered}$$

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10.2105/AJPH.2007.120253

$P(\mathrm{OR}-1)/1+P(\mathrm{OR}-1)\text{,}$

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10.2105/AJPH.2006.099416

$H_i\left(t\right)={\lambda }_0\left(t\right)\exp \{{\beta }_1{x}_i+\dots +{\beta }_k{x}_{\mathrm{ik}}\}$

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10.2105/AJPH.2007.116020

$$\begin{gathered} \mathrm{eGFR}(\mathrm{mL}/\min /1.73m^2)=186.3\times \\ \left(\mathrm{serum}{\mathrm{creatinine}}^{-}\right)\times \left({\mathrm{age}}^{-}\right)\times \\ \left(0.742\mathrm{if}\mathrm{female}\mathrm{and}1.21\mathrm{if}\mathrm{Black}\right)\text{.} \end{gathered}$$

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10.2105/AJPH.2007.127563

$$\begin{gathered} \left(\right[Y_1+Y_2+Y_3+Y_4+Y_5+Y_6+ \\ {Y}_7+Y_8]-[Y_9+Y_{10}+Y_{11}+Y_{12}+ \\ {Y}_{13}+Y_{14}+Y_{15}+Y_{16}\left]\right)÷16\text{,} \end{gathered}$$

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$$\begin{gathered} \left(\right[Y_1+Y_2+Y_3+Y_4+Y_{13}+Y_{14}+ \\ {Y}_{15}+Y_{16}]-[Y_5+Y_6+Y_7+Y_8+ \\ {Y}_9+Y_{10}+Y_{11}+Y_{12}\left]\right)÷16\text{,} \end{gathered}$$

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10.2105/AJPH.2007.124446

$Y_t\left(u\right)-Y_c\left(u\right)\text{,}$

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10.2105/AJPH.2007.124610

$\left[\right(1/{\sigma }_i^2{2}^{})/\sum _i^n{\sigma }_i^2{2}^{}]\times 100\text{.}$

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$\mathrm{PFE}=1-\mathrm{RR}\text{.}$

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10.2105/AJPH.2007.127027

$1+(m-1)\rho$

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$1+(m_1-1){\rho }_1$

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$1+(m_2-1){\rho }_2$

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$\hat{\sigma }{2}^{}{\Delta }_{}=2*2\left(\frac{\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{\mathrm{yy}\left(m\right)}_{})+m\hat{\sigma }{2}^{}{g}_{}(1-\hat{r}{\mathrm{yy}\left(g\right)}_{})}{\mathrm{mg}}\right)$

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$\hat{\sigma }{2}^{}{\Delta }_{}=2\left(\frac{\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{2}^{}{\mathrm{yy}\left(m\right)}_{})+m\hat{\sigma }{2}^{}{g}_{}(1-\hat{r}{2}^{}{\mathrm{yy}\left(g\right)}_{})}{\mathrm{mg}}\right)$

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$\hat{\sigma }{2}^{}{\Delta }_{}2=\left(\frac{2\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{\mathrm{yy}\left(m\right)}_{})+m\hat{\sigma }{2}^{}{g}_{}}{\mathrm{mg}}\right)$

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$\hat{\sigma }{2}^{}{\Delta }_{}=\left(\frac{2\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{2}^{}{\mathrm{yy}\left(m\right)}_{})+m\hat{\sigma }{2}^{}{g}_{}}{\mathrm{mg}}\right)$

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$\hat{\sigma }{2}^{}{\Delta }_{}2=(\frac{\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{\mathrm{yy}\left(m\right)}_{})}{N_1}+\frac{\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{\mathrm{yy}\left(m\right)}_{})+m\hat{\sigma }{2}^{}{g}_{}}{N_2})$

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$(\frac{\hat{\sigma }{2}^{}{\Delta }_{}=(\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{2}^{}{\mathrm{yy}\left(m\right)}_{})}{N_1}+\frac{\hat{\sigma }{2}^{}{m}_{}(1-\hat{r}{2}^{}{\mathrm{yy}\left(m\right)}_{})+1/2m\hat{\sigma }{2}^{}{g}_{}}{N_2})$

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$\hat{\Delta }=\sqrt{\hat{\sigma }{2}^{}{\Delta }_{}{(t}_{\mathrm{critical}:}{\alpha }_{/}{2}_{}+t_{\mathrm{critical}:}{\beta }_{}{)}^2}$

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10.2105/AJPH.2006.108233

$Y_{\mathrm{ij}}=u_{\mathrm{0i}}^{\left(}{\left(}^1+b_1{\left(}^1{X}_{\mathrm{ij}}+e_{\mathrm{ij}}^{\left(}{\left(}^1\text{,}$

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$Y_{\mathrm{ij}}=u{\mathrm{0i}}_{}{\left(}^2+b_1{\left(}^2{X}_{\mathrm{ij}}+b_2^{\left(}{\left(}^2\overline{X}{i}_{}+e_{\mathrm{ij}}^{\left(}{\left(}^2$

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$Y_{\mathrm{ij}}-Y_{\mathrm{ik}}=b_1^{\left(}{\left(}^3(X_{\mathrm{ij}}-X_{\mathrm{ij}})+e_{\mathrm{ij}}^{\left(}{\left(}^3\text{.}$

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10.2105/AJPH.2005.083600

$N_{\mathrm{est}}=\sum \frac{\mathrm{HOPE}\mathrm{count}\mathrm{in}\mathrm{stratum}}{\gamma \mathrm{stratum}}$

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10.2105/AJPH.2007.129924

$\left[P\times \right(\mathrm{RR}-1\left)\right]/\left[\right(1+P\left)\times \right(\mathrm{RR}-1\left)\right]\text{,}$

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