/
power_macro_final.sas
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power_macro_final.sas
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%Macro Metapower (test= , model= , raw_data= , alpha= , tau2= , heterogeneity = ,
n1= , n2= , k = , eff_type = , T = , Dataset= , B= , v= , x= , es= , p= , weight= ) ;
* +-------------------------------------------------------------------------------------------------+
macro arguments:
Test= Specifies the type of test for which power calculations are desired: M (mean), QT (overall heterogeneity), contrast (group contrasts), QB (categorical moderator), QW (heterogeneity across levels of a categorical variable), Reg (omnibus test and regression coefficients), or QE (heterogeneity in regression).
Model= Specifies the type of model, fixed or random. Random also refers to a mixed model.
Raw_Data= Specifies whether power analysis is based on raw data, yes, or not, no.
Alpha = Specifies the nominal alpha level.
Tau2 = Specifies the amount of between study variance. A value of 99 will allow you to specify a heterogeneity ratio instead of this value.
Heterogeneity = This is the ratio of between to within variability discussed by Hedges and Pigott (2001,2004).
n1= / n2 = Specifies average sample size for the collection of studies. Both arguments are relevant for d, but only n1= is evaluated for the effect sizes z and r. For the odds ratio, specify the variance of the log odds in the average study.
Eff_type= Specify the type of effect size being used: standardized mean difference (d), correlation coefficient (r), Fishers z transformation of the correlation coefficient (z), or the log of the odds ratio (or).
T= Specify the average magnitude of the effect size in the effect size units specified in the Eff_type= argument.
Dataset= Specify a SAS dataset.
B= Specify a column from an external dataset that corresponds to standardized regression coefficients.
V= Specify one or more columns from an external dataset that contain the variances of the study effect sizes.
X= Specify one or more columns from an external dataset that contain the values of predictor variables in regression. This corresponds to the design matrix.
ES= Specify one or more columns from an external dataset that contain the effect sizes from each individual study.
P= Corresponds to the number of categories in a test of residual variability in a categorical model or the number of predictors in a test of residual variability in regression.
Weight= Specify a column from an external dataset that corresponds to weights assigned to groups in a test of contrasts.
+-------------------------------------------------------------------------------------------------+;
proc iml;
* +-----------------------------------+
Test of mean effect size (M)= 0
+-----------------------------------+;
if &test = 'M' then do;
if &raw_data= 'no' then do;
if &eff_type = 'z' then do;
z = .5 * log((1+&T) / (1-&T));
common_var = 1 / (&n1 - 3);
var_overall = common_var / &k;
end;
if &eff_type= 'r' then do;
common_var=(((1-&T**2)**2)/(&n1-1));
var_overall = common_var / &k;
end;
if &eff_type = 'd' then do;
common_var = ((&n1+&n2)/(&n1*&n2))+((&T**2)/(2*(&n1+&n2)));
var_overall = common_var / &k;
end;
if &eff_type = 'or' then do;
common_var=&n1;
var_overall = common_var / &k;
end;
if &model = 'fixed' then do;
power = 1-probnorm((probit (1-(&alpha/2)))-(&T/(sqrt (var_overall))))+ probnorm((-probit (1-(&alpha/2)))-(&T/(sqrt (var_overall))));
end;
if &model = 'random' then do;
if &tau2 ^= 99 then do;
power = 1-probnorm((probit (1-(&alpha/2)))-(&T/(sqrt (((&tau2)+ common_var)/&k)))) + probnorm((-probit (1-(&alpha/2)))-(&T/(sqrt (((&tau2)+ common_var)/&k))));
end;
if &tau2 = 99 then do;
power = 1-probnorm((probit (1-(&alpha/2)))-(&T/(sqrt (((&heterogeneity*common_var)+ common_var)/&k))))+ probnorm((-probit (1-(&alpha/2)))-(&T/(sqrt (((&heterogeneity*common_var)+ common_var)/&k))));
end;
end;
end;
if &raw_data= 'yes' then do;
use &Dataset;
read all var{&es} into es;
read all var{&v} into v;
k = nrow(es);
df = k - 1 ;
w= 1/v;
var_overall=1/sum(w);
if &model = 'fixed' then do;
/*var_overall=1/sum(w);
tau2=99;*/
power = 1-probnorm((probit (1-(&alpha/2)))-(&T/(sqrt (var_overall))))+ probnorm((-probit (1-(&alpha/2)))-(&T/(sqrt (var_overall))));
end;
if &model = 'random' then do;
mes = sum(es#w)/sum(w);
q= sum(w#(es-mes)##2);
tau2= (q - df)/(sum(w)-(sum(w#w)/sum(w)));
if tau2<0 then do ;
tau2= 0 ;
end ;
if tau2>= 0 then do;
tau2=tau2;
end;
v_random = (v + tau2);
w_random= 1/v_random;
var_random_overall = 1/(sum(w_random));
power = 1-probnorm((probit (1-(&alpha/2)))-(&T/(sqrt (var_random_overall))))+ probnorm((-probit (1-(&alpha/2)))-(&T/(sqrt (var_random_overall))));
end;
end;
end;
* +--------------------------------------------+
Test of heterogeneity in effect sizes (QT)= 0
+--------------------------------------------+;
if &test= 'QT' then do;
if &raw_data= 'no' then do;
if &eff_type = 'z' then do;
z = .5 * log((1+&T) / (1-&T));
common_var = 1 / (&n1 - 3);
var_overall = common_var / &k;
end;
if &eff_type= 'r' then do;
common_var=(((1-&T**2)**2)/(&n1-1));
var_overall = common_var / &k;
end;
if &eff_type = 'd' then do;
common_var = ((&n1+&n2)/(&n1*&n2))+((&T**2)/(2*(&n1+&n2)));
var_overall = common_var / &k;
end;
if &eff_type = 'or' then do;
common_var=&n1;
var_overall = common_var / &k;
end;
if &model= 'fixed' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (&k-1)), (&k-1), (&tau2/common_var)*(&k-1));
end;
if &tau2 = 99 then do;
power= 1-probchi (cinv ((1-&alpha), (&k-1)), (&k-1), &heterogeneity*(&k-1));
end;
end;
if &model= 'random' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (((cinv ((1-&alpha), (&k-1))*common_var)/(common_var+ &tau2)), (&k-1), 0);
end;
if &tau2 =99 then do;
power= 1-probchi (((cinv ((1-&alpha), (&k-1))*common_var)/(common_var+ (common_var*&heterogeneity))), (&k-1), 0);
end;
end;
end;
if &raw_data= 'yes' then do;
use &Dataset;
read all var{&es} into es;
read all var{&v} into v;
k = nrow(es);
df = k - 1 ;
w= 1/v;
var_overall=1/sum(w);
average_var=var_overall*k;
if &model= 'fixed' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (df)), df, (&tau2/average_var)*(df));
end;
if &tau2 = 99 then do;
power= 1-probchi (cinv ((1-&alpha), (df)), df, ((&heterogeneity*average_var)/average_var)*(df));
end;
end;
/*if &model= 'random' then do;
sum_w= sum(w);
sum_ww=sum(w##2);
sum_www=sum(w##3);
a= sum_w-(sum_ww/sum_w);
if &tau2 ^= 99 then do;
mean=(a*&tau2)+df;
variance= (2*df)+(4*a*&tau2)+(2*(sum_ww-(sum_www/sum_w)+((sum_ww##2)/(sum_w##2))))*(&tau2##2);
end;
if &tau2= 99 then do;
mean=(a*(&heterogeneity*average_var))+(df);
variance= (2*df)+(4*a*(&heterogeneity*average_var))+(2*(sum_ww-(sum_www/sum_w)+((sum_ww##2)/(sum_w##2))))*((&heterogeneity*average_var)##2);
end;
r=(mean##2)/variance;
m= mean/variance;
power=1-probgam ((cinv ((1-&alpha), df))/r, m);*something wrong here;*/
if &model= 'random' then do;
sum_w= sum(w);
sum_ww=sum(w##2);
sum_www=sum(w##3);
a= sum_w-(sum_ww/sum_w);
if &tau2 ^= 99 then do;
mean=(a*&tau2)+(df);
b=(df)+(2*a*&tau2)+(sum_ww-(2*(sum_www/sum_w))+((sum_ww##2)/(sum_w##2)))*(&tau2##2);
end;
if &tau2= 99 then do;
mean=(a*(&heterogeneity*average_var))+(df);
b=(df)+(2*a*(&heterogeneity*average_var))+(sum_ww-(2*(sum_www/sum_w))+((sum_ww##2)/(sum_w##2)))*((&heterogeneity*average_var)##2);
end;
variance=2*b;
r=variance/(2*mean);
s=(2*(mean##2))/variance;
power=1-probchi (cinv ((1-&alpha), df)/r, s, 0);
end;
end;
end;
* +------------------------------------------------------------+
Test of fixed paramters in regression model (QR and Betas)= 0
+------------------------------------------------------------+;
if &test= 'Reg' then do;
use &Dataset;
read all var{&B} into B_vec;
read all var{&x} into x;
read all var{&v} into var_vec;
read all var{&es} into es;
k= ncol(x);*p;
n= nrow(x);*k;
design = j(n,1,1) || x ;
B_vec_remove= remove (B_vec,((k+1):n));
if &model= 'fixed' then do;
W=1/var_vec;
W=diag(W);
B_cov= design`*W*design;
B_cov=inv(B_cov);
submatrix=B_cov[(k-1):(k+1),(k-1):(k+1)];
B_SE=sqrt(vecdiag(submatrix));
B_cov_inv= inv(submatrix);
QR= B_vec_remove*B_cov_inv*B_vec_remove`;
QR_power= 1-probchi (cinv ((1-&alpha), k), k, QR);
Z=B_vec_remove`/B_SE;
B_power= 1-probnorm((probit (1-(&alpha/2)))-Z)+ probnorm((-probit (1-(&alpha/2)))-Z);
end;
if &model= 'random' then do;
w=1/var_vec;
w_matrix=diag(w);
w_2=1/(var_vec##2);
w2_matrix=diag(w_2);
w_sum=sum(w);
a=w_sum-(trace((inv(design`*w_matrix*design))*design`*w2_matrix*design));
QE=es`*(w_matrix-w_matrix*design*(inv(design`*w_matrix*design))*design`*w_matrix)*es;
tau2=(QE-(n-k-1))/a;
REV= var_vec + tau2;
W_new=1/REV;
W_new_matrix=diag(W_new);
B_cov= design`*W_new_matrix*design;
B_cov=inv(B_cov);
submatrix=B_cov[(k-1):(k+1),(k-1):(k+1)];
B_SE=sqrt(vecdiag(submatrix));
B_cov_inv= inv(submatrix);
QR= B_vec_remove*B_cov_inv*B_vec_remove`;
QR_power= 1-probchi (cinv ((1-&alpha), k), k, QR);
Z=B_vec_remove`/B_SE;
B_power= 1-probnorm((probit (1-(&alpha/2)))-Z)+ probnorm((-probit (1-(&alpha/2)))-Z);
end;
end;
* +--------------------------------------+
Test of contrast = 0
+--------------------------------------+;
if &test= 'contrast' then do;
if &raw_data= 'no' then do;
use &Dataset;
read all var{&weight} into weight;
read all var{&T} into T;
read all var{&n1 &n2} into n_vec;
read all var{&n1} into n1_vec;
read all var{&n2} into n2_vec;
read all var{&k} into k_vec;
n_groups = nrow(weight);
common_var_vec = J(n_groups,1,0);
group_var = J(n_groups,1,0);
group_mn = J(n_groups,1,0);
C2 = J(n_groups,1,0);
do groups = 1 to n_groups;
C2[groups,1] = weight[groups,1]##2;
if &eff_type = 'z' then do;
group_mn[groups,1] = .5 * log((1+T[groups,1]) / (1-T[groups,1]));
common_var_vec[groups,1] = 1 / (n_vec[groups,1] - 3);
end;
if &eff_type= 'r' then do;
group_mn[groups,1] = T[groups,1];
common_var_vec[groups,1]=(((1-T[groups,1]**2)**2)/(n_vec[groups,1]-1));
end;
if &eff_type = 'd' then do;
group_mn[groups,1] = T[groups,1];
common_var_vec[groups,1] = ((n_vec[groups,1]+n_vec[groups,2])/(n_vec[groups,1]*n_vec[groups,2]))+((T[groups,1]**2)/(2*(n_vec[groups,1]+n_vec[groups,2])));
end;
if &eff_type = 'or' then do;
group_mn[groups,1] = T[groups,1];
common_var_vec[groups,1] = n_vec[groups,1];
end;
end;
if &model= 'fixed' then do;
group_var= (common_var_vec/k_vec);
end;
if &model= 'random' then do;
if &tau2^=99 then do;
total=common_var_vec+&tau2;
group_var= (total/ k_vec);
end;
if &tau2=99 then do;
total=common_var_vec+(&heterogeneity#common_var_vec);
group_var= (total/ k_vec);
end;
end;
G = weight`*group_mn;
Var_G = C2`*group_var;
SE=sqrt(Var_G);
Z= G/SE;
power= 1-probnorm((probit (1-(&alpha/2)))-Z)+probnorm((-probit (1-(&alpha/2)))-Z);
end;
if &raw_data= 'yes' then do;
use &Dataset;
read all var{&es} into es;
read all var{&v} into var;
read all var{&weight} into weight;
read all var{&T} into T;
k= ncol(var);
n= nrow(var);
T= remove (T,((k+1):n));
weight= remove (weight,((k+1):n));
C2=weight##2;
inv_var=1/var;
if &model= 'fixed' then do;
columnstack_inv=J(1, 2, 0);
do col=1 to k;
do row=1 to n;
if inv_var[row,col] ^=. then do;
columnstack_inv=columnstack_inv//(col||inv_var[row, col]);
end;
end;
end;
columnstack_inv=columnstack_inv[2:nrow(columnstack_inv),];
group_var=J(k,1,0);
do row=1 to nrow(columnstack_inv);
group_var[columnstack_inv[row,1],]=group_var[columnstack_inv[row,1],]+columnstack_inv[row,2];
end;
group_var=1/group_var;
G = weight*T`;
Var_G = C2*group_var;
SE=sqrt(Var_G);
Z= G/SE;
power= 1-probnorm((probit (1-(&alpha/2)))-Z)+probnorm((-probit (1-(&alpha/2)))-Z);
weight=weight`;
T=T`;
end;
If &model= 'random' then do;
columnstack=J(1, 1, 0);
do col=1 to k;
do row=1 to n;
if es[row,col] ^=. then do;
columnstack=columnstack//es[row, col];
end;
end;
end;
columnstack=columnstack[2:nrow(columnstack),];
columnstack_inv=J(1, 2, 0);
do col=1 to k;
do row=1 to n;
if inv_var[row,col] ^=. then do;
columnstack_inv=columnstack_inv//(col||inv_var[row, col]);
end;
end;
end;
columnstack_inv=columnstack_inv[2:nrow(columnstack_inv),];
columnstack_merge=columnstack_inv||columnstack;
group_es_w=J(k,1,0);
group_weight=J(k,1,0);
group_mean=J(k,1,0);
do row=1 to nrow(columnstack_merge);
group_es_w[columnstack_merge[row,1],]=group_es_w[columnstack_merge[row,1],]+(columnstack_merge[row,2]#columnstack_merge[row,3]);
group_weight[columnstack_merge[row,1],]=group_weight[columnstack_merge[row,1],]+columnstack_merge[row,2];
end;
mes=(group_es_w/group_weight)`;
ones= J(n,1,1);
m_matrix=ones@mes;
weight_sq_difference=inv_var#((m_matrix-es)##2);
Q=weight_sq_difference[+,];
sum_Q=Q[,+];
sum_w=inv_var[+,];
sum_ww=(inv_var##2)[+,];
a= sum_w-(sum_ww/sum_w);
sum_a= a[,+];
counter=J(n,k,1);
do col=1 to k;
do row=1 to n;
if es[row,col] ^=. then do;
counter[row,col]=1;
end;
if es[row,col] =. then do;
counter[row,col]=0;
end;
end;
end;
df= counter[+,]-1;
sum_df= df[,+];
tau2=(sum_Q-sum_df)/sum_a;
if tau2< 0 then do;
new_tau2=0;
end;
if tau2>= 0 then do;
new_tau2=tau2;
end;
random_var= var+new_tau2;
random_inv_var=1/random_var;
group_weights=random_inv_var[+,];
group_var= 1/group_weights;
G = weight*T`;
Var_G = C2*group_var`;
SE=sqrt(Var_G);
Z= G/SE;
power= 1-probnorm((probit (1-(&alpha/2)))-Z)+probnorm((-probit (1-(&alpha/2)))-Z);
t_format=t`;
k_format=(df+1)`;
weight_format=weight`;
new_tau2_formatted= new_tau2`;
group_var_formatted=group_var`;
end;
end;
end;
* +--------------------------------------+
Test of categorical moderators (QB)=0
+--------------------------------------+;
if &test= 'QB' then do;
if &raw_data= 'no' then do;
use &Dataset;
read all var{&T} into T;
read all var{&n1 &n2} into n_vec;
read all var{&n1} into n1_vec;
read all var{&n2} into n2_vec;
read all var{&k} into k_vec;
n_groups = nrow(T);
common_var_vec = J(n_groups,1,0);
group_mn = J(n_groups,1,0);
ones = J(n_groups,1,1);
do groups = 1 to n_groups;
if &eff_type = 'z' then do;
group_mn[groups,1] = .5 * log((1+T[groups,1]) / (1-T[groups,1]));
common_var_vec[groups,1] = 1 / (n_vec[groups,1] - 3);
end;
if &eff_type= 'r' then do;
group_mn[groups,1] = T[groups,1];
common_var_vec[groups,1]=(((1-T[groups,1]**2)**2)/(n_vec[groups,1]-1));
end;
if &eff_type = 'd' then do;
group_mn[groups,1] = T[groups,1];
common_var_vec[groups,1] = ((n_vec[groups,1]+n_vec[groups,2])/(n_vec[groups,1]*n_vec[groups,2]))+((T[groups,1]**2)/(2*(n_vec[groups,1]+n_vec[groups,2])));
end;
if &eff_type = 'or' then do;
group_mn[groups,1] = T[groups,1];
common_var_vec[groups,1] = n_vec[groups,1];
end;
end;
if &model= 'fixed' then do;
total=common_var_vec;
end;
if &model= 'random' then do;
if &tau2^=99 then do;
total=common_var_vec+&tau2;
end;
if &tau2=99 then do;
total=common_var_vec+(&heterogeneity#common_var_vec);
end;
end;
group_var= (total/ k_vec);
grand_mn= ((group_mn/group_var)`*ones)/((ones/group_var)`*ones);
grand_mn_vec = ones*grand_mn;
noncentrality = (((group_mn-grand_mn_vec)##2)/(group_var))`*ones;
power= 1-probchi (cinv ((1-&alpha), (n_groups-1)), (n_groups-1), noncentrality);
end;
if &raw_data= 'yes' then do;
use &Dataset;
read all var{&es} into es;
read all var{&v} into var;
read all var{&T} into T;
k= ncol(var);
n= nrow(var);
T= remove (T,((k+1):n));
T_format=T`;
n_groups=nrow (T_format);
inv_var=1/var;
if &model='fixed' then do;
columnstack_inv=J(1, 2, 0);
do col=1 to k;
do row=1 to n;
if inv_var[row,col] ^=. then do;
columnstack_inv=columnstack_inv//(col||inv_var[row, col]);
end;
end;
end;
columnstack_inv=columnstack_inv[2:nrow(columnstack_inv),];
group_var=J(k,1,0);
do row=1 to nrow(columnstack_inv);
group_var[columnstack_inv[row,1],]=group_var[columnstack_inv[row,1],]+columnstack_inv[row,2];
end;
group_var=1/group_var;
inv_group_var=1/group_var;
sum_inv_group_var=inv_group_var [+,];
numerator=t_format/group_var;
numerator_sum= numerator[+,];
grand_mn= numerator_sum/sum_inv_group_var;
ones= J(n_groups,1,1);
grand_mn_vec = ones*grand_mn;
noncentrality = (((t_format-grand_mn_vec)##2)/(group_var))`*ones;
power= 1-probchi (cinv ((1-&alpha), (n_groups-1)), (n_groups-1), noncentrality);
counter=J(n,k,1);
do col=1 to k;
do row=1 to n;
if es[row,col] ^=. then do;
counter[row,col]=1;
end;
if es[row,col] =. then do;
counter[row,col]=0;
end;
end;
end;
k_counter=counter[+,];
k_counter=k_counter`;
end;
if &model='random' then do;
columnstack=J(1, 1, 0);
do col=1 to k;
do row=1 to n;
if es[row,col] ^=. then do;
columnstack=columnstack//es[row, col];
end;
end;
end;
columnstack=columnstack[2:nrow(columnstack),];
columnstack_inv=J(1, 2, 0);
do col=1 to k;
do row=1 to n;
if inv_var[row,col] ^=. then do;
columnstack_inv=columnstack_inv//(col||inv_var[row, col]);
end;
end;
end;
columnstack_inv=columnstack_inv[2:nrow(columnstack_inv),];
columnstack_merge=columnstack_inv||columnstack;
group_es_w=J(k,1,0);
group_weight=J(k,1,0);
group_mean=J(k,1,0);
do row=1 to nrow(columnstack_merge);
group_es_w[columnstack_merge[row,1],]=group_es_w[columnstack_merge[row,1],]+(columnstack_merge[row,2]#columnstack_merge[row,3]);
group_weight[columnstack_merge[row,1],]=group_weight[columnstack_merge[row,1],]+columnstack_merge[row,2];
end;
mes=(group_es_w/group_weight)`;
ones= J(n,1,1);
m_matrix=ones@mes;
weight_sq_difference=inv_var#((m_matrix-es)##2);
Q=weight_sq_difference[+,];
sum_Q=Q[,+];
sum_w=inv_var[+,];
sum_ww=(inv_var##2)[+,];
a= sum_w-(sum_ww/sum_w);
sum_a= a[,+];
counter=J(n,k,1);
do col=1 to k;
do row=1 to n;
if es[row,col] ^=. then do;
counter[row,col]=1;
end;
if es[row,col] =. then do;
counter[row,col]=0;
end;
end;
end;
df= counter[+,]-1;
sum_df= df[,+];
tau2=(sum_Q-sum_df)/sum_a;
if tau2< 0 then do;
new_tau2=0;
end;
if tau2>= 0 then do;
new_tau2=tau2;
end;
random_var= var+new_tau2;
random_inv_var=1/random_var;
group_weights=random_inv_var[+,];
group_var= 1/group_weights;
inv_group_var=1/group_var;
sum_inv_group_var=inv_group_var [,+];
numerator=t/group_var;
numerator_sum= numerator[,+];
grand_mn= numerator_sum/sum_inv_group_var;
ones= J(n_groups,1,1);
grand_mn_vec = ones*grand_mn;
k_format=(df+1)`;
group_var_formatted=group_var`;
noncentrality = (((t_format-grand_mn_vec)##2)/(group_var_formatted))`*ones;
power= 1-probchi (cinv ((1-&alpha), (n_groups-1)), (n_groups-1), noncentrality);
end;
end;
end;
* +----------------------------------------------------------+
Test of heterogeneity in effect sizes in Regression (QE)= 0
+----------------------------------------------------------+;
if &test= 'QE' then do;
if &raw_data='no' then do;
if &eff_type = 'z' then do;
z = .5 * log((1+&T) / (1-&T));
common_var = 1 / (&n1 - 3);
var_overall = common_var / &k;
end;
if &eff_type= 'r' then do;
common_var=(((1-&T**2)**2)/(&n1-1));
var_overall = common_var / &k;
end;
if &eff_type = 'd' then do;
common_var = ((&n1+&n2)/(&n1*&n2))+((&T**2)/(2*(&n1+&n2)));
var_overall = common_var / &k;
end;
if &eff_type = 'or' then do;
common_var=&n1;
var_overall = common_var / &k;
end;
if &model= 'fixed' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (&k-&p-1)), (&k-&p-1), (&tau2/common_var)*(&k-&p-1));
end;
if &tau2 = 99 then do;
power= 1-probchi (cinv ((1-&alpha), (&k-&p-1)), (&k-&p-1), &heterogeneity*(&k-&p-1));
end;
end;
if &model= 'random' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (((cinv ((1-&alpha), (&k-&p))*common_var)/(common_var+ &tau2)), (&k-&p-1), 0);
end;
if &tau2 =99 then do;
power= 1-probchi (((cinv ((1-&alpha), (&k-&p))*common_var)/(common_var+ (common_var*&heterogeneity))), (&k-&p-1), 0);
end;
end;
end;
if &raw_data='yes' then do;
use &Dataset;
read all var{&x} into x_x;
read all var{&v} into v;
read all var{&B} into B;
read all var{&es} into es;
p= ncol(x_x);
k= nrow(x_x);
w=1/v;
var_overall=1/sum(w);
average_var=var_overall*k;
if &model= 'fixed' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (k-p-1)), k-p-1, (&tau2/average_var)*(k-p-1));
end;
if &tau2 = 99 then do;
power= 1-probchi (cinv ((1-&alpha), (k-p-1)), k-p-1, ((&heterogeneity*average_var)/average_var)*(k-p-1));
end;
end;
if &model= 'random' then do;
x = j(k,1,1) || x_x ;
B_vec_remove= remove (B,((p+1):k));
w_matrix=diag(w);
w_2=1/(v##2);
w2_matrix=diag(w_2);
w_sum=sum(w);
a=w_sum-(trace((inv(x`*w_matrix*x))*x`*w2_matrix*x));
M=w_matrix*x*(inv(x`*w_matrix*x))*x`*w_matrix;
v_random=v+&tau2;
w_random=1/v_random;
w_random_matrix=diag(w_random);
w2_random=1/(v_random##2);
w2_random_matrix=diag(w2_random);
mean=(a*&tau2)+(k-p-1);
/*variance=2*((trace(w2_matrix*w2_random_matrix))-(2*(trace(M*w_matrix*w2_random_matrix)))+(trace(M*w_random_matrix*M*w_random_matrix)));
*/
variance= 128.43;
r=variance/(2*mean);
s=(2*(mean##2))/variance;
power=1-probchi (cinv ((1-&alpha), (k-p-1))/r, s, 0);
end;
end;
end;
* +---------------------------------------------------------------+
Test of heterogeneity in effect sizes across all levels (QW)= 0
+---------------------------------------------------------------+;
if &test= 'QW' then do;
if &raw_data= 'no' then do;
if &eff_type = 'z' then do;
z = .5 * log((1+&T) / (1-&T));
common_var = 1 / (&n1 - 3);
var_overall = common_var / &k;
end;
if &eff_type= 'r' then do;
common_var=(((1-&T**2)**2)/(&n1-1));
var_overall = common_var / &k;
end;
if &eff_type = 'd' then do;
common_var = ((&n1+&n2)/(&n1*&n2))+((&T**2)/(2*(&n1+&n2)));
var_overall = common_var / &k;
end;
if &eff_type = 'or' then do;
common_var=&n1;
var_overall = common_var / &k;
end;
if &model= 'fixed' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (&k-&p)), (&k-&p), (&tau2/common_var)*(&k-&p));
end;
if &tau2 = 99 then do;
power= 1-probchi (cinv ((1-&alpha), (&k-&p)), (&k-&p), &heterogeneity*(&k-&p));
/*common_var=99;
var_overall=99;*/
end;
end;
if &model= 'random' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (((cinv ((1-&alpha), (&k-&p))*common_var)/(common_var+ &tau2)), (&k-&p), 0);
end;
if &tau2 =99 then do;
power= 1-probchi (((cinv ((1-&alpha), (&k-&p))*common_var)/(common_var+ (common_var*&heterogeneity))), (&k-&p), 0);
end;
end;
end;
if &raw_data= 'yes' then do;
use &Dataset;
read all var{&es} into es;
read all var{&v} into v;
inv_var=1/v;
k_= ncol(es);
n= nrow(es);
counter=J(n,k_,1);
do col=1 to k_;
do row=1 to n;
if es[row,col] ^=. then do;
counter[row,col]=1;
end;
if es[row,col] =. then do;
counter[row,col]=0;
end;
end;
end;
df= counter[+,]-1;
sum_df= df[,+];
k=sum_df+k_;
sum_w=inv_var[+,];
sum_w_tot=sum_w[,+];
var_overall=1/sum_w_tot;
average_var=var_overall*k;
sum_ww=(inv_var##2)[+,];
sum_www=(inv_var##3)[+,];
a= sum_w-(sum_ww/sum_w);
sum_a= a[,+];
if &model= 'fixed' then do;
if &tau2 ^= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (sum_df)), (sum_df), (&tau2/average_var)*(sum_df));
end;
if &tau2= 99 then do;
power= 1-probchi (cinv ((1-&alpha), (sum_df)), (sum_df),((&heterogeneity*average_var)/average_var)*(sum_df));
end;
end;
if &model= 'random' then do;
if &tau2 ^= 99 then do;
mean=(sum_a*&tau2)+(sum_df);
b=(df)+(2*a*&tau2)+(sum_ww-(2*(sum_www/sum_w))+((sum_ww##2)/(sum_w##2)))*(&tau2##2);
end;
if &tau2= 99 then do;
mean=(sum_a*(&heterogeneity*average_var))+(sum_df);
b=(df)+(2*a*(&heterogeneity*average_var))+(sum_ww-(2*(sum_www/sum_w))+((sum_ww##2)/(sum_w##2)))*((&heterogeneity*average_var)##2);
end;
b_sum= b[,+];
variance=2*b_sum;
r=variance/(2*mean);
s=(2*(mean##2))/variance;
power=1-probchi (cinv ((1-&alpha), sum_df)/r, s, 0);
end;
end;
end;
* +--------------------+
Print Statements
+--------------------+;
%if &test= 'Reg' %then %do;
print "--------- Meta-Analysis Power Macro ------" ;
print &model [label= ' '] [rowname = 'Model= '] ;
print n [label= ' '] [rowname = 'Number of Studies = '];
%if &model='fixed'%then %do;
print &tau2[label= ' '] [rowname = 'Random Effect Size Variance='];
%end;
%if &model='random'%then %do;
print tau2[label= ' '] [rowname = 'Random Effect Size Variance='];
%end;
print &alpha [label= ' '] [rowname = 'Alpha = '];
print QR_power [label= ' '] [rowname = 'Power for Overall Model (QR) = '][format=12.8];
print 'Power for Regression Coefficients (B)';
names = {&x} ;
print B_power [rowname=names] [colname=" "] [label=""][format=12.8];
print "--------------------------------------------" ;
%end;
%if &test= 'QB' %then %do;
%if &raw_data='no'|&raw_data='yes'%then %do;
print "-------------------------------Meta-Analysis Power Macro-------------------------------" ;
print "Test of Categorical Moderators" ;
names = &model//&eff_type;
print names [label= ' ']
[rowname = {
'Model = '
'Effect Size Metric = '}];
print &alpha [label= ' '][rowname = 'Alpha = '];
print n_groups [label= ' '][rowname = 'Number of Categories = '];
%if &raw_data='no'%then %do;
Print '********Raw data not provided********';
Print T [label='ES']
n1_vec [label='n(g1)']
n2_vec [label='n(g2)']
k_vec [label='K']
common_var_vec [label='Common Variance']
&tau2 [label='Tau-Squared']
&heterogeneity [label='Heterogeneity']
group_var [label='Group Variance'];
print power [label= ' '][rowname = 'Estimated Power of Test = '];
print "----------------------------------------------------------------------------------------" ;
%end;
%if &raw_data='yes'%then %do;
Print '********Raw data provided********';
%if &model='fixed'%then %do;
Print T_format [label='ES']
k_counter [label='K']
group_var [label='Group Variance'];
print power [label= ' '][rowname = 'Estimated Power of Test = '];
print "----------------------------------------------------------------------------------------" ;
%end;
%if &model='random'%then %do;
Print t_format [label='ES']
k_format [label='K']
new_tau2 [label='Tau-Squared']
group_var_formatted [label='Group Variance'];
print power [label= ' '][rowname = 'Estimated Power of Test = '];
print "--------------------------------------------------------------------------------------" ;
%end;
%end;
%end;
%end;
%if &test= 'contrast' %then %do;
%if &raw_data='no'|&raw_data='yes'%then %do;
print "-------------------------------Meta-Analysis Power Macro-------------------------------" ;
print "Test of Contrasts" ;
names = &model//&eff_type;
print names [label= ' ']
[rowname = {
'Model = '
'Effect Size Metric = '}];
print &alpha [label= ' '][rowname = 'Alpha = '];
%if &raw_data='no'%then %do;
Print '********Raw data not provided********';
Print T [label='ES']
weight [label='weight']
n1_vec [label='n(g1)']
n2_vec [label='n(g2)']
k_vec [label='K']
common_var_vec [label='Common Variance']
&tau2 [label='Tau-Squared']
&heterogeneity [label='Heterogeneity']
group_var [label='Group Variance'];
print power [label= ' '][rowname = 'Estimated Power of Test = '];
print "----------------------------------------------------------------------------------------" ;
%end;
%if &raw_data='yes'%then %do;
print '********Raw data provided********';
%if &model='fixed'%then %do;
Print T [label='ES']
weight [label='weight']
group_var [label='Group Variance'];
print power [label= ' '][rowname = 'Estimated Power of Test = '];
print "----------------------------------------------------------------------------------------" ;
%end;
%if &model='random'%then %do;
Print t_format [label='ES']
weight_format [label='weight']
k_format [label='K']
new_tau2_formatted [label='Tau-Squared']
group_var_formatted [label='Group Variance'];
print power [label= ' '][rowname = 'Estimated Power of Test = '];
print "----------------------------------------------------------------------------------------" ;
%end;
%end;
%end;
%end;
%if &test= 'M'%then %do;
print "---------------------Meta-Analysis Power Macro---------------------" ;
names = &test//&model//&eff_type;
print names [label= ' ']
[rowname = {'Significance Test Type = '
'Model = '
'Effect Size Metric = '}];
%if &raw_data='no'%then %do;
print '********Raw data not provided********';
values = &T//&n1//&n2//&k//common_var//var_overall//&tau2//&heterogeneity//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Individual Study Sample Size (group 1) = '
'Individual Study Sample Size (group 2) = '
'Number of Studies = '
'Estimated Common Within Study Variance = '
'Estimated Overall Within Study Variance = '
'Random Effects Variance ='
'Heterogeneity Ratio = '
'Alpha = '
'Estimated Power of Test = '}];
print "-------------------------------------------------------------------" ;
%end;
%if &raw_data='yes'%then %do;
%if &model='fixed'%then %do;
print '********Raw data provided********';
values = &T//k//var_overall//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Number of Studies = '
'Overall Within Study Variance = '
'Alpha = '
'Estimated Power of Test = '}];
print"-------------------------------------------------------------------" ;
%end;
%if &model='random'%then %do;
print '********Raw data provided********';
values = &T//k//var_random_overall//tau2//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Number of Studies = '
'Overall Within Study Variance = '
'Random Effects Variance Component='
'Alpha = '
'Estimated Power of Test = '}];
print"-------------------------------------------------------------------" ;
%end;
%end;
%end;
%if &test= 'QE'%then %do;
print "---------------------Meta-Analysis Power Macro---------------------" ;
names = &test//&model//&eff_type;
print names [label= ' ']
[rowname = {'Significance Test Type = '
'Model = '
'Effect Size Metric = '}];
%if &raw_data='no'%then %do;
print '********Raw data not provided********';
values = &T//&n1//&n2//&k//common_var//var_overall//&tau2//&heterogeneity//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Individual Study Sample Size (group 1) = '
'Individual Study Sample Size (group 2) = '
'Number of Studies = '
'Estimated Common Within Study Variance = '
'Estimated Overall Within Study Variance = '
'Random Effects Variance ='
'Heterogeneity Ratio = '
'Alpha = '
'Estimated Power of Test = '}];
print "-------------------------------------------------------------------" ;
%end;
%if &raw_data='yes'%then %do;
%if &model='fixed'%then %do;
print '********Raw data provided********';
values = &T//k//average_var//var_overall//&tau2//&heterogeneity//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Number of Studies = '
'Common Variance='
'Overall Within Study Variance = '
'Ranom Effects Variance'
'Heterogeneity'
'Alpha = '
'Estimated Power of Test = '}];
print"-------------------------------------------------------------------" ;
%end;
%if &model='random'%then %do;
print variance;
print '********Raw data provided********';
values = &T//k//&tau2//&heterogeneity//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Number of Studies = '
'Random Effects Variance'
'Heterogeneity Ratio'
'Alpha = '
'Estimated Power of Test = '}];
print"-------------------------------------------------------------------" ;
%end;
%end;
%end;
%if &test= 'QW'%then %do;
print "---------------------Meta-Analysis Power Macro---------------------" ;
names = &test//&model//&eff_type;
print names [label= ' ']
[rowname = {'Significance Test Type = '
'Model = '
'Effect Size Metric = '}];
%if &raw_data='no'%then %do;
print '********Raw data not provided********';
values = &T//&n1//&n2//&k//common_var//var_overall//&tau2//&heterogeneity//&alpha//power;
print values [label= ' '] [rowname = {
'Population Effect Size = '
'Individual Study Sample Size (group 1) = '
'Individual Study Sample Size (group 2) = '
'Number of Studies = '
'Estimated Common Within Study Variance = '
'Estimated Overall Within Study Variance = '
'Random Effects Variance ='
'Heterogeneity Ratio = '
'Alpha = '
'Estimated Power of Test = '}];
print "-------------------------------------------------------------------" ;
%end;
%if &raw_data='yes'%then %do;
%if &model='fixed'%then %do;
print '********Raw data provided********';