Statistical Analysis of Quantitative RT-PCR Results

Abstract

Real-time reverse transcription polymerase chain reaction (RT-PCR) represents a benchmark technology in the detection and quantification of mRNA. Yet, accurate results cannot be realized without proper statistical analysis of RT-PCR data. Here, we examine some of the issues concerning RT-PCR experiments that would benefit from rigorous statistical treatment, including normalization, quantification, efficiency estimation, and sample size calculations. Examples are used to illustrate the methods.

Appendices

Appendix 1. SAS Code to Select an Optimum Housekeeping Gene Based on a Minimum F-statistic

data table2;

input ain dose$$ gene$$ Ct;

cards;

1 A HK001 20.30

2 A HK001 20.57

3 A HK001 20.54

4 A HK001 20.20

5 A HK001 20.20

.

Some data omitted for brevity

.

23 E HK002 20.07

24 E HK002 20.10

25 E HK002 20.25

;

proc sort;

by gene;

run;

ods listing close;

ods output OverallANOVA=ANOVA;

proc glm;

by gene;

class dose;

model Ct=dose;

run;

ods listing;

data ANOVA; set ANOVA;

if Source=’Model’;

proc print;

var gene FValue;

run;

Appendix 2. SAS Code to Perform the Relative Quantification Analysis Using ANOVA Methodology

data table6;

input ain treatment$$ gene$$ Ct;

cards;

1 Control TG001 23.22

1 Control TG001 23.34

1 Control TG001 23.12

2 Control TG001 24.06

2 Control TG001 24.15

2 Control TG001 24.15

.

Some data omitted for brevity

.

8 Treated HK002 20.10

8 Treated HK002 20.07

8 Treated HK002 20.10

;

proc summary nway;

class ain treatment gene;

var Ct;

output out=out mean=;

run;

proc sort data=out;

by gene;

run;

proc print data=out;

run;

*∼∼∼ The macro ‘loop’ allows Ct calculations

for all the genes in the data set ∼∼∼*;

%macro loop(gene);

proc mixed data=out;

where gene in (“HK002”,”&gene”);

class treatment gene;

model Ct=treatment*gene;

lsmeans treatment*gene;

*∼∼∼ The ‘e’ option for the ‘estimate’ statement allows a check of the linear combination, which is dependent on the treatment names ∼∼∼*;

estimate “delta delta Ct for &gene” treatment*gene 1 -1 -1 1 / cl e;

*∼∼∼ For an efficiency corrected estimate of the ratio, use the estimate statement below instead ∼∼∼*;

* estimate “efficiency corrected for &gene” treatment*gene -.8875 1.8875 -1 / e;

ods output estimates=estimates;

title “&gene”;

run;

%mend loop;

*∼∼∼ For additional target genes, simply add lines below ∼∼∼*;

%loop(TG001);

%loop(TG002);

Appendix 3. SAS Code to Perform the Four-Parameter Logistic Model Fit

data raw_curve;

input x FL;

cards;

1 -0.00576

2 -0.00568

3 0.00166

Some data omitted for brevity

.

48 5.91043

49 5.95599

50 5.90091

;

data log_curve; set raw_curve;

logFL=log10(FL); * <==== notice log10 ;

ods listing close;

proc nlin method=newton;

parms a=-10 to 0 by 1

b=0 to 5 by 1

c=25 to 30 by 1

d=1 to 3 by 1;

model logFL = a + b /(1+exp((c-x)/d));

ods output parameterestimates=pe(keep=parameter estimate);

output out=out p=p;

run;

ods listing;

proc transpose data=pe out=est(rename=(col1=a col2=b col3=c col4=d));

var estimate;

run;

data est; set est;

x=c;

slope=(b/d)*(exp((c-x)/d))/((1+2*exp((c-x)/d))+exp(2*(c-x)/d));

E=10**slope;

run;

proc print data=est;

run;

Appendix 4. SAS Code to Perform the Sample Size Calculations

*∼∼∼ To calculate sample size ∼∼∼*;

proc power;

twosamplemeans

meandiff = 1

stddev = 0.40 0.45 0.50

power = 0.8

npergroup =.;

run;