Binomial Test on Coin Flips and Clinical Data

Simulating Coin Flips

Set the seed for reproducibility and simulate 1000 coin flips using a Bernoulli distribution.

/* Set the seed for reproducibility */
%let seed = 19;

data coin_flips;
    call streaminit(&seed);
    do i = 1 to 1000;
        /* Simulate coin flips: 1 for Heads (H), 0 for Tails (T) */
        flip = rand("Bernoulli", 0.5);
/*         flip = rand("BINOMIAL", 0.5,1); */
        if flip = 1 then result = "H";
        else result = "T";
        output;
    end;
run;

Counting Heads and Tails

Use SQL to count how many heads and tails were observed in the simulation.

proc sql;
    select 
        sum(result = "H") as heads_count,
        sum(result = "T") as tails_count,
        count(*) as total_flips
    into :heads_count, :tails_count, :total_flips
    from coin_flips;
quit;

Display the Results

Print the counts using %put statements.

%put Heads Count: &heads_count;
%put Tails Count: &tails_count;
%put Total Flips: &total_flips;

Perform Binomial Test on Coin Flip Results

Use proc freq to check if the observed results differ significantly from the expected probability of 0.5.

proc freq data=coin_flips;
    tables result / binomial(p=0.5);
run;

Example: Binomial Test in Clinical Trial Data

We load a clinical dataset and test if the observed death proportion is significantly different from a hypothesized value (e.g., 19%).

Import Dataset

proc import datafile='/home/u63532805/CAMIS/lung_cancer.csv'
    out=lung_cancer
    dbms=csv
    replace;
    getnames=yes;
run;

Create Binary Flag for Deaths

data lung_cancer;
    set lung_cancer;
    death_flag = (status = 1);
run;

Perform Exact Binomial Test

proc freq data=lung_cancer;
    tables death_flag / binomial(p=0.19 level='1');
    title "Exact Binomial Test for Death Proportion";
run;

SAS Output

Coin Flip Summary

heads_count	tails_count	total_flips
520	480	1000

Binomial Test on Coin Flips

The FREQ Procedure

result	Frequency	Percent	Cumulative Frequency	Cumulative Percent
H	520	52.00	520	52.00
T	480	48.00	1000	100.00

Binomial Proportion for result = H

Proportion: 0.5200
ASE: 0.0158
95% Lower Conf Limit: 0.4890
95% Upper Conf Limit: 0.5510

Exact Confidence Limits

95% Lower Conf Limit: 0.4885
95% Upper Conf Limit: 0.5514

Test of H0: Proportion = 0.5

ASE under H0: 0.0158
Z: 1.2649
One-sided Pr > Z: 0.1030
Two-sided Pr > |Z|: 0.2059
Sample Size: 1000

Exact Binomial Test for Death Proportion

The FREQ Procedure

death_flag	Frequency	Percent	Cumulative Frequency	Cumulative Percent
0	165	72.37	165	72.37
1	63	27.63	228	100.00

Binomial Proportion for death_flag = 1

Proportion: 0.2763
ASE: 0.0296
95% Lower Conf Limit: 0.2183
95% Upper Conf Limit: 0.3344

Exact Confidence Limits

95% Lower Conf Limit: 0.2193
95% Upper Conf Limit: 0.3392

Test of H0: Proportion = 0.19

ASE under H0: 0.0260
Z: 3.3223
One-sided Pr > Z: 0.0004
Two-sided Pr > |Z|: 0.0009
Sample Size: 228