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{"sheet":"Calculation","index":0,"n_rows":60,"n_cols":29,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["KARCHE2005 friend connectedness",null,null,"From Table II",null,null,{"$f":"TEXT(TODAY(),\"          dd-mmm-yyyy\")","v":"          12-Nov-2019"},null,null,"Instructions: ",null,null,"T:\\Jan\\RRest\\RREst_trend.xlsm",null,null,null,null,null,"Release date: under development",null,null,null,null,null,null,"Trend (Dose as entered)"]
[null,null,null,null,null,null,null,null,null,"1) Select Study type (case control, prospective or cross-sectional) and Categorised by (exposure or disease).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"This uses the specified dose values and the RR (CI) values to estimate a Beta value, which represents "]
["Results:",null,null,null,null,null,null,null,null,"2) Enter values/estimates in the No. of participants 2x2 table (P and Z are calculated from these).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"the change in log relative risk per unit change in dose. The confidence interval (CI) for Beta is also "]
["Overall risk for the",{"$f":"IF(N57=2,\"RR\",\"OR\")","v":"OR"}," CI Lower"," CI Upper",null,"Decimal places:",5,null,null,"3) Enter RR, CI Lower and CI Upper (95% CI) for each category. A description can be entered for each one.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"estimated. The exponentiated values are presented. The method is described in Berlin 1993 with"]
["specified contrast",{"$f":"IF(P59=1,IF(OR(N57=1,N57=3,S57=1),N53*O53/(P53*M53),N53*H23/(P53*G23)),0)","v":2.2290934191164316},{"$f":"IF(P59=1,EXP(K57),0)","v":0.97546695082519519},{"$f":"IF(P59=1,EXP(K58),0)","v":5.093824518549587},null,null,null,null,null,"    For valid trend estimates, enter the rows of data in order of increasing exposure (increasing dose).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Greenland and Longnecker 1992 providing a correction to take account of the non-independence of the"]
[null,"    Chi-sq","     DF","       p",null,"Solver Precision:",null,null,null,"4) Enter the required Contrast to be used in estimating Overall risk: ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"RR (CI) values. The method for extending this to prospective studies is given in Orsini 2012."]
["Heterogeneity",{"$f":"IF(P59=1,((X55-1)*(1/W53+1/X53)*R53),0)","v":8.6540419412225429},{"$f":"IF(P59=1,S53-1,0)","v":2},{"$f":"IF(P59=1,CHIDIST(B7,C7),0)","v":1.3206832487557923E-2},null,null,null,null,null,"    0 for baseline, 1 for comparison, -1 to exclude the category.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Note: ","Trend is not calculated if the data are entered out of order of increasing dose."]
["Trend (Breslow 1980)",{"$f":"IF(T59=1,IF(S57=1,Q60,0),0)","v":8.4535897012395438},{"$f":"IF(T59=1,IF(S57=1,S60,0),0)","v":1},{"$f":"IF(T59=1,IF(S57=1,U60,0),0)","v":3.6432364343300027E-3},null,null,null,null,null,"    Note: For a prospective study categorised by disease, Ao and Bo are always the baseline.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The trend calculations ignore exposed rows with -1 in the Contrast column."]
[null,null,null,null,null,null,null,null,null,"5) Enter Dose values for the trend tests.  Dose should be proportional to amount of exposure. ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The method assumes zero dose for the first row, the unexposed. If a non-zero dose"]
["Trend: rate of increase in risk per unit dose",null,null,null,null,null,null,null,null,"    Note: Dose and Trend values are not meaningful for results categorised by disease type.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"is entered there, the code subtracts the \"unexposed\" dose from the dose for each category"]
[null,"      Rate"," CI Lower"," CI Upper",null,null,null,null,null,"6) Click Calculate to generate the table of Estimated nos. of participants in each category",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(see \"Dose values, adjusted\"). This has no effect on the trend (which equates to the slope)."]
["Dose as entered",1.9466981519420754,1.237109413232151,3.0632971136107132,null,null,null,null,null,"    and to calculate the values in Results. ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Trend (Uniform scale)"]
["Uniform scale",5.5864574004100129,1.7436887974215896,17.897979463275867," ",null,null,null,null,"    Generating the table of Estimated numbers of participants involves use of the Solver add-in: ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"This is calculated in the same way as Trend (Dose as entered) except that it does not use the specified "]
[null,null,null,null,null,null,null,null,null,"    this adjusts the first row of that table (Ao and Bo) to give the lowest Sum of Squares for the error in the",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"dose values. Instead a score is imputed for each category, using the order of the categories and the "]
["Data entry area:",null,"Study type:",null,null,"Categorised by:",null,null,null,"    resulting P' and Z' values. It uses the variance of each category, estimated using the CIs entered.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"distribution of the study population across the categories. This distribution is best approximated by the "]
[null,null,null,null,null,null,null,null,null,"7) Enter Heading and Notes to describe the study, the contrast etc. The spreadsheet can be saved to a file.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"controls (for case control), the at risk (for prospective) or the sum of cases and non-cases "]
[null,"No. of participants",{"$f":"IF(S57=1,\"Cases\",\"Exposed\")","v":"Cases"},{"$f":"IF(S57=1,IF(N57=1,\"Controls\",IF(N57=2,\"At Risk\",\"Non-cases\")),\"Unexposed\")","v":"Non-cases"},null,null,"Start values for",null,null,"If Calculate finds \"no feasible solution\", a) check the data entered, b) change the Solver Precision setting ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(for cross-sectional). The Estimated numbers (pseudo-numbers) are used. Score values lie between "]
[null,{"$f":"IF(S57=1,\"Unexposed\",IF(N57=1,\"Controls\",IF(N57=2,\"At Risk\",\"Non-cases\")))","v":"Unexposed"},19,37,null,null,{"$f":"IF(S57=1,\"  nos. of Unexposed\",IF(N57=1,\"   nos. of Controls\",IF(N57=2,\"    nos. At Risk\",\"  nos. of Non-cases\")))","v":"  nos. of Unexposed"},null,null,"    or c) change the Start values (Unprotect Sheet; overwrite the values in cells G20 and H20).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"0 and 1. The N individuals are each assigned a score value (\"dose\") of (n-0.5)/N. These values are then "]
[null,{"$f":"IF(S57=1,\"All Exposed\",\"All Cases\")","v":"All Exposed"},116,130,null,null,{"$f":"IF(S57=1,\"Cases\",\"Exposed\")","v":"Cases"},{"$f":"IF(S57=1,IF(N57=1,\"Controls\",IF(N57=2,\"At risk\",\"Non-cases\")),\"Unexposed\")","v":"Non-cases"},null,"See the documentation for the meanings of P, P', Z and Z'; and for details of the Sum of Squares calculations.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"averaged over category. Again, the vaues are adjusted to give zero scale value (dose) in the unexposed."]
[null,"Total",{"$f":"SUM(C18:C19)","v":135},{"$f":"SUM(D18:D19)","v":167},null,null,{"$f":"C18","v":19},{"$f":"D18","v":37},null,"Underlying calculations:",null,null,"Contrast:",null,null,null,"Heterogeneity and trend:",null,null,null,null,null,"No.(excluding",null,null,"Trend","Dose as entered","Uniform scale"]
[null,null,null,null,null,null,"---- Estimated nos. ----",null,null,null,"Variance:",null,"Base","Comp.","Base","Comp.",null,"Hetero:","DF+1","Trend",null,null,"contrast = -1)",null,null,null,"Dose values",null,"Scale values"]
["Category",{"$f":"IF(N57=2,\"RR\",\"OR\")","v":"OR"}," CI Lower"," CI Upper"," Contrast","Dose",{"$f":"IF(S57=1,\"Cases\",\"Exposed\")","v":"Cases"},{"$f":"IF(S57=1,IF(N57=1,\"Controls\",IF(N57=2,\"At risk\",\"Non-cases\")),\"Unexposed\")","v":"Non-cases"},null,"Category","V(i)","Vextra",{"$f":"IF(S57=1,\"cases\",\"exposed\")","v":"cases"},{"$f":"IF(S57=1,\"cases\",\"exposed\")","v":"cases"},{"$f":"IF(S57=1,IF(N57=1,\"cntrls\",IF(N57=2,\"at risk\",\"non-cs\")),\"unexp\")","v":"non-cs"},{"$f":"IF(S57=1,IF(N57=1,\"cntrls\",IF(N57=2,\"at risk\",\"non-cs\")),\"unexp\")","v":"non-cs"},"e","(a-e)^2/m",null,"x(a-e)","x^2m","xm",{"$f":"IF(S57=1,IF(N57=1,\"cases\",\"dead\"),\"exposed\")","v":"dead"},{"$f":"IF(S57=1,IF(N57=1,\"cntrls\",\"alive\"),\"unexp\")","v":"alive"},null,"Var by Ns","adjusted","Scale values","adjusted"]
["Low",1,"-","-",0,0,9.3274803083770248,22.578173522858062,null,{"$f":"IF(AND(N57=2,S57=2),\"At risk/Alive\",A23)","v":"Low"},null,null,{"$f":"IF(E23=0,G23,0)","v":9.3274803083770248},{"$f":"IF(E23=1,G23,0)","v":0},{"$f":"IF(E23=0,H23,0)","v":22.578173522858062},{"$f":"IF(E23=1,H23,0)","v":0},{"$f":"(W23+X23)*$W$53/$X$55","v":14.262462642921747},{"$f":"IF((W23+X23)=0,0,((W23-Q23)^2)/(W23+X23))","v":0.76331457650387602},{"$f":"IF(Q23=0,0,1)","v":1},{"$f":"F23*(W23-Q23)","v":0},{"$f":"(F23^2)*(W23+X23)","v":0},{"$f":"F23*(W23+X23)","v":0},{"$f":"IF(OR(E23=-1,G23+H23=0),0,IF(AND(N57=2,S57=2),G23-SUM(G24:G52),G23))","v":9.3274803083770248},{"$f":"IF(OR(E23=-1,G23+H23=0),0,IF(OR($N$57=1,$N$57=3),H23,IF($S$57=1,H23-G23,H23-SUM(H24:H52))))","v":22.578173522858062},null,null,0,8.6565253793516608E-2,0]
["Medium",1.7,0.72,4.04,1,1,{"$f":"IF(B24>0,IF(OR($N$57=1,$N$57=3),(1+($G$23*B24/$H$23))/L24,IF($S$57=1,(1-($G$23*B24/$H$23))/L24,(1+($G$23*B24/$H$23))/L24)),0)","v":40.439589363083456},{"$f":"IF(B24>0,IF(OR($N$57=1,$N$57=3),(1+$H$23/($G$23*B24))/L24,IF($S$57=1,(-1+$H$23/($G$23*B24))/L24,(1+$H$23/($G$23*B24))/L24)),0)","v":57.58140813307697},null,{"$f":"A24","v":"Medium"},{"$f":"IF(B24>0,((LN(D24/C24))/(2*NORMINV(0.975,0,1)))^2,0)","v":0.19359561174113588},{"$f":"IF(B24>0,IF(OR($N$57=1,$N$57=3),+K24-(1/$G$23)-(1/$H$23),IF($S$57=1,+K24-(1/$G$23)+(1/$H$23),+K24+(1/$G$23)+(1/$H$23))),0)","v":4.2094959844421728E-2},{"$f":"IF(E24=0,G24,0)","v":0},{"$f":"IF(E24=1,G24,0)","v":40.439589363083456},{"$f":"IF(E24=0,H24,0)","v":0},{"$f":"IF(E24=1,H24,0)","v":57.58140813307697},{"$f":"(W24+X24)*$W$53/$X$55","v":43.817337905242233},{"$f":"IF((W24+X24)=0,0,((W24-Q24)^2)/(W24+X24))","v":0.11639531840616754},{"$f":"IF(Q24=0,0,1)","v":1},{"$f":"F24*(W24-Q24)","v":-3.377748542158777},98.020997496160419,98.020997496160419,{"$f":"IF(OR(E24=-1,G24+H24=0),0,G24)","v":40.439589363083456},{"$f":"IF(OR(E24=-1,G24+H24=0),0,IF(AND($N$57=2,$S$57=1),H24-G24,H24))","v":57.58140813307697},null,{"$f":"IF(B24>0,IF(OR(N$57=1,N$57=3),(1/G$23)+(1/H$23)+(1/G24)+(1/H24),IF(S$57=1,(1/G$23)-(1/H$23)+(1/G24)-(1/H24),-(1/G$23)-(1/H$23)+(1/G24)+(1/H24))),0)","v":0.19359561174113588},0,0.43907749523478068,0.35251224144126408]
["High",3.63,1.43,9.3000000000000007,1,2,{"$f":"IF(B25>0,IF(OR($N$57=1,$N$57=3),(1+($G$23*B25/$H$23))/L25,IF($S$57=1,(1-($G$23*B25/$H$23))/L25,(1+($G$23*B25/$H$23))/L25)),0)","v":32.612765296400198},{"$f":"IF(B25>0,IF(OR($N$57=1,$N$57=3),(1+$H$23/($G$23*B25))/L25,IF($S$57=1,(-1+$H$23/($G$23*B25))/L25,(1+$H$23/($G$23*B25))/L25)),0)","v":21.747306010550044},null,"High",0.22814619875184319,{"$f":"IF(B25>0,IF(OR($N$57=1,$N$57=3),+K25-(1/$G$23)-(1/$H$23),IF($S$57=1,+K25-(1/$G$23)+(1/$H$23),+K25+(1/$G$23)+(1/$H$23))),0)","v":7.6645546855129046E-2},0,{"$f":"IF(E25=1,G25,0)","v":32.612765296400198},0,21.747306010550044,24.300034419696694,{"$f":"IF((W25+X25)=0,0,((W25-Q25)^2)/(W25+X25))","v":1.2711810887500583},1,16.625461753407009,217.44028522780098,108.72014261390049,{"$f":"IF(OR(E25=-1,G25+H25=0),0,G25)","v":32.612765296400198},{"$f":"IF(OR(E25=-1,G25+H25=0),0,IF(AND($N$57=2,$S$57=1),H25-G25,H25))","v":21.747306010550044},null,{"$f":"IF(B25>0,IF(OR(N$57=1,N$57=3),(1/G$23)+(1/H$23)+(1/G25)+(1/H25),IF(S$57=1,(1/G$23)-(1/H$23)+(1/G25)-(1/H25),-(1/G$23)-(1/H$23)+(1/G25)+(1/H25))),0)","v":0.22814619875184317},0,0.85251224144126414,0.76594698764774749]
[3,null,null,null,null,null,0,0,null,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[4,null,null,null,null,null,{"$f":"IF(B27>0,IF(OR($N$57=1,$N$57=3),(1+($G$23*B27/$H$23))/L27,IF($S$57=1,(1-($G$23*B27/$H$23))/L27,(1+($G$23*B27/$H$23))/L27)),0)","v":0},{"$f":"IF(B27>0,IF(OR($N$57=1,$N$57=3),(1+$H$23/($G$23*B27))/L27,IF($S$57=1,(-1+$H$23/($G$23*B27))/L27,(1+$H$23/($G$23*B27))/L27)),0)","v":0},null,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[5,null,null,null,null,null,0,0,null,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[6,null,null,null,null,null,0,0,null,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[7,null,null,null,null,null,0,0,null,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[8,null,null,null,null,null,0,0,null,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[9,null,null,null,null,null,0,0,null,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[10,null,null,null,null,null,0,0,null,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[11,null,null,null,null,null,0,0,null,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[12,null,null,null,null,null,0,0,null,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[13,null,null,null,null,null,0,0,null,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[14,null,null,null,null,null,0,0,null,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[15,null,null,null,null,null,0,0,null,15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[16,null,null,null,null,null,0,0,null,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[17,null,null,null,null,null,0,0,null,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[18,null,null,null,null,null,0,0,null,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[19,null,null,null,null,null,0,0,null,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[20,null,null,null,null,null,0,0,null,20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[21,null,null,null,null,null,0,0,null,21,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[22,null,null,null,null,null,0,0,null,22,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[23,null,null,null,null,null,0,0,null,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[24,null,null,null,null,null,0,0,null,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[25,null,null,null,null,null,0,0,null,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[26,null,null,null,null,null,0,0,null,26,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[27,null,null,null,null,null,0,0,null,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[28,null,null,null,null,null,0,0,null,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
[29,null,null,null,null,null,0,0,null,29,0,0,0,0,0,0,0,0,0,0,0,0,0,0,null,0,0,0,0]
["Notes:",null,null,null,null,null,null,null,null,"Col. totals:",null,null,{"$f":"SUM(M23:M52)","v":9.3274803083770248},73.052354659483655,22.578173522858062,79.32871414362701,null,2.1508909836601018,3,{"$f":"SUM(T23:T52)","v":13.247713211248232},{"$f":"SUM(U23:U52)","v":315.4612827239614},{"$f":"SUM(V23:V52)","v":206.74114011006091},{"$f":"SUM(W23:W52)","v":82.379834967860688},{"$f":"SUM(X23:X52)","v":101.90688766648508}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(S57=1,\"Tot cases:\",\"Tot exposed:\")","v":"Tot cases:"},{"$f":"SUM(G23:G52)","v":82.379834967860688},"Study",1,"Case control",null,null,null,null,"RRs by category of","Total participants included in",null,null,null,null,null,"Ln (RR) values:"]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(S57=1,IF(N57=1,\"Tot cntrls:\",IF(N57=3,\"Tot non-cs:\",\"Tot at risk:\")),\"Tot unexp:\")","v":"Tot non-cs:"},{"$f":"SUM(H23:H52)","v":101.90688766648508},"types",2,"Prospective",null,null,1,"Exposure",null,null,null,null,"hetero/trend analyses (N):",{"$f":"SUM(W53:X53)","v":184.28672263434578},null,null,"Dose as entered","Uniform scale"]
[null,null,null,null,null,null,null,null,null,"Variance:",{"$f":"IF(OR(N57=1,N57=3),(1/M53)+(1/N53)+(1/O53)+(1/P53),IF(S57=1,(1/M53)+(1/N53)-(1/O53)-(1/P53),-(1/G23)+(1/N53)-(1/H23)+(1/P53)))","v":0.17779524058272428},null,3,"Cross-sectional",null,null,2,"Disease",null,null,null,"Sum of squares:",{"$f":"((V57-V58)/V57)^2+((X57-X58)/X57)^2","v":3.712022789215564E-14},null,null,"Beta",0.6661346819840761,1.720345347523754]
[null,null,null,null,null,null,null,null,null,"Ln(Lower):",{"$f":"LN(B5)-(NORMINV(0.975,0,1)*SQRT(K56))","v":-2.4838998708471394E-2},"Current type:",null,3,null,null,null,"Curr cat:",1,"Initial:","P",{"$f":"D18/D20","v":0.22155688622754491},"Z",{"$f":"D20/C20","v":1.2370370370370369},null,"Var (Beta)",5.3503813995988178E-2,0.3529110875731194]
[null,null,null,null,null,null,null,null,null,"Ln(Upper):",{"$f":"LN(B5)+(NORMINV(0.975,0,1)*SQRT(K56))","v":1.6280289273085349},null,null,null,null,"Current no. of decimal places:",5,null,null,"Soln.:","P'",{"$f":"H23/K55","v":0.22155689413997798},"Z'",{"$f":"K55/K54","v":1.2370368028321808},null,"se (Beta)",0.23130891464876183,0.59406320166554616]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Estimated numbers valid?",1,null,"Trend valid?",null,1,null,"1 = True; 0 = False"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Trend (Breslow 1980):","ChiSq:",{"$f":"((X55^2)*(X55-1)*(T53^2))/(W53*X53*(X55*U53-(V53^2)))","v":8.4535897012395438},"DF:",1,"p:",{"$f":"CHIDIST(Q60,S60)","v":3.6432364343300027E-3}]

{"sheet":"ByDistribution","index":1,"n_rows":98,"n_cols":11,"rows_kept":98,"cut":false,"hidden":true,"merged":[]}
["Trend by Distribution"]
[]
["Examples: Peter's example",null,null,"Individuals."]
[null,"Low","High"]
["N",5,5]
[]
["Participant","Rank","Scaled rank","Mean scaled rank"]
[1,0.5,{"$f":"B8/A$18","v":0.05},{"$f":"SUM(C8:C12)/5","v":0.25}]
[2,1.5,{"$f":"B9/A$18","v":0.15}]
[3,2.5,0.25]
[4,3.5,0.35]
[5,4.5,0.45]
[6,5.5,0.55000000000000004,{"$f":"SUM(C13:C17)/5","v":0.75}]
[7,6.5,{"$f":"B14/A$18","v":0.65}]
[8,7.5,0.75]
[9,8.5,0.85]
[10,9.5,0.95]
[{"$f":"COUNT(A8:A17)","v":10}]
[]
["Rank = mid-point of range"]
[]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N"]
["Lowest",5,"0-5",2.5,{"$f":"B23","v":5},{"$f":"D23","v":2.5},{"$f":"F23/B$25","v":0.25},null,{"$f":"B23*G23","v":1.25}]
["Highest",5,">5-10",2.5,{"$f":"E23+B24","v":10},{"$f":"E23+D24","v":7.5},{"$f":"F24/B$25","v":0.75},null,{"$f":"B24*G24","v":3.75}]
["Total",{"$f":"SUM(B23:B24)","v":10},null,null,null,null,null,null,{"$f":"SUM(I23:I24)","v":5}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I25/B25","v":0.5}]
[]
["Examples: PA26's example",null,null,"Groups of known size."]
[]
["100 individuals:"]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N"]
["Lowest",30,"1-30",15,{"$f":"B32","v":30},{"$f":"D32","v":15},{"$f":"F32/B$36","v":0.15},null,{"$f":"B32*G32","v":4.5}]
["Group 2",20,"31-50",10,{"$f":"E32+B33","v":50},{"$f":"E32+D33","v":40},{"$f":"F33/B$36","v":0.4},null,{"$f":"B33*G33","v":8}]
["Group 3",40,"51-90",20,{"$f":"E33+B34","v":90},{"$f":"E33+D34","v":70},0.7,null,28]
["Highest",10,"91-100",5,{"$f":"E34+B35","v":100},95,0.95,null,9.5]
["Total",{"$f":"SUM(B32:B35)","v":100},null,null,null,null,null,null,{"$f":"SUM(I32:I35)","v":50}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I36/B36","v":0.5}]
[]
["Dose = running total (to start of range) + mid point (of range)"]
["Dose, scaled = Dose / Total N"]
[]
[]
["Greenland & Longnecker 1992 values"]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N",null,"Adjusted dose"]
["unexp",176.5,null,{"$f":"B45/2","v":88.25},{"$f":"B45","v":176.5},{"$f":"D45","v":88.25},{"$f":"F45/B$49","v":0.19567627494456763},null,{"$f":"B45*G45","v":34.536862527716188},null,{"$f":"G45-G$45","v":0}]
["<2.5",96.7,null,{"$f":"B46/2","v":48.35},{"$f":"E45+B46","v":273.2},{"$f":"E45+D46","v":224.85},{"$f":"F46/B$49","v":0.49855875831485585},null,{"$f":"B46*G46","v":48.210631929046563},null,{"$f":"G46-G$45","v":0.30288248337028822}]
["2.5-9.3",90.5,null,45.25,{"$f":"E46+B47","v":363.7},{"$f":"E46+D47","v":318.45},0.70609756097560972,null,63.90182926829268,null,0.51042128603104209]
[">9.3",87.3,null,43.65,451,407.34999999999997,0.90321507760532138,null,78.850676274944547,null,0.70753880266075375]
["Total",{"$f":"SUM(B45:B48)","v":451},null,null,null,null,null,null,{"$f":"SUM(I45:I48)","v":225.5}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I49/B49","v":0.5}]
[]
[]
["Berlin 1993:"]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N",null,"Adjusted dose"]
["Never",156,null,{"$f":"B55/2","v":78},{"$f":"B55","v":156},{"$f":"D55","v":78},{"$f":"F55/B$60","v":0.14800759013282733},null,{"$f":"B55*G55","v":23.089184060721063},null,{"$f":"G55-G$55","v":0}]
["0-3 yrs",205,null,{"$f":"B56/2","v":102.5},{"$f":"E55+B56","v":361},{"$f":"E55+D56","v":258.5},{"$f":"F56/B$60","v":0.49051233396584443},null,{"$f":"B56*G56","v":100.55502846299811},null,{"$f":"G56-G$55","v":0.3425047438330171}]
["4-7 yrs",93,null,46.5,{"$f":"E56+B57","v":454},{"$f":"E56+D57","v":407.5},0.77324478178368117,null,71.911764705882348,null,0.6252371916508539]
["8-11 yrs",50,null,25,504,{"$f":"E57+D58","v":479},0.90891840607210628,null,45.445920303605313,null,0.76091081593927901]
["12+ yrs",23,null,11.5,527,{"$f":"E58+D59","v":515.5},0.9781783681214421,null,22.498102466793167,null,0.83017077798861472]
["Total",{"$f":"SUM(B55:B59)","v":527},null,null,null,null,null,null,{"$f":"SUM(I55:I59)","v":263.5}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I60/B60","v":0.5}]
[]
[]
["YUAN1996"]
[null,"N at risk","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N",null,"Adjusted dose"]
["Never",6761.4790000000003,null,{"$f":"B66/2","v":3380.7395000000001},{"$f":"B66","v":6761.4790000000003},{"$f":"D66","v":3380.7395000000001},{"$f":"F66/B$69","v":0.21341262777818956},null,{"$f":"B66*G66","v":1442.9850010570453},null,{"$f":"G66-G$66","v":0}]
["<20 cigs/day",4593.6656000000003,null,{"$f":"B67/2","v":2296.8328000000001},{"$f":"E66+B67","v":11355.1446},{"$f":"E66+D67","v":9058.3117999999995},{"$f":"F67/B$69","v":0.57181516779751351},null,{"$f":"B67*G67","v":2626.7276658696655},null,{"$f":"G67-G$66","v":0.35840254001932392}]
["20+ cigs/day",4486.1836999999996,null,2243.0918499999998,{"$f":"E67+B68","v":15841.328299999999},{"$f":"E67+D68","v":13598.23645},0.85840254001932403,null,{"$f":"B68*G68","v":3850.9514830732887},null,0.64498991224113444]
["Total",{"$f":"SUM(B66:B68)","v":15841.328299999999},null,null,null,null,null,null,{"$f":"SUM(I66:I68)","v":7920.6641499999996}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I69/B69","v":0.5}]
[]
[]
["KARCHE2005","Parental connectedness"]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N",null,"Adjusted dose"]
["Low",{"$f":"SUM(KARCHE2005_P!C16:D16)","v":66.898723772316828},null,{"$f":"B75/2","v":33.449361886158414},{"$f":"B75","v":66.898723772316828},{"$f":"D75","v":33.449361886158414},{"$f":"F75/B$78","v":8.5736703008569393E-2},null,{"$f":"B75*G75","v":5.7356760117194492},null,{"$f":"G75-G$75","v":0}]
["Medium",{"$f":"SUM(KARCHE2005_P!C17:D17)","v":170.75890113889119},null,{"$f":"B76/2","v":85.379450569445595},{"$f":"E75+B76","v":237.65762491120802},{"$f":"E75+D76","v":152.27817434176242},{"$f":"F76/B$78","v":0.39031622345027256},null,{"$f":"B76*G76","v":66.649969413050457},null,{"$f":"G76-G$75","v":0.30457952044170317}]
["High",{"$f":"SUM(KARCHE2005_P!C18:D18)","v":152.48289498743029},null,76.241447493715143,{"$f":"E76+B77","v":390.14051989863833},{"$f":"E76+D77","v":313.89907240492317},0.80457952044170311,null,{"$f":"B77*G77","v":122.68461452454923},null,0.71884281743313372]
["Total",{"$f":"SUM(B75:B77)","v":390.14051989863833},null,null,null,null,null,null,{"$f":"SUM(I75:I77)","v":195.07025994931914}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I78/B78","v":0.49999999999999994}]
[]
[]
["KARCHE2005","Friend connectedness"]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N",null,"Adjusted dose"]
["Low",{"$f":"SUM(KARCHE2005_F!C16:D16)","v":31.905694672581458},null,{"$f":"B84/2","v":15.952847336290729},{"$f":"B84","v":31.905694672581458},{"$f":"D84","v":15.952847336290729},{"$f":"F84/B$87","v":8.6565240039871136E-2},null,{"$f":"B84*G84","v":2.7619241179708518},null,{"$f":"G84-G$84","v":0}]
["Medium",{"$f":"SUM(KARCHE2005_F!C17:D17)","v":98.021220267603113},null,{"$f":"B85/2","v":49.010610133801556},{"$f":"E84+B85","v":129.92691494018456},{"$f":"E84+D85","v":80.91630480638301},{"$f":"F85/B$87","v":0.43907768945857545},null,{"$f":"B85*G85","v":43.03893091300926},null,{"$f":"G85-G$84","v":0.3525124494187043}]
["High",{"$f":"SUM(KARCHE2005_F!C18:D18)","v":54.360072873203322},null,27.180036436601661,{"$f":"E85+B86","v":184.2869878133879},{"$f":"E85+D86","v":157.10695137678621},0.85251244941870419,null,{"$f":"B86*G86","v":46.342638875713817},null,0.76594720937883309]
["Total",{"$f":"SUM(B84:B86)","v":184.2869878133879},null,null,null,null,null,null,{"$f":"SUM(I84:I86)","v":92.143493906693919}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I87/B87","v":0.49999999999999983}]
[]
[]
["GALLO2010"]
[null,"N","Range of ranks","Mid point","Running total","Dose","Dose, scaled",null,"Scaled Dose x N",null,"Adjusted dose"]
["unexp",{"$f":"GALLO2010!D11","v":21683.577113680567},null,{"$f":"B93/2","v":10841.788556840283},{"$f":"B93","v":21683.577113680567},{"$f":"D93","v":10841.788556840283},{"$f":"F93/B$97","v":0.45423118794025447},null,{"$f":"B93*G93","v":9849.3569911412378},null,{"$f":"G93-G$93","v":0}]
["0.5 pack/day",{"$f":"GALLO2010!D12","v":1016.6079127950323},null,{"$f":"B94/2","v":508.30395639751617},{"$f":"E93+B94","v":22700.185026475599},{"$f":"E93+D94","v":22191.881070078081},{"$f":"F94/B$97","v":0.92975844790208539},null,{"$f":"B94*G94","v":945.19979512528789},null,{"$f":"G94-G$93","v":0.47552725996183093}]
["1 pack/day",{"$f":"GALLO2010!D13","v":763.92164464401537},null,381.96082232200769,{"$f":"E94+B95","v":23464.106671119614},{"$f":"E94+D95","v":23082.145848797609},0.96705727787825235,null,738.75598618171909,null,0.51282608993799794]
["1.5+ packs/day",{"$f":"GALLO2010!D14","v":404.3304698948341},null,202.16523494741705,23868.437141014449,23666.271906067032,0.99153001791642126,null,400.90579805897988,null,0.53729882997616674]
["Total",{"$f":"SUM(B93:B96)","v":23868.437141014449},null,null,null,null,null,null,{"$f":"SUM(I93:I96)","v":11934.218570507226}]
["Mean dose",null,null,null,null,null,null,null,{"$f":"I97/B97","v":0.50000000000000011}]

{"sheet":"GREENL1992","index":2,"n_rows":75,"n_cols":28,"rows_kept":75,"cut":false,"hidden":true,"merged":[]}
["GREENL1992",null,null,"Note: our effective numbers are not used in testing: the code has an option to use the numbers given in the paper."]
["Data from Table 1 and text"]
[]
[null,"X","Fitted values (n)",null,"Adjusted results",null,null,"v(i)","v(i)","s(i)"]
[null,"Dose","Cases","Controls","RR","CI Lower","CI Upper","based on CI","based on n","based on n","1/Ao+1/Bo","r(x,2)","r(x,6)","r(x,11)","C(x,2)","C(x,6)","C(x,11)"]
["None",0,160.5,176.5,null,null,null,null,null,null,{"$f":"1/C6+1/D6","v":1.1896251974618976E-2}]
["<2.5 g",2,70.3,96.7,0.8,0.51,1.27,{"$f":"(LN(G7/F7)/(2*NORMINV(0.975,0,1)))^2","v":5.4172350994360845E-2},{"$f":"1/C$6+1/D$6+1/C7+1/D7","v":3.6462264675394644E-2},{"$f":"SQRT(I7)","v":0.1909509483490319},null,null,{"$f":"K6/(J7*J8)","v":0.34080302136564378},{"$f":"K6/(J7*J9)","v":0.35174613318129655},{"$f":"H7","v":5.4172350994360845E-2},{"$f":"M7*SQRT(H7*H8)","v":1.8816929178908301E-2},{"$f":"N7*SQRT(H7*H9)","v":1.9430257436283658E-2}]
["2.5-9.3 g",6,95.5,90.5,1.1599999999999999,0.73,1.85,{"$f":"(LN(G8/F8)/(2*NORMINV(0.975,0,1)))^2","v":5.6274668375185168E-2},{"$f":"1/C$6+1/D$6+1/C8+1/D8","v":3.3417179920006729E-2},{"$f":"SQRT(I8)","v":0.18280366495233821},null,{"$f":"K6/(J7*J8)","v":0.34080302136564378},null,{"$f":"K6/(J8*J9)","v":0.36742292736081344},{"$f":"L8*SQRT(H8*H7)","v":1.8816929178908301E-2},{"$f":"H8","v":5.6274668375185168E-2},{"$f":"N8*SQRT(H8*H9)","v":2.0686313695635193E-2}]
[">9.3 g",11,124.7,87.3,1.57,0.99,2.5099999999999998,5.6327537068760473E-2,3.1370251888271999E-2,0.1771164924231281,null,{"$f":"K6/(J9*J7)","v":0.35174613318129655},{"$f":"K6/(J9*J8)","v":0.36742292736081344},null,{"$f":"L9*SQRT(H9*H7)","v":1.9430257436283658E-2},{"$f":"M9*SQRT(H9*H8)","v":2.0686313695635193E-2},{"$f":"H9","v":5.6327537068760473E-2}]
[null,null,{"$f":"SUM(C6:C9)","v":451},{"$f":"SUM(D6:D9)","v":451}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Note:"]
["Check",1.0405810995291653,1.0025027096347201,1.0801058334215055,null,null,null,null,null,null,null,null,null,null,"C uses v(i) for diagonals and a calculation using r for off-diagonals."]
[null,1.4299932695602444,0.89595546669866033,2.2823464189826295,"L",null,null,null,"N Cases","N Controls",null,null,null,null,"v(i) are based on CIs."]
["None",null,null,null,null,null,null,"Unexposed",165,172,null,null,null,null,"r is calculated using the s(i) which are based on n values"]
["<2.5 g",null,{"$f":"(C7/D7)/(C$6/D$6)","v":0.79946328529962274},null,{"$f":"LN(E7)","v":-0.22314355131420971},null,null,"Exposed",{"$f":"451-I14","v":286},{"$f":"451-J14","v":279},null,null,null,null,null,"This is the best estimate we have for correlation."]
["2.5-9.3 g",null,{"$f":"(C8/D8)/(C$6/D$6)","v":1.1604447427755118},null,{"$f":"LN(E8)","v":0.14842000511827322},null,null,"Total",{"$f":"I14+I15","v":451},{"$f":"J14+J15","v":451}]
[">9.3 g",null,1.5708035813055565,null,0.45107561936021673]
[]
["Matrix with zero values:"]
[{"$f":"O7","v":5.4172350994360845E-2},{"$f":"P7","v":1.8816929178908301E-2},1.9430257436283658E-2,0,0,null,{"$f":"MINVERSE(A20:E24)","v":{"$error":"#NUM!"}},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},null,"We can't use MINVERSE to invert a generalised table of values:"]
[{"$f":"O8","v":1.8816929178908301E-2},5.6274668375185168E-2,2.0686313695635193E-2,0,0,null,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},null,"we need to provide MINVERSE with a fully-populated matrix"]
[1.9430257436283658E-2,2.0686313695635193E-2,5.6327537068760473E-2,0,0,null,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},null,"i.e. the parameters to MINVERSE need to specify "]
[0,0,0,0,0,null,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},null,"only the populated rows/columns."]
[0,0,0,0,0,null,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},null,"We can't do this in a variable way, dependent on the data entered."]
[]
["Matrix without zero values",null,null,null,null,null,"Inverted matrix"]
[{"$f":"O7","v":5.4172350994360845E-2},{"$f":"P7","v":1.8816929178908301E-2},1.9430257436283658E-2,null,null,null,{"$f":"MINVERSE(A27:C29)","v":22.388026621110807},-5.3724511336978296,-5.7497438753101404]
[{"$f":"O8","v":1.8816929178908301E-2},{"$f":"P8","v":5.6274668375185168E-2},{"$f":"Q8","v":2.0686313695635193E-2},null,null,null,-5.3724511336978296,21.832551905642404,-6.1647806201940023]
[1.9430257436283658E-2,2.0686313695635193E-2,5.6327537068760473E-2,null,null,null,-5.7497438753101413,-6.1647806201940032,22.000706119127805]
[null,null,null,null,null,null,null,null,null,null,"Dose by distribution"]
["X inverted",null,null,null,null,null,null,null,null,null,"Values from ByDistribution sheet",null,null,null,{"$f":"T32","v":"X(0)"},{"$f":"T33","v":"X(1)"},{"$f":"T34","v":"X(2)"},{"$f":"T35","v":"X(3)"}]
[{"$f":"B7","v":2},{"$f":"B8","v":6},{"$f":"B9","v":11},null,null,null,null,null,null,null,null,null,null,"X inverted",{"$f":"U32","v":0},{"$f":"U33","v":0.30288248337028822},{"$f":"U34","v":0.51042128603104209},{"$f":"U35","v":0.70753880266075375},null,"X(0)",{"$f":"ByDistribution!K45","v":0},"ignored"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ignored",null,null,null,null,"X(1)",{"$f":"ByDistribution!K46","v":0.30288248337028822}]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(G27:I29,E15:E17)","v":-8.3866922716309702},null,"x' C-1 L:",{"$f":"MMULT(A32:C32,D34:D36)","v":106.38947377141182},null,null,null,null,null,null,null,null,null,null,null,null,"X(2)",{"$f":"ByDistribution!K47","v":0.51042128603104209}]
[null,null,null,1.6584330543419266,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X(3)",{"$f":"ByDistribution!K48","v":0.70753880266075375}]
[null,null,null,10.29202363532929]
[]
[null,null,"x' C-1",{"$f":"MMULT(A32:C32,G27:I29)","v":-50.705836188376914},52.437822344324729,193.51959583862157,null,null,null,null,"x' C-1",{"$f":"MMULT(P32:R32,G27:I29)","v":-2.9439213181751356E-2},5.1547563811792712,10.678221309263098]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D38:F38,E15:E17)","v":106.38947377141182},null,null,null,null,null,null,"x' C-1 L:",{"$f":"MMULT(L38:N38,E15:E17)","v":5.5883234297966666}]
[]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D38:F38,B7:B9)","v":2341.9308159140319},null,"Vb*",{"$f":"1/D42","v":4.2699809627369805E-4},null,null,null,"x' C-1 x",{"$f":"MMULT(L38:N38,U33:U35)","v":10.177436678963847},null,"Vb*",{"$f":"1/L42","v":9.8256568087221829E-2}]
[]
[null,null,"b*",{"$f":"G42*D40","v":4.5428102763953378E-2},null,null,null,null,null,null,"b*",{"$f":"O42*L40","v":0.54908948157323323}]
[]
[]
["Identity matrix?",null,{"$f":"MMULT(A27:C29,G27:I29)","v":1},-1.3877787807814457E-17,0,null,"Yes!"]
[null,null,6.9388939039072284E-17,0.99999999999999978,5.5511151231257827E-17]
[null,null,5.5511151231257827E-17,0,1]
[]
["Exp(b*)",null,null,{"$f":"EXP(D44)","v":1.0464757631941928},null,"OR",null,null,"Exp(b*)",null,null,{"$f":"EXP(L44)","v":1.7316755773097059},null,"OR"]
["Exp(b*-1.96*Vb*)",null,null,{"$f":"EXP(D44-(NORMINV(0.975,0,1)*SQRT(G42)))","v":1.0049397000528357},null,"CI (lower)",null,null,"Exp(b*-1.96*Vb*)",null,null,{"$f":"EXP(L44-(NORMINV(0.975,0,1)*SQRT(O42)))","v":0.93680611213961862},null,"CI (lower)"]
["Exp(b*+1.96*Vb*)",null,null,{"$f":"EXP(D44+(NORMINV(0.975,0,1)*SQRT(G42)))","v":1.0897285905764209},null,"CI (upper)",null,null,"Exp(b*+1.96*Vb*)",null,null,{"$f":"EXP(L44+(NORMINV(0.975,0,1)*SQRT(O42)))","v":3.2009828567429186},null,"CI (upper)"]
[]
[]
["Increased dose values"]
["X inverted",null,null,null,null,null,null,null,"X"]
[3,7,12,null,null,null,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.9779306658150507E-2,0.35766973765951215]
[null,null,null,null,null,null,null,null,7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.6178385751231638E-4,5.6902426566579851E-2]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(G27:I29,E15:E17)","v":-8.3866922716309702},null,"x' C-1 L:",{"$f":"MMULT(A58:C58,D60:D62)","v":109.95323818945205},null,12]
[null,null,null,1.6584330543419266]
[null,null,null,10.29202363532929]
[]
[null,null,"x' C-1",{"$f":"MMULT(A58:C58,G27:I29)","v":-39.440004576274085},62.733142496075317,203.60577746224521]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D64:F64,E15:E17)","v":109.95323818945207}]
[]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D64:F64,I58:I60)","v":2764.0813132906478},null,"Vb*",{"$f":"1/D68","v":3.6178385751231638E-4}]
[]
[null,null,"b*",{"$f":"G68*D66","v":3.9779306658150507E-2}]
[]
[]
["Exp(b*)",null,null,{"$f":"EXP(D70)","v":1.0405810995291653},null,"OR"]
["Exp(b*-1.96*Vb*)",null,null,{"$f":"EXP(D70-(NORMINV(0.975,0,1)*SQRT(G68)))","v":1.0025027096347201},null,"CI (lower)"]
["Exp(b*+1.96*Vb*)",null,null,{"$f":"EXP(D70+(NORMINV(0.975,0,1)*SQRT(G68)))","v":1.0801058334215055},null,"CI (upper)"]

{"sheet":"BERLIN1993","index":3,"n_rows":40,"n_cols":23,"rows_kept":40,"cut":false,"hidden":true,"merged":[]}
["BERLIN1993",null,"Note: our effective numbers are not used in testing: the code has an option to use the numbers given in the paper."]
["Data from Table 1 and text"]
[null,null,null,null,null,null,null,"v(i)","v(i)","s(i)","rNum ="]
[null,"Dose","Cases","Controls","RR","CI Lower","CI Upper","based on CI","based on n","based on n","1/Ao+1/Bo","r(x,0-3)","r(x,4-7)","r(x,8-11)","r(x,12+)","C(x,0-3)","C(x,4-7)","C(x,8-11)","C(x,12+)",null,"L = Ln(RR)"]
["Never",0,96,156,null,null,null,null,null,null,{"$f":"1/C5+1/D5","v":1.6826923076923076E-2}]
["0-3 yrs",1.5,156,205,1.1000000000000001,0.8,1.6,{"$f":"(LN(G6/F6)/(2*NORMINV(0.975,0,1)))^2","v":3.1267614488666252E-2},{"$f":"1/C$5+1/D$5+1/C6+1/D6","v":2.8115228267667294E-2},{"$f":"SQRT(I6)","v":0.16767596210449276},null,null,{"$f":"K5/(J6*J7)","v":0.50127050609100321},{"$f":"K5/(J6*J8)","v":0.42243562611000152},{"$f":"K5/(J6*J9)","v":0.34231075027311569},{"$f":"H6","v":3.1267614488666252E-2},{"$f":"M6*SQRT(H6*H7)","v":1.9559432987432561E-2},{"$f":"N6*SQRT(H6*H8)","v":2.0124050831304228E-2},{"$f":"O6*SQRT(H6*H9)","v":1.8591160624625774E-2},null,{"$f":"LN(E6)","v":9.5310179804324935E-2}]
["4-7 yrs",5.5,80,93,1.2,0.8,1.9,{"$f":"(LN(G7/F7)/(2*NORMINV(0.975,0,1)))^2","v":4.869377766251793E-2},{"$f":"1/C$5+1/D$5+1/C7+1/D7","v":4.0079611248966085E-2},{"$f":"SQRT(I7)","v":0.20019892919035828},null,{"$f":"K5/(J6*J7)","v":0.50127050609100321},null,{"$f":"K5/(J7*J8)","v":0.35380958490471093},{"$f":"K5/(J7*J9)","v":0.28670125571041127},{"$f":"L7*SQRT(H7*H6)","v":1.9559432987432561E-2},{"$f":"H7","v":4.869377766251793E-2},{"$f":"N7*SQRT(H7*H8)","v":2.1033610248450973E-2},{"$f":"O7*SQRT(H7*H9)","v":1.9431437036346616E-2},null,{"$f":"LN(E7)","v":0.18232155679395459}]
["8-11 yrs",9.5,51,50,1.4,0.8,2.2999999999999998,7.2579669784642531E-2,5.6434766214177978E-2,0.23756002654945546,null,{"$f":"K5/(J8*J6)","v":0.42243562611000152},{"$f":"K5/(J8*J7)","v":0.35380958490471093},null,{"$f":"K5/(J8*J9)","v":0.24161171062508877},{"$f":"L8*SQRT(H8*H6)","v":2.0124050831304228E-2},{"$f":"M8*SQRT(H8*H7)","v":2.1033610248450973E-2},{"$f":"H8","v":7.2579669784642531E-2},{"$f":"O8*SQRT(H8*H9)","v":1.9992360049290784E-2},null,0.33647223662121289]
["12+ yrs",14.4,39,23,2.2000000000000002,1.2,4,{"$f":"(LN(G9/F9)/(2*NORMINV(0.975,0,1)))^2","v":9.4335939887449829E-2},{"$f":"1/C$5+1/D$5+1/C9+1/D9","v":8.5946209587513936E-2},{"$f":"SQRT(I9)","v":0.29316583973497651},null,{"$f":"K5/(J9*J6)","v":0.34231075027311569},{"$f":"K5/(J9*J7)","v":0.28670125571041127},{"$f":"K5/(J9*J8)","v":0.24161171062508877},null,{"$f":"L9*SQRT(H9*H6)","v":1.8591160624625774E-2},{"$f":"M9*SQRT(H9*H7)","v":1.9431437036346616E-2},{"$f":"N9*SQRT(H9*H8)","v":1.9992360049290784E-2},{"$f":"H9","v":9.4335939887449829E-2},null,0.78845736036427028]
["Total",null,{"$f":"SUM(C5:C9)","v":422},{"$f":"SUM(D5:D9)","v":527}]
[]
["Check",null,"OR"]
["None"]
["0-3 yrs",null,{"$f":"(C6/D6)/(C$5/D$5)","v":1.2365853658536585}]
["4-7 yrs",null,{"$f":"(C7/D7)/(C$5/D$5)","v":1.3978494623655913}]
["8-11 yrs",null,{"$f":"(C8/D8)/(C$5/D$5)","v":1.6575}]
["12+ yrs",null,{"$f":"(C9/D9)/(C$5/D$5)","v":2.7554347826086953}]
[]
["Inverted matrix",null,null,null,null,null,null,{"$f":"MINVERSE(P6:S9)","v":49.073475017748045},-14.204617057253367,-8.1051743137892576,-5.0275130762717719,null,null,"Check:",{"$f":"MMULT(P6:S9,H19:K22)","v":1},-6.9388939039072284E-18,-6.9388939039072284E-18,0]
[null,null,null,null,null,null,null,-14.204617057253367,28.80023762160782,-3.7646058933704203,-2.3351262567826465,null,null,null,-1.3877787807814457E-17,0.99999999999999978,4.163336342344337E-17,0]
[null,null,null,null,null,null,null,-8.1051743137892593,-3.7646058933704216,17.48327793570553,-1.3324263005221266,null,null,null,-5.5511151231257827E-17,-8.3266726846886741E-17,1,-2.7755575615628914E-17]
[null,null,null,null,null,null,null,-5.0275130762717728,-2.335126256782647,-1.3324263005221266,12.354575676074878,null,null,null,-5.5511151231257827E-17,2.7755575615628914E-17,0,1]
[]
[]
["X inverted",null,null,null,null,null,null,null,null,null,"Dose by distribution"]
[{"$f":"B6","v":1.5},{"$f":"B7","v":5.5},{"$f":"B8","v":9.5},{"$f":"B9","v":14.4},null,null,null,null,null,null,"Values from ByDistribution sheet",null,null,null,{"$f":"U27","v":"X(0)"},{"$f":"U28","v":"X(1)"},{"$f":"U29","v":"X(2)"},{"$f":"U30","v":"X(3)"},"X(4)",null,null,"X"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"X inverted",{"$f":"V27","v":0},{"$f":"V28","v":0.3425047438330171},{"$f":"V29","v":0.6252371916508539},{"$f":"V30","v":0.76091081593927901},{"$f":"V31","v":0.83017077798861472},null,"X(0)",{"$f":"ByDistribution!K55","v":0},"ignored"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ignored",null,null,null,null,null,"X(1)",{"$f":"ByDistribution!K56","v":0.3425047438330171}]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(H19:K22,U6:U9)","v":-4.603751986855352},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X(2)",{"$f":"ByDistribution!K57","v":0.6252371916508539}]
[null,null,null,0.78922670394906858,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X(3)",{"$f":"ByDistribution!K58","v":0.76091081593927901}]
[null,null,null,3.373201878319894,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X(4)",{"$f":"ByDistribution!K59","v":0.83017077798861472}]
[null,null,null,8.3878146387939001]
[]
[null,null,"x' C-1",{"$f":"MMULT(A26:D26,H19:K22)","v":-153.91052556758297},67.704807248273809,114.04110777746271,144.86337585380582,null,null,null,"x' C-1",{"$f":"MMULT(P27:S27,H19:K22)","v":-2.4143661297150967},8.3387480396614748,7.0672416323244276,6.0605952559704921]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D34:G34,U6:U9)","v":150.265067534108},null,{"$f":"MMULT(A26:D26,D29:D32)","v":150.265067534108},null,null,null,null,"x' C-1 L:",{"$f":"MMULT(L34:O34,U6:U9)","v":8.4466713908964639},null,{"$f":"MMULT(P27:S27,D29:D32)","v":8.4466713908964621}]
[null,null,null,null,null,null,null,null,"se(B*)",null,null,null,null,null,null,null,"se(B*)"]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D34:G34,B6:B9)","v":3310.9337876948312},null,"Vb*",{"$f":"1/D38","v":3.0202959772754296E-4},null,{"$f":"SQRT(G38)","v":1.7378998755036002E-2},null,"x' C-1 x",{"$f":"MMULT(L34:O34,V28:V31)","v":14.795633229039973},null,"Vb*",{"$f":"1/L38","v":6.7587509403602988E-2},null,{"$f":"SQRT(O38)","v":0.25997597851263682}]
[]
[null,null,"b*",{"$f":"G38*D36","v":4.5384497899828714E-2},null,null,null,null,null,null,"b*",{"$f":"O38*L36","v":0.57088948206135903}]

{"sheet":"YUAN1996","index":4,"n_rows":57,"n_cols":23,"rows_kept":57,"cut":false,"hidden":true,"merged":[]}
["YUAN1996",null,"Prospective study.",null,null,"Note: our effective numbers are not used in testing: the code has an option to use the numbers given in the paper."]
["This paper was included in IESLC dose response project. See FRY2013B."]
["For relevant output see N:\\rlmeta\\IESLC3_DR\\CDAY_DOSE.rtf"]
[null,"Table 1: study details including CC/Prosp study type."]
[null,"Table 2: cigs/day ranges, as available in each paper."]
[null,"Table 3: detailed parameters used: mean dose, RR(CI), effective numbers; and results: beta, se(beta)."]
[]
["Not rounded:",null,"Cases","At Risk"]
[null,"Unexp",14,7787,null,null,null,"Unexposed case: given in database.",null,null,null,"Unexposed At risk: given in paper and database."]
[null,"Exp",{"$f":"C11-C9","v":128.0083738466428},{"$f":"D11-D9","v":10458.079662605436}]
[null,"Total",{"$f":"D11/128.4789","v":142.0083738466428},{"$f":"D9/0.4268","v":18245.079662605436}]
[null,"Check",{"$f":"SUM(C9:C10)","v":142.0083738466428},{"$f":"SUM(D9:D10)","v":18245.079662605436}]
[]
["Unexp At risk / Total At risk",null,null,{"$f":"D9/D11","v":0.42680000000000001},null,"PRUNCO",null,"As given in database."]
["Total At risk / Total Cases",null,null,{"$f":"D11/C11","v":128.47890000000001},null,"RCOCA",null,"As given in database."]
[]
[]
["Rounded:",null,"Cases","At Risk",null,null,null,"Don't use these."]
[null,"Unexp",14,7787]
[null,"Exp",{"$f":"C21-C19","v":128},{"$f":"D21-D19","v":10458}]
[null,"Total",{"$f":"ROUND(D21/128.4789,0)","v":142},{"$f":"ROUND(D19/0.4268,0)","v":18245}]
[null,"Check",{"$f":"SUM(C19:C20)","v":142},{"$f":"SUM(D19:D20)","v":18245}]
[]
["Unexp / At risk",null,null,{"$f":"D19/D21","v":0.4268018635242532},null,"PRUNCO"]
["At risk / Cases",null,null,{"$f":"D21/C21","v":128.48591549295776},null,"RCOCA"]
[]
[null,"--------- Given in database ----------"]
[null,null,null,null,null,null,null,"v(i)","v(i)","s(i)","rNum ="]
["Cigs/day","Dose","Cases","At Risk","RR","CI Lower","CI Upper","based on CI","based on n","based on n","1/Ao-1/Bo","r(x,<20)","r(x,20+)",null,null,"C(x,<20)","C(x,20+)",null,null,null,"L = Ln(RR)"]
["Never",0,12.7341,6761.4790000000003,null,null,null,null,null,null,{"$f":"1/C30-1/D30","v":7.8381406573268517E-2}]
["<20",10,31.1449,4593.6656000000003,3.6,1.88,6.91,{"$f":"(LN(G31/F31)/(2*NORMINV(0.975,0,1)))^2","v":0.11027173531328321},{"$f":"1/C$30-1/D$30+1/C31-1/D31","v":0.11027170107593925},{"$f":"SQRT(I31)","v":0.33207183119912365},null,null,{"$f":"K30/(J31*J32)","v":0.78353472218097286},null,null,{"$f":"H31","v":0.11027173531328321},{"$f":"M31*SQRT(H31*H32)","v":7.8381457168899896E-2},null,null,null,{"$f":"LN(E31)","v":1.2809338454620642}]
["20+",26.029399999999999,79.420100000000005,4486.1836999999996,9.4,5.21,16.97,{"$f":"(LN(G32/F32)/(2*NORMINV(0.975,0,1)))^2","v":9.0749859921668175E-2},{"$f":"1/C$30-1/D$30+1/C32-1/D32","v":9.074977093884215E-2},{"$f":"SQRT(I32)","v":0.3012470264398342},null,{"$f":"K30/(J31*J32)","v":0.78353472218097286},null,null,null,{"$f":"L32*SQRT(H32*H31)","v":7.8381457168899896E-2},{"$f":"H32","v":9.0749859921668175E-2},null,null,null,{"$f":"LN(E32)","v":2.2407096892759584}]
["Total",null,{"$f":"SUM(C30:C32)","v":123.29910000000001},{"$f":"SUM(D30:D32)","v":15841.328299999999}]
[]
["Check",null,"OR"]
["Never"]
["<20",null,{"$f":"(C31/D31)/(C$30/D$30)","v":3.599987651950185}]
["20+",null,{"$f":"(C32/D32)/(C$30/D$30)","v":9.3999777147427466}]
[]
["Inverted matrix",null,null,null,null,null,null,{"$f":"MINVERSE(P31:Q32)","v":23.489078494034885},-20.287724978377902,null,null,null,null,"Check:",null,{"$f":"MMULT(P31:Q32,H40:I41)","v":0.99999999999999978},0]
[null,null,null,null,null,null,null,-20.287724978377902,28.541988369821112,null,null,null,null,null,null,0,0.99999999999999978]
[]
[]
["X inverted",null,null,null,null,null,null,null,null,null,"Dose by distribution"]
[{"$f":"B31","v":10},{"$f":"B32","v":26.029399999999999},null,null,null,null,null,null,null,null,"Values from ByDistribution sheet",null,null,null,{"$f":"U46","v":"X(0)"},{"$f":"U47","v":"X(1)"},{"$f":"U48","v":"X(2)"},null,null,null,null,"X"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"X inverted",{"$f":"V46","v":0},{"$f":"V47","v":0.35840254001932392},{"$f":"V48","v":0.64498991224113444},null,null,null,"X(0)",{"$f":"ByDistribution!K66","v":0},"ignored"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ignored",null,null,null,null,null,"X(1)",{"$f":"ByDistribution!K67","v":0.35840254001932392}]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(H40:I41,U31:U32)","v":-15.370946290692871},null,null,null,null,null,null,"C-1 L",{"$f":"MMULT(H40:I41,U31:U32)","v":-15.370946290692871},null,null,null,null,null,null,null,null,"X(2)",{"$f":"ByDistribution!K68","v":0.64498991224113444}]
[null,null,null,37.967076319229498,null,null,null,null,null,null,null,37.967076319229498]
[]
[null,null,"x' C-1",{"$f":"MMULT(A45:B45,H40:I41)","v":-293.18652361184087},540.05358228964258,null,null,null,null,null,"x' C-1",{"$f":"MMULT(P46:Q46,H40:I41)","v":-4.6668325584008556},11.138122410374274]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D51:E51,U31:U32)","v":834.55075343682347},null,{"$f":"MMULT(A45:B45,D48:D49)","v":834.55075343682358},null,null,null,null,"x' C-1 L:",{"$f":"MMULT(L51:M51,U31:U32)","v":18.979395030107355},null,{"$f":"MMULT(P46:Q46,L48:L49)","v":18.979395030107359}]
[null,null,null,null,null,null,null,null,"se(B*)",null,null,null,null,null,null,null,"se(B*)"]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D51:E51,B31:B32)","v":11125.405478731613},null,"Vb*",{"$f":"1/D55","v":8.9884364386690941E-5},null,{"$f":"SQRT(G55)","v":9.4807364896768928E-3},null,"x' C-1 x",{"$f":"MMULT(L51:M51,V47:V48)","v":5.5113719532225698},null,"Vb*",{"$f":"1/L55","v":0.18144302516459393},null,{"$f":"SQRT(O55)","v":0.4259612953832706}]
[]
[null,null,"b*",{"$f":"G55*D53","v":7.5013064021102902E-2},null,null,null,null,null,null,"b*",{"$f":"O55*L53","v":3.4436788500565378}]

{"sheet":"KARCHE2005_P","index":5,"n_rows":43,"n_cols":23,"rows_kept":43,"cut":false,"hidden":true,"merged":[]}
["KARCHE2005",null,"Cross-sectional study",null,null,"Note: uses our effective numbers."]
["Number of subjects: see Table I, Parental connectedness."]
[null,null,null,"n","%","N, estimated",null,"Non-cases, estimated and rounded"]
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[null,"Medium",null,54,50,{"$f":"D5*100/E5","v":108},null,{"$f":"ROUND(F5-D5,0)","v":54}]
[null,"High",null,38,32,118.75,null,81]
[null,"Total",null,{"$f":"SUM(D4:D6)","v":135},null,{"$f":"SUM(F4:F6)","v":304.93181818181819},null,{"$f":"SUM(H4:H6)","v":170}]
[]
[null,null,"Cases","Non-cases"]
[null,"Unexp",{"$f":"D4","v":43},{"$f":"H4","v":35}]
[null,"Exp",{"$f":"SUM(D5:D6)","v":92},{"$f":"SUM(H5:H6)","v":135}]
[null,"Total",{"$f":"SUM(C10:C11)","v":135},{"$f":"SUM(D10:D11)","v":170}]
[]
[null,null,"Our effective numbers",null,"See Table II",null,null,"v(i)","v(i)","s(i)","rNum ="]
[null,"Dose","Cases","Non-cases","RR","CI Lower","CI Upper","based on CI","based on n","based on n","1/Ao+1/Bo","r(x,<20)","r(x,20+)",null,null,"C(x,<20)","C(x,20+)",null,null,null,"L = Ln(RR)"]
["Low",0,22.128539020954346,44.770184751362486,null,null,null,null,null,null,{"$f":"1/C16+1/D16","v":6.7526805428906142E-2}]
["Medium",1,65.532721432741297,105.22617970614988,1.26,0.69,2.27,{"$f":"(LN(G17/F17)/(2*NORMINV(0.975,0,1)))^2","v":9.2289696334816193E-2},{"$f":"1/C$16+1/D$16+1/C17+1/D17","v":9.2289696334816193E-2},{"$f":"SQRT(I17)","v":0.30379219268245883},null,null,{"$f":"K16/(J17*J18)","v":0.7245643993852019},null,null,{"$f":"H17","v":9.2289696334816193E-2},{"$f":"M17*SQRT(H17*H18)","v":6.7526805428906142E-2},null,null,null,{"$f":"LN(E17)","v":0.23111172096338664}]
["High",2,85.024149472398349,67.458745515031936,2.5499999999999998,1.4,4.66,{"$f":"(LN(G18/F18)/(2*NORMINV(0.975,0,1)))^2","v":9.4112044607492062E-2},{"$f":"1/C$16+1/D$16+1/C18+1/D18","v":9.4112044607492062E-2},{"$f":"SQRT(I18)","v":0.30677686452451408},null,{"$f":"K16/(J17*J18)","v":0.7245643993852019},null,null,null,{"$f":"L18*SQRT(H18*H17)","v":6.7526805428906142E-2},{"$f":"H18","v":9.4112044607492062E-2},null,null,null,{"$f":"LN(E18)","v":0.93609335917033476}]
["Total",null,{"$f":"SUM(C16:C18)","v":172.685409926094},{"$f":"SUM(D16:D18)","v":217.45510997254428}]
[]
["Check",null,"OR"]
["Low"]
["Medium",null,{"$f":"(C17/D17)/(C$16/D$16)","v":1.26}]
["High",null,{"$f":"(C18/D18)/(C$16/D$16)","v":2.5499999999999998}]
[]
["Inverted matrix",null,null,null,null,null,null,{"$f":"MINVERSE(P17:Q18)","v":22.811155938358819},-16.367346975430262,null,null,null,null,"Check:",null,{"$f":"MMULT(P17:Q18,H26:I27)","v":0.99999999999999978},0]
[null,null,null,null,null,null,null,-16.367346975430262,22.369449769978555,null,null,null,null,null,null,-2.2204460492503131E-16,1.0000000000000002]
[]
[]
["X inverted",null,null,null,null,null,null,null,null,null,"Dose by distribution"]
[{"$f":"B17","v":1},{"$f":"B18","v":2},null,null,null,null,null,null,null,null,"Values from ByDistribution sheet",null,null,null,{"$f":"U32","v":"X(0)"},{"$f":"U33","v":"X(1)"},{"$f":"U34","v":"X(2)"},null,null,null,null,"X"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"X inverted",{"$f":"V32","v":0},{"$f":"V33","v":0.30457952044170317},{"$f":"V34","v":0.71884281743313372},null,null,null,"X(0)",{"$f":"ByDistribution!K75","v":0},"ignored"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ignored",null,null,null,null,null,"X(1)",{"$f":"ByDistribution!K76","v":0.30457952044170317}]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(H26:I27,U17:U18)","v":-10.049439304858648},null,null,null,null,null,null,"C-1 L",{"$f":"MMULT(H26:I27,U17:U18)","v":-10.049439304858648},null,null,null,null,null,null,null,null,"X(2)",{"$f":"ByDistribution!K77","v":0.71884281743313372}]
[null,null,null,17.157207650874728,null,null,null,null,null,null,null,17.157207650874728]
[]
[null,null,"x' C-1",{"$f":"MMULT(A31:B31,H26:I27)","v":-9.9235380125017052},28.371552564526848,null,null,null,null,null,"x' C-1",{"$f":"MMULT(P32:Q32,H26:I27)","v":-4.8177388772977316},11.09495960440084]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D37:E37,U17:U18)","v":24.264975996890808},null,{"$f":"MMULT(A31:B31,D34:D35)","v":24.264975996890808},null,null,null,null,"x' C-1 L:",{"$f":"MMULT(L37:M37,U17:U18)","v":9.2724820828582573},null,{"$f":"MMULT(P32:Q32,L34:L35)","v":9.2724820828582573}]
[null,null,null,null,null,null,null,null,"se(B*)",null,null,null,null,null,null,null,"se(B*)"]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D37:E37,B17:B18)","v":46.819567116551994},null,"Vb*",{"$f":"1/D41","v":2.1358591323807279E-2},null,{"$f":"SQRT(G41)","v":0.14614578790990618},null,"x' C-1 x",{"$f":"MMULT(L37:M37,V33:V34)","v":6.5081474244736137},null,"Vb*",{"$f":"1/L41","v":0.15365355680781634},null,{"$f":"SQRT(O41)","v":0.39198667937548126}]
[]
[null,null,"b*",{"$f":"G41*D39","v":0.51826570579958386},null,null,null,null,null,null,"b*",{"$f":"O41*L39","v":1.4247498524679203}]

{"sheet":"KARCHE2005_F","index":6,"n_rows":43,"n_cols":23,"rows_kept":43,"cut":false,"hidden":true,"merged":[]}
["KARCHE2005",null,"Friend connectedness",null,"Cross-sectional study",null,null,"Note: uses our effective numbers."]
["Number of subjects: see Table I, Friend connectedness."]
[null,null,null,"n","%","N, estimated",null,"Non-cases, estimated and rounded"]
[null,"Low",null,19,34,{"$f":"D4*100/E4","v":55.882352941176471},null,{"$f":"ROUND(F4-D4,0)","v":37}]
[null,"Medium",null,51,43,{"$f":"D5*100/E5","v":118.6046511627907},null,{"$f":"ROUND(F5-D5,0)","v":68}]
[null,"High",null,65,51,127.45098039215686,null,62]
[null,"Total",null,{"$f":"SUM(D4:D6)","v":135},null,{"$f":"SUM(F4:F6)","v":301.93798449612405},null,{"$f":"SUM(H4:H6)","v":167}]
[]
[null,null,"Cases","Non-cases"]
[null,"Unexp",{"$f":"D4","v":19},{"$f":"H4","v":37}]
[null,"Exp",{"$f":"SUM(D5:D6)","v":116},{"$f":"SUM(H5:H6)","v":130}]
[null,"Total",{"$f":"SUM(C10:C11)","v":135},{"$f":"SUM(D10:D11)","v":167}]
[]
[null,null,"Our effective numbers",null,"See Table II",null,null,"v(i)","v(i)","s(i)","rNum ="]
[null,"Dose","Cases","Non-cases","OR","CI Lower","CI Upper","based on CI","based on n","based on n","1/Ao+1/Bo","r(x,<20)","r(x,20+)",null,null,"C(x,<20)","C(x,20+)",null,null,null,"L = Ln(RR)"]
["Low",0,9.327465049727941,22.578229622853517,null,null,null,null,null,null,{"$f":"1/C16+1/D16","v":0.15150071723146261}]
["Medium",1,40.439583381866605,57.581636885736508,1.7,0.72,4.04,{"$f":"(LN(G17/F17)/(2*NORMINV(0.975,0,1)))^2","v":0.19359561174113588},{"$f":"1/C$16+1/D$16+1/C17+1/D17","v":0.19359561174113588},{"$f":"SQRT(I17)","v":0.43999501331394186},null,null,{"$f":"K16/(J17*J18)","v":0.72087558331700541},null,null,{"$f":"H17","v":0.19359561174113588},{"$f":"M17*SQRT(H17*H18)","v":0.15150071723146261},null,null,null,{"$f":"LN(E17)","v":0.53062825106217038}]
["High",2,32.612712474531818,21.747360398671503,3.63,1.43,9.3000000000000007,{"$f":"(LN(G18/F18)/(2*NORMINV(0.975,0,1)))^2","v":0.22814619875184319},{"$f":"1/C$16+1/D$16+1/C18+1/D18","v":0.22814619875184322},{"$f":"SQRT(I18)","v":0.47764652071573099},null,{"$f":"K16/(J17*J18)","v":0.72087558331700541},null,null,null,{"$f":"L18*SQRT(H18*H17)","v":0.15150071723146261},{"$f":"H18","v":0.22814619875184319},null,null,null,{"$f":"LN(E18)","v":1.2892326482767593}]
["Total",null,{"$f":"SUM(C16:C18)","v":82.379760906126364},{"$f":"SUM(D16:D18)","v":101.90722690726153}]
[]
["Check",null,"OR"]
["Low"]
["Medium",null,{"$f":"(C17/D17)/(C$16/D$16)","v":1.7}]
["High",null,{"$f":"(C18/D18)/(C$16/D$16)","v":3.63}]
[]
["Inverted matrix",null,null,null,null,null,null,{"$f":"MINVERSE(P17:Q18)","v":10.7536820078335},-7.1409935645604854,null,null,null,null,"Check:",null,{"$f":"MMULT(P17:Q18,H26:I27)","v":1.0000000000000002},0]
[null,null,null,null,null,null,null,-7.1409935645604863,9.1251384338892159,null,null,null,null,null,null,2.2204460492503131E-16,1]
[]
[]
["X inverted",null,null,null,null,null,null,null,null,null,"Dose by distribution"]
[{"$f":"B17","v":1},{"$f":"B18","v":2},null,null,null,null,null,null,null,null,"Values from ByDistribution sheet",null,null,null,{"$f":"U32","v":"X(0)"},{"$f":"U33","v":"X(1)"},{"$f":"U34","v":"X(2)"},null,null,null,null,"X"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"X inverted",{"$f":"V32","v":0},{"$f":"V33","v":0.3525124494187043},{"$f":"V34","v":0.76594720937883309},null,null,null,"X(0)",{"$f":"ByDistribution!K84","v":0},"ignored"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ignored",null,null,null,null,null,"X(1)",{"$f":"ByDistribution!K85","v":0.3525124494187043}]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(H26:I27,U17:U18)","v":-3.5001945682701914},null,null,null,null,null,null,"C-1 L",{"$f":"MMULT(H26:I27,U17:U18)","v":-3.5001945682701914},null,null,null,null,null,null,null,null,"X(2)",{"$f":"ByDistribution!K86","v":0.76594720937883309}]
[null,null,null,7.9752134630060887,null,null,null,null,null,null,null,7.9752134630060887]
[]
[null,null,"x' C-1",{"$f":"MMULT(A31:B31,H26:I27)","v":-3.5283051212874721},11.109283303217946,null,null,null,null,null,"x' C-1",{"$f":"MMULT(P32:Q32,H26:I27)","v":-1.6788173081160735},4.4720851859065593]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D37:E37,U17:U18)","v":12.450232357741987},null,{"$f":"MMULT(A31:B31,D34:D35)","v":12.450232357741985},null,null,null,null,"x' C-1 L:",{"$f":"MMULT(L37:M37,U17:U18)","v":4.8747303354870448},null,{"$f":"MMULT(P32:Q32,L34:L35)","v":4.8747303354870439}]
[null,null,null,null,null,null,null,null,"se(B*)",null,null,null,null,null,null,null,"se(B*)"]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D37:E37,B17:B18)","v":18.690261485148419},null,"Vb*",{"$f":"1/D41","v":5.350379933392671E-2},null,{"$f":"SQRT(G41)","v":0.23130888295507959},null,"x' C-1 x",{"$f":"MMULT(L37:M37,V33:V34)","v":2.8335771668390364},null,"Vb*",{"$f":"1/L41","v":0.35291080536039832},null,{"$f":"SQRT(O41)","v":0.5940629641379761}]
[]
[null,null,"b*",{"$f":"G41*D39","v":0.66613473372938847},null,null,null,null,null,null,"b*",{"$f":"O41*L39","v":1.7203450086114978}]

{"sheet":"GALLO2010","index":7,"n_rows":73,"n_cols":28,"rows_kept":73,"cut":false,"hidden":true,"merged":[]}
["GALLO2010",null,"Prospective study",null,"Note: uses our effective numbers."]
["Data from Table 5:",null,"All cardiovascular deaths, packs/day spousal exposure."]
[]
[null,null,"Cases","At risk"]
[null,"Unexp",92,47112]
[null,"Exp",9,4752]
[null,"Total",{"$f":"SUM(C5:C6)","v":101},{"$f":"SUM(D5:D6)","v":51864}]
[]
[null,"X","Fitted values (n)",null,"Adjusted results",null,null,"v(i)","v(i)","s(i)"]
[null,"Dose","Cases","At risk","RR","CI Lower","CI Upper","based on CI","based on n","based on n","1/Ao-1/Bo","r(x,2)","r(x,6)","r(x,11)","C(x,2)","C(x,6)","C(x,11)"]
["None",0,38.730170107695315,21683.577113680567,null,null,null,null,null,null,{"$f":"1/C11-1/D11","v":2.577354669426013E-2}]
["<0.5 packs/day",0.5,3.3955768802975084,1016.6079127950323,1.87,0.62,5.68,{"$f":"(LN(G12/F12)/(2*NORMINV(0.975,0,1)))^2","v":0.31929065156987418},{"$f":"1/C$11-1/D$11+1/C12-1/D12","v":0.31929065156987413},{"$f":"SQRT(I12)","v":0.56505809574757371},null,null,{"$f":"K11/(J12*J13)","v":7.1041228561539549E-2},{"$f":"K11/(J12*J14)","v":5.9575580871391962E-2},{"$f":"H12","v":0.31929065156987418},{"$f":"M12*SQRT(H12*H13)","v":2.577354669426013E-2},{"$f":"N12*SQRT(H12*H14)","v":2.5773546694260133E-2}]
["1 pack/day",1,2.5788678925897495,763.92164464401537,1.89,0.54,6.69,{"$f":"(LN(G13/F13)/(2*NORMINV(0.975,0,1)))^2","v":0.41223156383666248},{"$f":"1/C$11-1/D$11+1/C13-1/D13","v":0.41223156383666248},{"$f":"SQRT(I13)","v":0.6420526176542406},null,{"$f":"K11/(J12*J13)","v":7.1041228561539549E-2},null,{"$f":"K11/(J13*J14)","v":5.2431316927319102E-2},{"$f":"L13*SQRT(H13*H12)","v":2.577354669426013E-2},{"$f":"H13","v":0.41223156383666248},{"$f":"N13*SQRT(H13*H14)","v":2.5773546694260137E-2}]
["1.5+ packs/day",1.5,1.7766016178863449,404.3304698948341,2.46,0.55000000000000004,11.06,0.58617271296480833,0.58617271296480822,0.76561916966910393,null,{"$f":"K11/(J14*J12)","v":5.9575580871391962E-2},{"$f":"K11/(J14*J13)","v":5.2431316927319102E-2},null,{"$f":"L14*SQRT(H14*H12)","v":2.5773546694260133E-2},{"$f":"M14*SQRT(H14*H13)","v":2.5773546694260137E-2},{"$f":"H14","v":0.58617271296480833}]
[null,null,{"$f":"SUM(C11:C14)","v":46.481216498468918},{"$f":"SUM(D11:D14)","v":23868.437141014449}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Note:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C uses v(i) for diagonals and a calculation using r for off-diagonals."]
[null,null,null,null,"L",null,null,null,null,null,null,null,null,null,"v(i) are based on CIs."]
["None",null,"Check",null,null,null,null,null,null,null,null,null,null,null,"r is calculated using the s(i) which are based on n values"]
["<0.5 packs/day",null,{"$f":"(C12/D12)/(C$11/D$11)","v":1.8700000000000006},null,{"$f":"LN(E12)","v":0.62593843086649537},null,null,null,null,null,null,null,null,null,null,"This is the best estimate we have for correlation."]
["1 pack/day",null,{"$f":"(C13/D13)/(C$11/D$11)","v":1.8899999999999997},null,{"$f":"LN(E13)","v":0.636576829071551}]
["1.5+ packs/day",null,2.4600000000000004,null,0.90016134994427144]
[]
["Matrix without zero values",null,null,null,null,null,"Inverted matrix"]
[{"$f":"O12","v":0.31929065156987418},{"$f":"P12","v":2.577354669426013E-2},2.5773546694260133E-2,null,null,null,{"$f":"MINVERSE(A25:C27)","v":3.1577565423176446},-0.18926879131076027,-0.13052203893105557]
[{"$f":"O13","v":2.577354669426013E-2},0.41223156383666248,2.5773546694260137E-2,null,null,null,-0.18926879131076027,2.4438524508165358,-9.9132245393136628E-2]
[2.5773546694260133E-2,2.5773546694260137E-2,0.58617271296480833,null,null,null,-0.13052203893105557,-9.9132245393136614E-2,1.7160795498867896]
[null,null,null,null,null,null,null,null,null,null,"Dose by distribution"]
["X inverted",null,null,null,null,null,null,null,null,null,"Values from ByDistribution sheet",null,null,null,{"$f":"T30","v":"X(0)"},{"$f":"T31","v":"X(1)"},{"$f":"T32","v":"X(2)"},{"$f":"T33","v":"X(3)"}]
[{"$f":"B12","v":0.5},{"$f":"B13","v":1},{"$f":"B14","v":1.5},null,null,null,null,null,null,null,null,null,null,"X inverted",{"$f":"U30","v":0},{"$f":"U31","v":0.47552725996183093},{"$f":"U32","v":0.51282608993799794},{"$f":"U33","v":0.53729882997616674},null,"X(0)",{"$f":"ByDistribution!K93","v":0},"ignored"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ignored",null,null,null,null,"X(1)",{"$f":"ByDistribution!K94","v":0.47552725996183093}]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(G25:I27,E20:E22)","v":1.7385861533802498},null,"x' C-1 L:",{"$f":"MMULT(A30:C30,D32:D34)","v":4.3172039448156223},null,null,null,null,null,null,null,null,null,null,null,null,"X(2)",{"$f":"ByDistribution!K95","v":0.51282608993799794}]
[null,null,null,1.3479942177783808,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X(3)",{"$f":"ByDistribution!K96","v":0.53729882997616674}]
[null,null,null,1.399944433564744]
[]
[null,null,"x' C-1",{"$f":"MMULT(A30:C30,G25:I27)","v":1.1938264214514787},2.2005196870714507,2.4097260599715202,null,null,null,null,"x' C-1",{"$f":"MMULT(P30:R30,G25:I27)","v":1.3344080031959069},1.1100051875467014,0.8091431449709463]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D36:F36,E20:E22)","v":4.3172039448156223},null,null,null,null,null,null,"x' C-1 L:",{"$f":"MMULT(L36:N36,E20:E22)","v":2.2702202198727912}]
[]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D36:F36,B12:B14)","v":6.4120219877544704},null,"Vb*",{"$f":"1/D40","v":0.15595704473717911},null,null,null,"x' C-1 x",{"$f":"MMULT(L36:N36,U31:U33)","v":1.6385386666474819},null,"Vb*",{"$f":"1/L40","v":0.61029990952001245}]
[]
[null,null,"b*",{"$f":"G40*D38","v":0.67329836876113613},null,null,null,null,null,null,"b*",{"$f":"O40*L38","v":1.3855151947788673}]
[]
[]
["Identity matrix?",null,{"$f":"MMULT(A25:C27,G25:I27)","v":1},-1.3010426069826053E-18,0,null,"Yes!"]
[null,null,9.1072982488782372E-18,0.99999999999999989,-6.9388939039072284E-18]
[null,null,0,-6.9388939039072284E-18,1.0000000000000002]
[]
["Exp(b*)",null,null,{"$f":"EXP(D42)","v":1.9606937579683494},null,"OR",null,null,"Exp(b*)",null,null,{"$f":"EXP(L42)","v":3.9968845485209874},null,"OR"]
["Exp(b*-1.96*Vb*)",null,null,{"$f":"EXP(D42-(NORMINV(0.975,0,1)*SQRT(G40)))","v":0.90418726182876696},null,"CI (lower)",null,null,"Exp(b*-1.96*Vb*)",null,null,{"$f":"EXP(L42-(NORMINV(0.975,0,1)*SQRT(O40)))","v":0.86446723554711324},null,"CI (lower)"]
["Exp(b*+1.96*Vb*)",null,null,{"$f":"EXP(D42+(NORMINV(0.975,0,1)*SQRT(G40)))","v":4.2516856571952877},null,"CI (upper)",null,null,"Exp(b*+1.96*Vb*)",null,null,{"$f":"EXP(L42+(NORMINV(0.975,0,1)*SQRT(O40)))","v":18.479689498116532},null,"CI (upper)"]
[]
[]
["Increased dose values"]
["X inverted",null,null,null,null,null,null,null,"X"]
[3,7,12,null,null,null,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.9779306658150507E-2,0.35766973765951215]
[null,null,null,null,null,null,null,null,7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.6178385751231638E-4,5.6902426566579851E-2]
["x' C-1 L:",null,"C-1 L",{"$f":"MMULT(G25:I27,E20:E22)","v":1.7385861533802498},null,"x' C-1 L:",{"$f":"MMULT(A56:C56,D58:D60)","v":31.451051187366346},null,12]
[null,null,null,1.3479942177783808]
[null,null,null,1.399944433564744]
[]
[null,null,"x' C-1",{"$f":"MMULT(A56:C56,G25:I27)","v":6.5821236206049445},15.349573837065829,19.507462764096353]
[]
[null,null,"x' C-1 L:",{"$f":"MMULT(D62:F62,E20:E22)","v":31.451051187366339}]
[]
["Vb*:",null,"x' C-1 x",{"$f":"MMULT(D62:F62,I56:I58)","v":361.28294089043186},null,"Vb*",{"$f":"1/D66","v":2.7679136953861188E-3}]
[]
[null,null,"b*",{"$f":"G66*D64","v":8.7053795315801138E-2}]
[]
[]
["Exp(b*)",null,null,{"$f":"EXP(D68)","v":1.0909553664281906},null,"OR"]
["Exp(b*-1.96*Vb*)",null,null,{"$f":"EXP(D68-(NORMINV(0.975,0,1)*SQRT(G66)))","v":0.98406650056275435},null,"CI (lower)"]
["Exp(b*+1.96*Vb*)",null,null,{"$f":"EXP(D68+(NORMINV(0.975,0,1)*SQRT(G66)))","v":1.2094544533909464},null,"CI (upper)"]

{"sheet":"Parameters","index":8,"n_rows":12,"n_cols":5,"rows_kept":12,"cut":false,"hidden":true,"merged":[]}
["Solver precision values:",null,null,null,"Row number for"]
[null,"Id","Value","Selected Id","selected value"]
[null,1,1E-4,8,{"$f":"D3+2","v":10}]
[null,2,1.0000000000000001E-5]
[null,3,9.9999999999999995E-7]
[null,4,9.9999999999999995E-8]
[null,5,1E-8]
[null,6,1.0000000000000001E-9]
[null,7,1E-10]
[null,8,9.9999999999999994E-12]
[null,9,9.9999999999999998E-13]
[null,10,1E-13]